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Research ArticleDesigning a Multistage Supply Chain in Cross-StageReverse Logistics Environments Application of Particle SwarmOptimization Algorithms
Tzu-An Chiang1 Z H Che2 and Zhihua Cui34
1 Department of Business Administration National Taipei College of Business Taipei 10051 Taiwan2Department of Industrial Engineering and Management National Taipei University of Technology Taipei 10608 Taiwan3 Complex System and Computational Intelligent Laboratory Taiyuan University of Science and Technology Taiyuan 030024 China4 State Key Laboratory for Novel Software Technology Nanjing University Nanjing 210023 China
Correspondence should be addressed to Z H Che zhchentutedutw
Received 11 October 2013 Accepted 23 December 2013 Published 18 February 2014
Academic Editors C H Aladag and C-C Jane
Copyright copy 2014 Tzu-An Chiang et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
This study designed a cross-stage reverse logistics course for defective products so that damaged products generated in downstreampartners can be directly returned to upstream partners throughout the stages of a supply chain for rework and maintenance Tosolve this reverse supply chain design problem an optimal cross-stage reverse logistics mathematical model was developed Inaddition we developed a genetic algorithm (GA) and three particle swarm optimization (PSO) algorithms the inertia weightmethod (PSOA IWM) 119881Max method (PSOA VMM) and constriction factor method (PSOA CFM) which we employed to findsolutions to support this mathematical model Finally a real case and five simulative cases with different scopes were used tocompare the execution times convergence times and objective function values of the four algorithms used to validate the modelproposed in this study Regarding system execution time the GA consumed more time than the other three PSOs did Regardingobjective function value the GA PSOA IWM and PSOA CFM could obtain a lower convergence value than PSOA VMM couldFinally PSOA IWM demonstrated a faster convergence speed than PSOA VMM PSOA CFM and the GA did
1 Introduction
Intense competition within the global market has promptedenterprise competition to change from a competition amongcompanies to that among supply chains In addition to reduc-ing operating costs and improving competitiveness effec-tively integrating the upstream and downstream suppliersand manufacturers of a supply chain can reflect marketchanges and meet consumer needs efficiently
Previous studies on the design problems of supply net-works include [1ndash8] In addition Che and Cui [9] addressedthe network design on unbalanced supply chain system Forthe integrity of supply chain circulation reverse logisticsshould be implemented to form a complete logistics circula-tion Reverse logistics was first proposed by Stock [10] thenTrebilcock [11] indicated that in the past most enterprisesfocused only on forward logistics andmisunderstood reverselogistics as a nonprofitable activity
Cohen [12] suggested that enterprises could save 40ndash60 ofmanufacturing costs annually by adopting the remakemethod compared with using newmaterials In recent yearsenterprises have begun paying increased attention to reverselogistics activities such as customer returns product mainte-nance replacement and recyclingWhite et al [13] describedin detail the essential aspects and challenges in acquiringassessing disassembling and reprocessing computer equip-ment as it moves through this reversemanufacturing processProper planning of a comprehensive product recycling plancan reduce the environmental damage caused by disposingof used equipment
Based on literature review reverse logistics includesman-agement functions related to returned products depot repairrework material reprocessing material recycling and dis-posal of waste and hazardous materialsThese allow productsto be returned upstream for processing in a reverse logisticssystem thus the circulation of an integral supply chain can be
Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 595902 19 pageshttpdxdoiorg1011552014595902
Final productProductAlternate parts Distribution centers
RegionalityTerritoriality
Customer
DisposalBurialIncineration
Forward logistics
Reverse logistics
∙∙
∙∙
∙∙
∙∙
∙∙
∙∙
∙∙
∙∙
Figure 1 The reverse logistics flow of the products (Gattorna [14])
implemented The reverse logistics flow of products is shownin Figure 1
Many scholars have defined reverse logistics briefly andclearly [10 15ndash18] and some have studied the reverse logisticsnetwork design for different fields such as the steel industry[19] electronic equipment [20] sand recycling [21] reusablepackaging [22] and general recovery networks [23] Aminiet al [24] demonstrated how an effective and profitablereverse logistics operation for an RSSC was designed foran MDM in which customer operations demanded a quickrepair service Fleischmann et al [25] considered a logisticsnetwork design in a reverse logistics context and presented ageneric facility location model by discussing the differencescompared with traditional logistics settings This model wasthen used to analyze the impact of product return flow onlogistics networks
In addition Savaskan et al [26] developed a detailedunderstanding of the implications that a manufacturerrsquosreverse channel choice has on forward channel decisions andthe used product return rate from customers Chouinardet al [27] addressed problems related to integrating reverselogistics activities within an organization and to coordinat-ing this new system Kainuma and Tawara [28] proposedthe multiple-attribute utility theory method for assessing asupply chain including reusing and recycling throughout thelife cycle of products and services Nagurney and Toyasaki[29] developed a model linking these decisions to prices andmaterial shipments among end-of-life electronics sourcesrecyclers processors and suppliers for deterministic scenar-ios Nikolaidis [30] proposed a single-period mathematicalmodel for determining a reverse supply chain plan that con-siders procurement and returnsrsquo remanufacturing andNenesand Nikolaidis [31] extended Nikolaidisrsquos model to a multi-period model Salema et al [32] developed a multiperiodmultiproduct model for designing supply chain networksregarding reverse flowsMore recently Pinto-Varela et al [33]considered an environmental perspective to develop amixed-integer linear programming model for planning reversesupply chains Amin and Zhang [34] presented a mixed-integer linear programming model for designing a closed-loop supply chain network regarding product life cycles In
additionHuang et al [35] analyzed strategies of a closed-loopsupply chain containing a dual recycling channel Althoughcross-stage logistics in reverse supply chains generally existsin practice our research suggests that it has yet to be ade-quately addressed Hence the motivation of this study is todesign the reverse supply chain with cross-stage logistics
Reverse logistics is more complex than forward logisticsand this study aimed to develop a mathematical foundationfor modeling a cross-stage reverse logistics plan that enablesdefective products with differing degrees of damage to bereturned to upstream partners in the stages of a supply chainfor maintenance replacement or restructuring This cross-stage reverse logisticsmodel can help save time lessen unnec-essary deliveries and more importantly meet the conditionsof reverse logistics operation more efficiently
Recently GAs have been regarded as a novel approachto solving complex large-scale and real-world optimiza-tion problems [6 36ndash42] Moreover the PSO proposed byKennedy and Eberhart [43] was an iteration optimizationinstrument generating a group of initial solutions at thebeginning and then acquiring the optimal value throughiteration Liao and Rittscher [44] applied this instrumentto scheduling problems related to industrial piece workrequiring minimal completion time Zhang et al [45] appliedPSO to solve the minimization problems of the projectduration for resource-constrained scheduling Shi et al [46]applied a PSO to the traveling salesman problem Che [47]developed a PSO-based back-propagation artificial neuralnetwork for estimating the product and mold costs of plasticinjection molding and Che [48] proposed a modified PSOmethod for solving multiechelon unbalanced supply chainplanning problems Priya and Lakshmi [49] applied PSO forperforming the real time control of spherical tank systemand Ali et al [50] used the PSO for solving the constrainednumerical and engineering benchmark problems Otherrelated studies concerning the use of PSO for the optimizationproblems are [51ndash54]
In addition Dong et al [55] compared the improved PSOa combinatorial particle swarm optimization (CPSO) withGA and the results showed that the improved PSO was moreeffective in solving nonlinear problems Yin and Wang [56]
The Scientific World Journal 3
Stage 1 Stage 2 Stage 3 Stage 4
Demand
21
22
23
21
31
32
33
34
41
42
43
44
11
12
13
14
Reverse logisticsForward logistics
middot middot middot
Figure 2 The transportation model of reverse logistics
used PSO to solve nonlinear resource allocation problemsand compared PSO with the GA They found that theefficiency and potency of a PSO were higher than those ofa GA Salman et al [57] applied PSO to solve the efficiencyrates of tasks assigned to computers or parallel computersystems and compared the results with those of GA Theresults showed that PSOhas faster execution and convergencespeeds than the GA Based on our research no previous stud-ies have applied PSO to cross-stage reverse logistics problemstherefore to solve this problem this study used three updatedPSO methods the inertia weight method (PSOA IWM)constriction factor method (PSOA CFM) and 119881Max method(PSOA VMM) The results were then compared with thoseusing the GA regarding system execution time convergencetime and objective function value
The remainder of this paper is structured as followsSection 2 introduces the proposed mathematical foundationand solving algorithms for modeling and solving cross-stage reverse logistics problems Section 3 presents illustrativeexamples and the comparative and analytical results of thealgorithms Finally Section 4 provides the conclusion of thisstudy and offers suggestions for future research
2 Mathematical Foundation andSolving Models for Cross-Stage ReverseLogistics Problems
21 Problem Description Reverse logistics activities includerecycling rework replacement and waste disposal howeverthe reverse logistics activity of each function differs There-fore this study designed a forward and reverse cross-stagelogistics system for maintaining reassembling and packag-ing recycled defective products The structure is shown inFigure 2
When downstream partners generate defective productsthe products can be returned directly to upstream supplychain partners for maintenance to restore product functionand value based on the degree of damage Therefore thisstudy supposed that when defective products are generatedthey can be divided into N parts according to the averagevolume of defective products generated by a particularsupplier Downstream partners can then return defectiveproducts based on the divided quantity to upstreampartnersfor maintenance For example when the first partner of thefourth stage generates defective products the total defectiveamount is divided into three parts and then sent to the firstsecond and third stage partners separately in the supplychain thereby reducing general reverse logistics costs andtransportation time
For supply chain partner selection this study consideredproductivity restrictions transportation costs manufactur-ing costs transportation time manufacturing quality andother parameters The 119879-transfer approach is a common sta-tistical technology that is employed to integrate variables Inthis study the119879-transfer of transportation costs manufactur-ing costs transportation time andmanufacturing qualitywasintegrated into the objective function standards 119879-transferis a common statistics technology first proposed by McCall[58] it is defined as follows ldquo119879-Scores are a transformationof raw scores into a standard form where the transformationis made when there is no knowledge of the populationrsquosmean and standard deviationrdquo 119879-scores have a mean of 50and a standard deviation of 10 Che [59] considered themanufacturing cost and time transportation cost and timeproduct quality and green appraisal score in selecting greensuppliers when establishing a green supply chain and used119879-transfer technology to transform the data Cost timequality and green appraisal score aremeasurable criteria withdifferent units thus in this study the119879-transfer approachwas
4 The Scientific World Journal
Establish the database of multistage supply chain with cross-stage
reverse logistics
Develop the optimal mathematical model for multistage supply chain
with cross-stage reverse logistics
Information of supply chain
Production costManufacture defective product rateTransportation costTransportation loss rateTransportation timeManufacturing qualityUpper and lower limits of productivity
hellip
Develop four solving models to solve the optimal mathematical
modelSolving algorithms
GAPSOA_VMMPSOA_IWMPSOA_CFM Analyze and compare the solving
performances for four solving models
Performance indicators
Execution timeConvergence timeObjective function value
Statistical techniques
ANOVA
Obtain the optimal multistage supply chain plan with cross-stage
reverse logistics
Optimal mathematical model
ObjectiveMinimize
Constraints
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowastlowast
lowast
lowast
Z = wPC(fPC + rPC) + wTC(fTC + rTC) minus
wPQ(fPQ+ rPQ) + wTS(fTS + rTS)
+
RUnminus1((rsj)(si)) le MaxCP(si)
JS
rs = s + 1 j = 1
sum sum
(MinCP(si) le Un((sminus1j)(si)) 1 minus TFR((sminus1j)(si))
J
j = 1
sum )
Scheff e method
Figure 3 The structure of this study
also employed to first transform the original scores of eachcriterion into a standard form and then to integrate them
To satisfy the conditions of the actual production situa-tion this study used transportation losses andmanufacturinglosses to construct an unbalanced supply chain network Inconsidering the characteristics of all the suppliers addressedin this study we developed a cross-stage reverse logisticscourse planning system for single-product and multiperiodprogramming
We programmed the reverse logistics for recycled defec-tive products which were returned directly to the upstreamsupply chain partners for maintenance reassembly andrepackaging through the cross-stage reverse logistics courseprogramming based on the degree and nature of the damageFor selecting supply chain partners this study consideredthe manufacturing characteristics (transportation costs pro-duction costs upper and lower limit of productivity man-ufacturerrsquos defective product rate transportation losses rateand manufacturing quality) to construct the reverse logisticsprogramming model Based on these data optimal manufac-turing quality with minimal production cost transportationcost and transportation time can be determined
In considering the different evaluation criteria this study119879-transferred the database and used theVisual Basic programlanguage to compile four solution models including GAPSOA IWM PSOA VMM and PSOA CFM The consid-ered parameters in the supplier database were combined todevelop a set for designing reverse logistics course planningsystems The framework of this study is shown in Figure 3
Analysis of variance (ANOVA) and Scheffe analyseswere per-formed to compare the objective function values (119879-score)convergence times and run times of the four algorithms toverify the validity of this study and the performance of thefour algorithms
22 Mathematical Foundation for Cross-Stage Reverse Logis-tics Problems The optimal mathematical model of cross-stage reverse logistics was developed as described in thefollowing steps The definitions of notations used in thismodel are listed as followsNotations for developing the optimal mathematical model
Parameters
119894 119895 Serial number of supplier119894 = 1 2 3 119868 119895 = 1 2 3 119869
119899 Production period 119899 = 1 2 3 119873
119904 119903119904 Stages of the supply chain network119904 = 1 2 3 119878 119903119904 = 1 2 3 119878
119868 119869 Total number of suppliers119873 Total production periods119878 Total stages of supply chain network119862119863119899
(119904119894) Customer requirement of supplier 119894 at
stage 119904 for period 119899
Min119862119875(119904119894)
Minimal starting up productivity ofsupplier 119894 at stage 119904
Max119862119875(119904119894)
Maximal starting up productivity ofsupplier 119894 at stage 119904
The Scientific World Journal 5
119875119862(119904119894)
Manufacturing cost of supplier 119894 atstage 119904
119875119876(119904119894)
Product quality of supplier 119894 at stage 119904119879119862((119904119894)(119904+1119895))
Transportation cost from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1
119879119878((119904119894)(119904+1119895))
Transportation time from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1
119875119862(119904119894)
Average manufacturing cost of supplier119894 at stage 119904
119875119876119904119894 Average product quality of supplier 119894 at
Transportation loss rate from supplier 119894at stage 119904 to supplier 119895 at stage 119904 + 1
119908119875119862
119908119879119862
119908119879119878
119908119875119876
Weights of manufacturing costtransportation cost transportationtime and product quality
Integer function for obtaining theinteger value of the real number byeliminating its decimal
Decision Variables
119880119899
((119904119894)(119904+1119895)) Transportation quantity from supplier 119894 at
stage 119904 to supplier 119895 at stage 119904 + 1 for period119899
119877119880119899
((119903119904119895)(119904119894)) Defective products quantity from supplier
119895 at stage 119903119904 to supplier 119894 at stage 119904 stage forterm 119899
Notations for developing the update models for the positionand velocity of each particle
1198881 1198882 Learning factors
119870 Constriction factorrand() Random numbers between 0 and 1119904lowast
119894 Pbest memory value of particle 119894
119904119894 Gbest memory value of particle 119894
119904new119894
New position of particle 119894Vold119894 Original velocity of particle 119894
Vnew119894
New velocity of particle 119894Vmax The set maximal velocity119908 Inertia weight
120601Totaling of cognition parameter and socialparameter which must exceed 4
Notations for performing hypotheses on the objective func-tion value convergence time and completion time amongfour proposed approaches
119862119879GA Convergence time of GA119862119879PSOA IWM Convergence time of PSOA IWM119862119879PSOA VMM Convergence time of PSOA VMM119862119879PSOA CFM Convergence time of PSOA CFM119865119879GA Completion time of GA119865119879PSOA IWM Completion time of PSOA IWM119865119879PSOA VMM Completion time of PSOA VMM119865119879PSOA CFM Completion time of PSOA CFMObjGA Objective function value of GAObjPSOA IWM Objective function value of PSOA IWMObjPSOA VMM Objective function value of PSOA VMMObjPSOA CFM Objective function value of PSOA CFM
Acquire the minimization of manufacturing costs trans-portation costs and transportation time as well as themaximization of the manufacturing quality of the differentsuppliers at various stages of forward and reverse logistics
23 Proposed Models for Solving Cross-Stage Reverse LogisticsProblems
231 GA-Solving Model The detailed procedures of a GA-solving model are described as follows
Step 1 The encoding of this study was performed accordingto the cross-stage reverse logistics problem including forwardand reverse transportation routes therefore one route is oneencoding value The scope is randomly generated based onthe demands and (10)ndash(14) The chromosome structure isshown in Figure 4 The gene cell index 11ndash21 in the figurerepresents the products sent from the first supplier of the firststage to the initial supplier of the second stage within thesupply chain structure whereas the gene value represents thetransportation volumes from upstream to downstream
Step 2 Substitute all the generated encoding values in theobjective function equation (1) of this study to acquire thefitness function value of each gene
Step 3 This study adopted the roulette wheel selectionproposed by Goldberg [60] which is performed beforecloning to solve the minimization problem of this studyIt then selects the reciprocal of fitness function generated inStep 2 and calculates the cumulative probability of each stripof chromosome the larger probability value indicates thatthis chromosome has a greater likelihood of being duplicatedOne probability value between 0 and 1 is generated thesuitable fitness function is determined and cloning is carriedout
Step 4 The crossover of this study involves using the single-point crossover method Randomly select two chromosomesfrom the parent body for crossover and generate onecrossover point then exchange the genes of the chromosomeThe crossover course is shown in Figure 5
Step 5 The mutation of this study also adopts a single-pointmutationmethod and treats the delivery route of one supplieras a ldquosingle-pointrdquo of valueThemutationmethod is shown inFigure 6
Step 6 The new filial generation was generated through thegene evolution of Steps 3ndash5 if the optimal fitness functionvalue of the filial generation is higher than that of the parental
Figure 8 Particle swarm encoding for reverse logistics
generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation
Step 7 This study sets the iteration times as the terminationcondition for gene evolution
232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows
Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and
reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage
The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own
The Scientific World Journal 9
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Final productProductAlternate parts Distribution centers
RegionalityTerritoriality
Customer
DisposalBurialIncineration
Forward logistics
Reverse logistics
∙∙
∙∙
∙∙
∙∙
∙∙
∙∙
∙∙
∙∙
Figure 1 The reverse logistics flow of the products (Gattorna [14])
implemented The reverse logistics flow of products is shownin Figure 1
Many scholars have defined reverse logistics briefly andclearly [10 15ndash18] and some have studied the reverse logisticsnetwork design for different fields such as the steel industry[19] electronic equipment [20] sand recycling [21] reusablepackaging [22] and general recovery networks [23] Aminiet al [24] demonstrated how an effective and profitablereverse logistics operation for an RSSC was designed foran MDM in which customer operations demanded a quickrepair service Fleischmann et al [25] considered a logisticsnetwork design in a reverse logistics context and presented ageneric facility location model by discussing the differencescompared with traditional logistics settings This model wasthen used to analyze the impact of product return flow onlogistics networks
In addition Savaskan et al [26] developed a detailedunderstanding of the implications that a manufacturerrsquosreverse channel choice has on forward channel decisions andthe used product return rate from customers Chouinardet al [27] addressed problems related to integrating reverselogistics activities within an organization and to coordinat-ing this new system Kainuma and Tawara [28] proposedthe multiple-attribute utility theory method for assessing asupply chain including reusing and recycling throughout thelife cycle of products and services Nagurney and Toyasaki[29] developed a model linking these decisions to prices andmaterial shipments among end-of-life electronics sourcesrecyclers processors and suppliers for deterministic scenar-ios Nikolaidis [30] proposed a single-period mathematicalmodel for determining a reverse supply chain plan that con-siders procurement and returnsrsquo remanufacturing andNenesand Nikolaidis [31] extended Nikolaidisrsquos model to a multi-period model Salema et al [32] developed a multiperiodmultiproduct model for designing supply chain networksregarding reverse flowsMore recently Pinto-Varela et al [33]considered an environmental perspective to develop amixed-integer linear programming model for planning reversesupply chains Amin and Zhang [34] presented a mixed-integer linear programming model for designing a closed-loop supply chain network regarding product life cycles In
additionHuang et al [35] analyzed strategies of a closed-loopsupply chain containing a dual recycling channel Althoughcross-stage logistics in reverse supply chains generally existsin practice our research suggests that it has yet to be ade-quately addressed Hence the motivation of this study is todesign the reverse supply chain with cross-stage logistics
Reverse logistics is more complex than forward logisticsand this study aimed to develop a mathematical foundationfor modeling a cross-stage reverse logistics plan that enablesdefective products with differing degrees of damage to bereturned to upstream partners in the stages of a supply chainfor maintenance replacement or restructuring This cross-stage reverse logisticsmodel can help save time lessen unnec-essary deliveries and more importantly meet the conditionsof reverse logistics operation more efficiently
Recently GAs have been regarded as a novel approachto solving complex large-scale and real-world optimiza-tion problems [6 36ndash42] Moreover the PSO proposed byKennedy and Eberhart [43] was an iteration optimizationinstrument generating a group of initial solutions at thebeginning and then acquiring the optimal value throughiteration Liao and Rittscher [44] applied this instrumentto scheduling problems related to industrial piece workrequiring minimal completion time Zhang et al [45] appliedPSO to solve the minimization problems of the projectduration for resource-constrained scheduling Shi et al [46]applied a PSO to the traveling salesman problem Che [47]developed a PSO-based back-propagation artificial neuralnetwork for estimating the product and mold costs of plasticinjection molding and Che [48] proposed a modified PSOmethod for solving multiechelon unbalanced supply chainplanning problems Priya and Lakshmi [49] applied PSO forperforming the real time control of spherical tank systemand Ali et al [50] used the PSO for solving the constrainednumerical and engineering benchmark problems Otherrelated studies concerning the use of PSO for the optimizationproblems are [51ndash54]
In addition Dong et al [55] compared the improved PSOa combinatorial particle swarm optimization (CPSO) withGA and the results showed that the improved PSO was moreeffective in solving nonlinear problems Yin and Wang [56]
The Scientific World Journal 3
Stage 1 Stage 2 Stage 3 Stage 4
Demand
21
22
23
21
31
32
33
34
41
42
43
44
11
12
13
14
Reverse logisticsForward logistics
middot middot middot
Figure 2 The transportation model of reverse logistics
used PSO to solve nonlinear resource allocation problemsand compared PSO with the GA They found that theefficiency and potency of a PSO were higher than those ofa GA Salman et al [57] applied PSO to solve the efficiencyrates of tasks assigned to computers or parallel computersystems and compared the results with those of GA Theresults showed that PSOhas faster execution and convergencespeeds than the GA Based on our research no previous stud-ies have applied PSO to cross-stage reverse logistics problemstherefore to solve this problem this study used three updatedPSO methods the inertia weight method (PSOA IWM)constriction factor method (PSOA CFM) and 119881Max method(PSOA VMM) The results were then compared with thoseusing the GA regarding system execution time convergencetime and objective function value
The remainder of this paper is structured as followsSection 2 introduces the proposed mathematical foundationand solving algorithms for modeling and solving cross-stage reverse logistics problems Section 3 presents illustrativeexamples and the comparative and analytical results of thealgorithms Finally Section 4 provides the conclusion of thisstudy and offers suggestions for future research
2 Mathematical Foundation andSolving Models for Cross-Stage ReverseLogistics Problems
21 Problem Description Reverse logistics activities includerecycling rework replacement and waste disposal howeverthe reverse logistics activity of each function differs There-fore this study designed a forward and reverse cross-stagelogistics system for maintaining reassembling and packag-ing recycled defective products The structure is shown inFigure 2
When downstream partners generate defective productsthe products can be returned directly to upstream supplychain partners for maintenance to restore product functionand value based on the degree of damage Therefore thisstudy supposed that when defective products are generatedthey can be divided into N parts according to the averagevolume of defective products generated by a particularsupplier Downstream partners can then return defectiveproducts based on the divided quantity to upstreampartnersfor maintenance For example when the first partner of thefourth stage generates defective products the total defectiveamount is divided into three parts and then sent to the firstsecond and third stage partners separately in the supplychain thereby reducing general reverse logistics costs andtransportation time
For supply chain partner selection this study consideredproductivity restrictions transportation costs manufactur-ing costs transportation time manufacturing quality andother parameters The 119879-transfer approach is a common sta-tistical technology that is employed to integrate variables Inthis study the119879-transfer of transportation costs manufactur-ing costs transportation time andmanufacturing qualitywasintegrated into the objective function standards 119879-transferis a common statistics technology first proposed by McCall[58] it is defined as follows ldquo119879-Scores are a transformationof raw scores into a standard form where the transformationis made when there is no knowledge of the populationrsquosmean and standard deviationrdquo 119879-scores have a mean of 50and a standard deviation of 10 Che [59] considered themanufacturing cost and time transportation cost and timeproduct quality and green appraisal score in selecting greensuppliers when establishing a green supply chain and used119879-transfer technology to transform the data Cost timequality and green appraisal score aremeasurable criteria withdifferent units thus in this study the119879-transfer approachwas
4 The Scientific World Journal
Establish the database of multistage supply chain with cross-stage
reverse logistics
Develop the optimal mathematical model for multistage supply chain
with cross-stage reverse logistics
Information of supply chain
Production costManufacture defective product rateTransportation costTransportation loss rateTransportation timeManufacturing qualityUpper and lower limits of productivity
hellip
Develop four solving models to solve the optimal mathematical
modelSolving algorithms
GAPSOA_VMMPSOA_IWMPSOA_CFM Analyze and compare the solving
performances for four solving models
Performance indicators
Execution timeConvergence timeObjective function value
Statistical techniques
ANOVA
Obtain the optimal multistage supply chain plan with cross-stage
reverse logistics
Optimal mathematical model
ObjectiveMinimize
Constraints
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowastlowast
lowast
lowast
Z = wPC(fPC + rPC) + wTC(fTC + rTC) minus
wPQ(fPQ+ rPQ) + wTS(fTS + rTS)
+
RUnminus1((rsj)(si)) le MaxCP(si)
JS
rs = s + 1 j = 1
sum sum
(MinCP(si) le Un((sminus1j)(si)) 1 minus TFR((sminus1j)(si))
J
j = 1
sum )
Scheff e method
Figure 3 The structure of this study
also employed to first transform the original scores of eachcriterion into a standard form and then to integrate them
To satisfy the conditions of the actual production situa-tion this study used transportation losses andmanufacturinglosses to construct an unbalanced supply chain network Inconsidering the characteristics of all the suppliers addressedin this study we developed a cross-stage reverse logisticscourse planning system for single-product and multiperiodprogramming
We programmed the reverse logistics for recycled defec-tive products which were returned directly to the upstreamsupply chain partners for maintenance reassembly andrepackaging through the cross-stage reverse logistics courseprogramming based on the degree and nature of the damageFor selecting supply chain partners this study consideredthe manufacturing characteristics (transportation costs pro-duction costs upper and lower limit of productivity man-ufacturerrsquos defective product rate transportation losses rateand manufacturing quality) to construct the reverse logisticsprogramming model Based on these data optimal manufac-turing quality with minimal production cost transportationcost and transportation time can be determined
In considering the different evaluation criteria this study119879-transferred the database and used theVisual Basic programlanguage to compile four solution models including GAPSOA IWM PSOA VMM and PSOA CFM The consid-ered parameters in the supplier database were combined todevelop a set for designing reverse logistics course planningsystems The framework of this study is shown in Figure 3
Analysis of variance (ANOVA) and Scheffe analyseswere per-formed to compare the objective function values (119879-score)convergence times and run times of the four algorithms toverify the validity of this study and the performance of thefour algorithms
22 Mathematical Foundation for Cross-Stage Reverse Logis-tics Problems The optimal mathematical model of cross-stage reverse logistics was developed as described in thefollowing steps The definitions of notations used in thismodel are listed as followsNotations for developing the optimal mathematical model
Parameters
119894 119895 Serial number of supplier119894 = 1 2 3 119868 119895 = 1 2 3 119869
119899 Production period 119899 = 1 2 3 119873
119904 119903119904 Stages of the supply chain network119904 = 1 2 3 119878 119903119904 = 1 2 3 119878
119868 119869 Total number of suppliers119873 Total production periods119878 Total stages of supply chain network119862119863119899
(119904119894) Customer requirement of supplier 119894 at
stage 119904 for period 119899
Min119862119875(119904119894)
Minimal starting up productivity ofsupplier 119894 at stage 119904
Max119862119875(119904119894)
Maximal starting up productivity ofsupplier 119894 at stage 119904
The Scientific World Journal 5
119875119862(119904119894)
Manufacturing cost of supplier 119894 atstage 119904
119875119876(119904119894)
Product quality of supplier 119894 at stage 119904119879119862((119904119894)(119904+1119895))
Transportation cost from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1
119879119878((119904119894)(119904+1119895))
Transportation time from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1
119875119862(119904119894)
Average manufacturing cost of supplier119894 at stage 119904
119875119876119904119894 Average product quality of supplier 119894 at
Transportation loss rate from supplier 119894at stage 119904 to supplier 119895 at stage 119904 + 1
119908119875119862
119908119879119862
119908119879119878
119908119875119876
Weights of manufacturing costtransportation cost transportationtime and product quality
Integer function for obtaining theinteger value of the real number byeliminating its decimal
Decision Variables
119880119899
((119904119894)(119904+1119895)) Transportation quantity from supplier 119894 at
stage 119904 to supplier 119895 at stage 119904 + 1 for period119899
119877119880119899
((119903119904119895)(119904119894)) Defective products quantity from supplier
119895 at stage 119903119904 to supplier 119894 at stage 119904 stage forterm 119899
Notations for developing the update models for the positionand velocity of each particle
1198881 1198882 Learning factors
119870 Constriction factorrand() Random numbers between 0 and 1119904lowast
119894 Pbest memory value of particle 119894
119904119894 Gbest memory value of particle 119894
119904new119894
New position of particle 119894Vold119894 Original velocity of particle 119894
Vnew119894
New velocity of particle 119894Vmax The set maximal velocity119908 Inertia weight
120601Totaling of cognition parameter and socialparameter which must exceed 4
Notations for performing hypotheses on the objective func-tion value convergence time and completion time amongfour proposed approaches
119862119879GA Convergence time of GA119862119879PSOA IWM Convergence time of PSOA IWM119862119879PSOA VMM Convergence time of PSOA VMM119862119879PSOA CFM Convergence time of PSOA CFM119865119879GA Completion time of GA119865119879PSOA IWM Completion time of PSOA IWM119865119879PSOA VMM Completion time of PSOA VMM119865119879PSOA CFM Completion time of PSOA CFMObjGA Objective function value of GAObjPSOA IWM Objective function value of PSOA IWMObjPSOA VMM Objective function value of PSOA VMMObjPSOA CFM Objective function value of PSOA CFM
Acquire the minimization of manufacturing costs trans-portation costs and transportation time as well as themaximization of the manufacturing quality of the differentsuppliers at various stages of forward and reverse logistics
23 Proposed Models for Solving Cross-Stage Reverse LogisticsProblems
231 GA-Solving Model The detailed procedures of a GA-solving model are described as follows
Step 1 The encoding of this study was performed accordingto the cross-stage reverse logistics problem including forwardand reverse transportation routes therefore one route is oneencoding value The scope is randomly generated based onthe demands and (10)ndash(14) The chromosome structure isshown in Figure 4 The gene cell index 11ndash21 in the figurerepresents the products sent from the first supplier of the firststage to the initial supplier of the second stage within thesupply chain structure whereas the gene value represents thetransportation volumes from upstream to downstream
Step 2 Substitute all the generated encoding values in theobjective function equation (1) of this study to acquire thefitness function value of each gene
Step 3 This study adopted the roulette wheel selectionproposed by Goldberg [60] which is performed beforecloning to solve the minimization problem of this studyIt then selects the reciprocal of fitness function generated inStep 2 and calculates the cumulative probability of each stripof chromosome the larger probability value indicates thatthis chromosome has a greater likelihood of being duplicatedOne probability value between 0 and 1 is generated thesuitable fitness function is determined and cloning is carriedout
Step 4 The crossover of this study involves using the single-point crossover method Randomly select two chromosomesfrom the parent body for crossover and generate onecrossover point then exchange the genes of the chromosomeThe crossover course is shown in Figure 5
Step 5 The mutation of this study also adopts a single-pointmutationmethod and treats the delivery route of one supplieras a ldquosingle-pointrdquo of valueThemutationmethod is shown inFigure 6
Step 6 The new filial generation was generated through thegene evolution of Steps 3ndash5 if the optimal fitness functionvalue of the filial generation is higher than that of the parental
Figure 8 Particle swarm encoding for reverse logistics
generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation
Step 7 This study sets the iteration times as the terminationcondition for gene evolution
232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows
Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and
reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage
The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own
The Scientific World Journal 9
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Figure 2 The transportation model of reverse logistics
used PSO to solve nonlinear resource allocation problemsand compared PSO with the GA They found that theefficiency and potency of a PSO were higher than those ofa GA Salman et al [57] applied PSO to solve the efficiencyrates of tasks assigned to computers or parallel computersystems and compared the results with those of GA Theresults showed that PSOhas faster execution and convergencespeeds than the GA Based on our research no previous stud-ies have applied PSO to cross-stage reverse logistics problemstherefore to solve this problem this study used three updatedPSO methods the inertia weight method (PSOA IWM)constriction factor method (PSOA CFM) and 119881Max method(PSOA VMM) The results were then compared with thoseusing the GA regarding system execution time convergencetime and objective function value
The remainder of this paper is structured as followsSection 2 introduces the proposed mathematical foundationand solving algorithms for modeling and solving cross-stage reverse logistics problems Section 3 presents illustrativeexamples and the comparative and analytical results of thealgorithms Finally Section 4 provides the conclusion of thisstudy and offers suggestions for future research
2 Mathematical Foundation andSolving Models for Cross-Stage ReverseLogistics Problems
21 Problem Description Reverse logistics activities includerecycling rework replacement and waste disposal howeverthe reverse logistics activity of each function differs There-fore this study designed a forward and reverse cross-stagelogistics system for maintaining reassembling and packag-ing recycled defective products The structure is shown inFigure 2
When downstream partners generate defective productsthe products can be returned directly to upstream supplychain partners for maintenance to restore product functionand value based on the degree of damage Therefore thisstudy supposed that when defective products are generatedthey can be divided into N parts according to the averagevolume of defective products generated by a particularsupplier Downstream partners can then return defectiveproducts based on the divided quantity to upstreampartnersfor maintenance For example when the first partner of thefourth stage generates defective products the total defectiveamount is divided into three parts and then sent to the firstsecond and third stage partners separately in the supplychain thereby reducing general reverse logistics costs andtransportation time
For supply chain partner selection this study consideredproductivity restrictions transportation costs manufactur-ing costs transportation time manufacturing quality andother parameters The 119879-transfer approach is a common sta-tistical technology that is employed to integrate variables Inthis study the119879-transfer of transportation costs manufactur-ing costs transportation time andmanufacturing qualitywasintegrated into the objective function standards 119879-transferis a common statistics technology first proposed by McCall[58] it is defined as follows ldquo119879-Scores are a transformationof raw scores into a standard form where the transformationis made when there is no knowledge of the populationrsquosmean and standard deviationrdquo 119879-scores have a mean of 50and a standard deviation of 10 Che [59] considered themanufacturing cost and time transportation cost and timeproduct quality and green appraisal score in selecting greensuppliers when establishing a green supply chain and used119879-transfer technology to transform the data Cost timequality and green appraisal score aremeasurable criteria withdifferent units thus in this study the119879-transfer approachwas
4 The Scientific World Journal
Establish the database of multistage supply chain with cross-stage
reverse logistics
Develop the optimal mathematical model for multistage supply chain
with cross-stage reverse logistics
Information of supply chain
Production costManufacture defective product rateTransportation costTransportation loss rateTransportation timeManufacturing qualityUpper and lower limits of productivity
hellip
Develop four solving models to solve the optimal mathematical
modelSolving algorithms
GAPSOA_VMMPSOA_IWMPSOA_CFM Analyze and compare the solving
performances for four solving models
Performance indicators
Execution timeConvergence timeObjective function value
Statistical techniques
ANOVA
Obtain the optimal multistage supply chain plan with cross-stage
reverse logistics
Optimal mathematical model
ObjectiveMinimize
Constraints
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowastlowast
lowast
lowast
Z = wPC(fPC + rPC) + wTC(fTC + rTC) minus
wPQ(fPQ+ rPQ) + wTS(fTS + rTS)
+
RUnminus1((rsj)(si)) le MaxCP(si)
JS
rs = s + 1 j = 1
sum sum
(MinCP(si) le Un((sminus1j)(si)) 1 minus TFR((sminus1j)(si))
J
j = 1
sum )
Scheff e method
Figure 3 The structure of this study
also employed to first transform the original scores of eachcriterion into a standard form and then to integrate them
To satisfy the conditions of the actual production situa-tion this study used transportation losses andmanufacturinglosses to construct an unbalanced supply chain network Inconsidering the characteristics of all the suppliers addressedin this study we developed a cross-stage reverse logisticscourse planning system for single-product and multiperiodprogramming
We programmed the reverse logistics for recycled defec-tive products which were returned directly to the upstreamsupply chain partners for maintenance reassembly andrepackaging through the cross-stage reverse logistics courseprogramming based on the degree and nature of the damageFor selecting supply chain partners this study consideredthe manufacturing characteristics (transportation costs pro-duction costs upper and lower limit of productivity man-ufacturerrsquos defective product rate transportation losses rateand manufacturing quality) to construct the reverse logisticsprogramming model Based on these data optimal manufac-turing quality with minimal production cost transportationcost and transportation time can be determined
In considering the different evaluation criteria this study119879-transferred the database and used theVisual Basic programlanguage to compile four solution models including GAPSOA IWM PSOA VMM and PSOA CFM The consid-ered parameters in the supplier database were combined todevelop a set for designing reverse logistics course planningsystems The framework of this study is shown in Figure 3
Analysis of variance (ANOVA) and Scheffe analyseswere per-formed to compare the objective function values (119879-score)convergence times and run times of the four algorithms toverify the validity of this study and the performance of thefour algorithms
22 Mathematical Foundation for Cross-Stage Reverse Logis-tics Problems The optimal mathematical model of cross-stage reverse logistics was developed as described in thefollowing steps The definitions of notations used in thismodel are listed as followsNotations for developing the optimal mathematical model
Parameters
119894 119895 Serial number of supplier119894 = 1 2 3 119868 119895 = 1 2 3 119869
119899 Production period 119899 = 1 2 3 119873
119904 119903119904 Stages of the supply chain network119904 = 1 2 3 119878 119903119904 = 1 2 3 119878
119868 119869 Total number of suppliers119873 Total production periods119878 Total stages of supply chain network119862119863119899
(119904119894) Customer requirement of supplier 119894 at
stage 119904 for period 119899
Min119862119875(119904119894)
Minimal starting up productivity ofsupplier 119894 at stage 119904
Max119862119875(119904119894)
Maximal starting up productivity ofsupplier 119894 at stage 119904
The Scientific World Journal 5
119875119862(119904119894)
Manufacturing cost of supplier 119894 atstage 119904
119875119876(119904119894)
Product quality of supplier 119894 at stage 119904119879119862((119904119894)(119904+1119895))
Transportation cost from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1
119879119878((119904119894)(119904+1119895))
Transportation time from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1
119875119862(119904119894)
Average manufacturing cost of supplier119894 at stage 119904
119875119876119904119894 Average product quality of supplier 119894 at
Transportation loss rate from supplier 119894at stage 119904 to supplier 119895 at stage 119904 + 1
119908119875119862
119908119879119862
119908119879119878
119908119875119876
Weights of manufacturing costtransportation cost transportationtime and product quality
Integer function for obtaining theinteger value of the real number byeliminating its decimal
Decision Variables
119880119899
((119904119894)(119904+1119895)) Transportation quantity from supplier 119894 at
stage 119904 to supplier 119895 at stage 119904 + 1 for period119899
119877119880119899
((119903119904119895)(119904119894)) Defective products quantity from supplier
119895 at stage 119903119904 to supplier 119894 at stage 119904 stage forterm 119899
Notations for developing the update models for the positionand velocity of each particle
1198881 1198882 Learning factors
119870 Constriction factorrand() Random numbers between 0 and 1119904lowast
119894 Pbest memory value of particle 119894
119904119894 Gbest memory value of particle 119894
119904new119894
New position of particle 119894Vold119894 Original velocity of particle 119894
Vnew119894
New velocity of particle 119894Vmax The set maximal velocity119908 Inertia weight
120601Totaling of cognition parameter and socialparameter which must exceed 4
Notations for performing hypotheses on the objective func-tion value convergence time and completion time amongfour proposed approaches
119862119879GA Convergence time of GA119862119879PSOA IWM Convergence time of PSOA IWM119862119879PSOA VMM Convergence time of PSOA VMM119862119879PSOA CFM Convergence time of PSOA CFM119865119879GA Completion time of GA119865119879PSOA IWM Completion time of PSOA IWM119865119879PSOA VMM Completion time of PSOA VMM119865119879PSOA CFM Completion time of PSOA CFMObjGA Objective function value of GAObjPSOA IWM Objective function value of PSOA IWMObjPSOA VMM Objective function value of PSOA VMMObjPSOA CFM Objective function value of PSOA CFM
Acquire the minimization of manufacturing costs trans-portation costs and transportation time as well as themaximization of the manufacturing quality of the differentsuppliers at various stages of forward and reverse logistics
23 Proposed Models for Solving Cross-Stage Reverse LogisticsProblems
231 GA-Solving Model The detailed procedures of a GA-solving model are described as follows
Step 1 The encoding of this study was performed accordingto the cross-stage reverse logistics problem including forwardand reverse transportation routes therefore one route is oneencoding value The scope is randomly generated based onthe demands and (10)ndash(14) The chromosome structure isshown in Figure 4 The gene cell index 11ndash21 in the figurerepresents the products sent from the first supplier of the firststage to the initial supplier of the second stage within thesupply chain structure whereas the gene value represents thetransportation volumes from upstream to downstream
Step 2 Substitute all the generated encoding values in theobjective function equation (1) of this study to acquire thefitness function value of each gene
Step 3 This study adopted the roulette wheel selectionproposed by Goldberg [60] which is performed beforecloning to solve the minimization problem of this studyIt then selects the reciprocal of fitness function generated inStep 2 and calculates the cumulative probability of each stripof chromosome the larger probability value indicates thatthis chromosome has a greater likelihood of being duplicatedOne probability value between 0 and 1 is generated thesuitable fitness function is determined and cloning is carriedout
Step 4 The crossover of this study involves using the single-point crossover method Randomly select two chromosomesfrom the parent body for crossover and generate onecrossover point then exchange the genes of the chromosomeThe crossover course is shown in Figure 5
Step 5 The mutation of this study also adopts a single-pointmutationmethod and treats the delivery route of one supplieras a ldquosingle-pointrdquo of valueThemutationmethod is shown inFigure 6
Step 6 The new filial generation was generated through thegene evolution of Steps 3ndash5 if the optimal fitness functionvalue of the filial generation is higher than that of the parental
Figure 8 Particle swarm encoding for reverse logistics
generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation
Step 7 This study sets the iteration times as the terminationcondition for gene evolution
232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows
Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and
reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage
The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own
The Scientific World Journal 9
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Establish the database of multistage supply chain with cross-stage
reverse logistics
Develop the optimal mathematical model for multistage supply chain
with cross-stage reverse logistics
Information of supply chain
Production costManufacture defective product rateTransportation costTransportation loss rateTransportation timeManufacturing qualityUpper and lower limits of productivity
hellip
Develop four solving models to solve the optimal mathematical
modelSolving algorithms
GAPSOA_VMMPSOA_IWMPSOA_CFM Analyze and compare the solving
performances for four solving models
Performance indicators
Execution timeConvergence timeObjective function value
Statistical techniques
ANOVA
Obtain the optimal multistage supply chain plan with cross-stage
reverse logistics
Optimal mathematical model
ObjectiveMinimize
Constraints
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowast
lowastlowast
lowast
lowast
Z = wPC(fPC + rPC) + wTC(fTC + rTC) minus
wPQ(fPQ+ rPQ) + wTS(fTS + rTS)
+
RUnminus1((rsj)(si)) le MaxCP(si)
JS
rs = s + 1 j = 1
sum sum
(MinCP(si) le Un((sminus1j)(si)) 1 minus TFR((sminus1j)(si))
J
j = 1
sum )
Scheff e method
Figure 3 The structure of this study
also employed to first transform the original scores of eachcriterion into a standard form and then to integrate them
To satisfy the conditions of the actual production situa-tion this study used transportation losses andmanufacturinglosses to construct an unbalanced supply chain network Inconsidering the characteristics of all the suppliers addressedin this study we developed a cross-stage reverse logisticscourse planning system for single-product and multiperiodprogramming
We programmed the reverse logistics for recycled defec-tive products which were returned directly to the upstreamsupply chain partners for maintenance reassembly andrepackaging through the cross-stage reverse logistics courseprogramming based on the degree and nature of the damageFor selecting supply chain partners this study consideredthe manufacturing characteristics (transportation costs pro-duction costs upper and lower limit of productivity man-ufacturerrsquos defective product rate transportation losses rateand manufacturing quality) to construct the reverse logisticsprogramming model Based on these data optimal manufac-turing quality with minimal production cost transportationcost and transportation time can be determined
In considering the different evaluation criteria this study119879-transferred the database and used theVisual Basic programlanguage to compile four solution models including GAPSOA IWM PSOA VMM and PSOA CFM The consid-ered parameters in the supplier database were combined todevelop a set for designing reverse logistics course planningsystems The framework of this study is shown in Figure 3
Analysis of variance (ANOVA) and Scheffe analyseswere per-formed to compare the objective function values (119879-score)convergence times and run times of the four algorithms toverify the validity of this study and the performance of thefour algorithms
22 Mathematical Foundation for Cross-Stage Reverse Logis-tics Problems The optimal mathematical model of cross-stage reverse logistics was developed as described in thefollowing steps The definitions of notations used in thismodel are listed as followsNotations for developing the optimal mathematical model
Parameters
119894 119895 Serial number of supplier119894 = 1 2 3 119868 119895 = 1 2 3 119869
119899 Production period 119899 = 1 2 3 119873
119904 119903119904 Stages of the supply chain network119904 = 1 2 3 119878 119903119904 = 1 2 3 119878
119868 119869 Total number of suppliers119873 Total production periods119878 Total stages of supply chain network119862119863119899
(119904119894) Customer requirement of supplier 119894 at
stage 119904 for period 119899
Min119862119875(119904119894)
Minimal starting up productivity ofsupplier 119894 at stage 119904
Max119862119875(119904119894)
Maximal starting up productivity ofsupplier 119894 at stage 119904
The Scientific World Journal 5
119875119862(119904119894)
Manufacturing cost of supplier 119894 atstage 119904
119875119876(119904119894)
Product quality of supplier 119894 at stage 119904119879119862((119904119894)(119904+1119895))
Transportation cost from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1
119879119878((119904119894)(119904+1119895))
Transportation time from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1
119875119862(119904119894)
Average manufacturing cost of supplier119894 at stage 119904
119875119876119904119894 Average product quality of supplier 119894 at
Transportation loss rate from supplier 119894at stage 119904 to supplier 119895 at stage 119904 + 1
119908119875119862
119908119879119862
119908119879119878
119908119875119876
Weights of manufacturing costtransportation cost transportationtime and product quality
Integer function for obtaining theinteger value of the real number byeliminating its decimal
Decision Variables
119880119899
((119904119894)(119904+1119895)) Transportation quantity from supplier 119894 at
stage 119904 to supplier 119895 at stage 119904 + 1 for period119899
119877119880119899
((119903119904119895)(119904119894)) Defective products quantity from supplier
119895 at stage 119903119904 to supplier 119894 at stage 119904 stage forterm 119899
Notations for developing the update models for the positionand velocity of each particle
1198881 1198882 Learning factors
119870 Constriction factorrand() Random numbers between 0 and 1119904lowast
119894 Pbest memory value of particle 119894
119904119894 Gbest memory value of particle 119894
119904new119894
New position of particle 119894Vold119894 Original velocity of particle 119894
Vnew119894
New velocity of particle 119894Vmax The set maximal velocity119908 Inertia weight
120601Totaling of cognition parameter and socialparameter which must exceed 4
Notations for performing hypotheses on the objective func-tion value convergence time and completion time amongfour proposed approaches
119862119879GA Convergence time of GA119862119879PSOA IWM Convergence time of PSOA IWM119862119879PSOA VMM Convergence time of PSOA VMM119862119879PSOA CFM Convergence time of PSOA CFM119865119879GA Completion time of GA119865119879PSOA IWM Completion time of PSOA IWM119865119879PSOA VMM Completion time of PSOA VMM119865119879PSOA CFM Completion time of PSOA CFMObjGA Objective function value of GAObjPSOA IWM Objective function value of PSOA IWMObjPSOA VMM Objective function value of PSOA VMMObjPSOA CFM Objective function value of PSOA CFM
Acquire the minimization of manufacturing costs trans-portation costs and transportation time as well as themaximization of the manufacturing quality of the differentsuppliers at various stages of forward and reverse logistics
23 Proposed Models for Solving Cross-Stage Reverse LogisticsProblems
231 GA-Solving Model The detailed procedures of a GA-solving model are described as follows
Step 1 The encoding of this study was performed accordingto the cross-stage reverse logistics problem including forwardand reverse transportation routes therefore one route is oneencoding value The scope is randomly generated based onthe demands and (10)ndash(14) The chromosome structure isshown in Figure 4 The gene cell index 11ndash21 in the figurerepresents the products sent from the first supplier of the firststage to the initial supplier of the second stage within thesupply chain structure whereas the gene value represents thetransportation volumes from upstream to downstream
Step 2 Substitute all the generated encoding values in theobjective function equation (1) of this study to acquire thefitness function value of each gene
Step 3 This study adopted the roulette wheel selectionproposed by Goldberg [60] which is performed beforecloning to solve the minimization problem of this studyIt then selects the reciprocal of fitness function generated inStep 2 and calculates the cumulative probability of each stripof chromosome the larger probability value indicates thatthis chromosome has a greater likelihood of being duplicatedOne probability value between 0 and 1 is generated thesuitable fitness function is determined and cloning is carriedout
Step 4 The crossover of this study involves using the single-point crossover method Randomly select two chromosomesfrom the parent body for crossover and generate onecrossover point then exchange the genes of the chromosomeThe crossover course is shown in Figure 5
Step 5 The mutation of this study also adopts a single-pointmutationmethod and treats the delivery route of one supplieras a ldquosingle-pointrdquo of valueThemutationmethod is shown inFigure 6
Step 6 The new filial generation was generated through thegene evolution of Steps 3ndash5 if the optimal fitness functionvalue of the filial generation is higher than that of the parental
Figure 8 Particle swarm encoding for reverse logistics
generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation
Step 7 This study sets the iteration times as the terminationcondition for gene evolution
232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows
Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and
reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage
The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own
The Scientific World Journal 9
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Transportation loss rate from supplier 119894at stage 119904 to supplier 119895 at stage 119904 + 1
119908119875119862
119908119879119862
119908119879119878
119908119875119876
Weights of manufacturing costtransportation cost transportationtime and product quality
Integer function for obtaining theinteger value of the real number byeliminating its decimal
Decision Variables
119880119899
((119904119894)(119904+1119895)) Transportation quantity from supplier 119894 at
stage 119904 to supplier 119895 at stage 119904 + 1 for period119899
119877119880119899
((119903119904119895)(119904119894)) Defective products quantity from supplier
119895 at stage 119903119904 to supplier 119894 at stage 119904 stage forterm 119899
Notations for developing the update models for the positionand velocity of each particle
1198881 1198882 Learning factors
119870 Constriction factorrand() Random numbers between 0 and 1119904lowast
119894 Pbest memory value of particle 119894
119904119894 Gbest memory value of particle 119894
119904new119894
New position of particle 119894Vold119894 Original velocity of particle 119894
Vnew119894
New velocity of particle 119894Vmax The set maximal velocity119908 Inertia weight
120601Totaling of cognition parameter and socialparameter which must exceed 4
Notations for performing hypotheses on the objective func-tion value convergence time and completion time amongfour proposed approaches
119862119879GA Convergence time of GA119862119879PSOA IWM Convergence time of PSOA IWM119862119879PSOA VMM Convergence time of PSOA VMM119862119879PSOA CFM Convergence time of PSOA CFM119865119879GA Completion time of GA119865119879PSOA IWM Completion time of PSOA IWM119865119879PSOA VMM Completion time of PSOA VMM119865119879PSOA CFM Completion time of PSOA CFMObjGA Objective function value of GAObjPSOA IWM Objective function value of PSOA IWMObjPSOA VMM Objective function value of PSOA VMMObjPSOA CFM Objective function value of PSOA CFM
Acquire the minimization of manufacturing costs trans-portation costs and transportation time as well as themaximization of the manufacturing quality of the differentsuppliers at various stages of forward and reverse logistics
23 Proposed Models for Solving Cross-Stage Reverse LogisticsProblems
231 GA-Solving Model The detailed procedures of a GA-solving model are described as follows
Step 1 The encoding of this study was performed accordingto the cross-stage reverse logistics problem including forwardand reverse transportation routes therefore one route is oneencoding value The scope is randomly generated based onthe demands and (10)ndash(14) The chromosome structure isshown in Figure 4 The gene cell index 11ndash21 in the figurerepresents the products sent from the first supplier of the firststage to the initial supplier of the second stage within thesupply chain structure whereas the gene value represents thetransportation volumes from upstream to downstream
Step 2 Substitute all the generated encoding values in theobjective function equation (1) of this study to acquire thefitness function value of each gene
Step 3 This study adopted the roulette wheel selectionproposed by Goldberg [60] which is performed beforecloning to solve the minimization problem of this studyIt then selects the reciprocal of fitness function generated inStep 2 and calculates the cumulative probability of each stripof chromosome the larger probability value indicates thatthis chromosome has a greater likelihood of being duplicatedOne probability value between 0 and 1 is generated thesuitable fitness function is determined and cloning is carriedout
Step 4 The crossover of this study involves using the single-point crossover method Randomly select two chromosomesfrom the parent body for crossover and generate onecrossover point then exchange the genes of the chromosomeThe crossover course is shown in Figure 5
Step 5 The mutation of this study also adopts a single-pointmutationmethod and treats the delivery route of one supplieras a ldquosingle-pointrdquo of valueThemutationmethod is shown inFigure 6
Step 6 The new filial generation was generated through thegene evolution of Steps 3ndash5 if the optimal fitness functionvalue of the filial generation is higher than that of the parental
Figure 8 Particle swarm encoding for reverse logistics
generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation
Step 7 This study sets the iteration times as the terminationcondition for gene evolution
232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows
Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and
reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage
The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own
The Scientific World Journal 9
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
23 Proposed Models for Solving Cross-Stage Reverse LogisticsProblems
231 GA-Solving Model The detailed procedures of a GA-solving model are described as follows
Step 1 The encoding of this study was performed accordingto the cross-stage reverse logistics problem including forwardand reverse transportation routes therefore one route is oneencoding value The scope is randomly generated based onthe demands and (10)ndash(14) The chromosome structure isshown in Figure 4 The gene cell index 11ndash21 in the figurerepresents the products sent from the first supplier of the firststage to the initial supplier of the second stage within thesupply chain structure whereas the gene value represents thetransportation volumes from upstream to downstream
Step 2 Substitute all the generated encoding values in theobjective function equation (1) of this study to acquire thefitness function value of each gene
Step 3 This study adopted the roulette wheel selectionproposed by Goldberg [60] which is performed beforecloning to solve the minimization problem of this studyIt then selects the reciprocal of fitness function generated inStep 2 and calculates the cumulative probability of each stripof chromosome the larger probability value indicates thatthis chromosome has a greater likelihood of being duplicatedOne probability value between 0 and 1 is generated thesuitable fitness function is determined and cloning is carriedout
Step 4 The crossover of this study involves using the single-point crossover method Randomly select two chromosomesfrom the parent body for crossover and generate onecrossover point then exchange the genes of the chromosomeThe crossover course is shown in Figure 5
Step 5 The mutation of this study also adopts a single-pointmutationmethod and treats the delivery route of one supplieras a ldquosingle-pointrdquo of valueThemutationmethod is shown inFigure 6
Step 6 The new filial generation was generated through thegene evolution of Steps 3ndash5 if the optimal fitness functionvalue of the filial generation is higher than that of the parental
Figure 8 Particle swarm encoding for reverse logistics
generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation
Step 7 This study sets the iteration times as the terminationcondition for gene evolution
232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows
Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and
reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage
The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own
The Scientific World Journal 9
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
23 Proposed Models for Solving Cross-Stage Reverse LogisticsProblems
231 GA-Solving Model The detailed procedures of a GA-solving model are described as follows
Step 1 The encoding of this study was performed accordingto the cross-stage reverse logistics problem including forwardand reverse transportation routes therefore one route is oneencoding value The scope is randomly generated based onthe demands and (10)ndash(14) The chromosome structure isshown in Figure 4 The gene cell index 11ndash21 in the figurerepresents the products sent from the first supplier of the firststage to the initial supplier of the second stage within thesupply chain structure whereas the gene value represents thetransportation volumes from upstream to downstream
Step 2 Substitute all the generated encoding values in theobjective function equation (1) of this study to acquire thefitness function value of each gene
Step 3 This study adopted the roulette wheel selectionproposed by Goldberg [60] which is performed beforecloning to solve the minimization problem of this studyIt then selects the reciprocal of fitness function generated inStep 2 and calculates the cumulative probability of each stripof chromosome the larger probability value indicates thatthis chromosome has a greater likelihood of being duplicatedOne probability value between 0 and 1 is generated thesuitable fitness function is determined and cloning is carriedout
Step 4 The crossover of this study involves using the single-point crossover method Randomly select two chromosomesfrom the parent body for crossover and generate onecrossover point then exchange the genes of the chromosomeThe crossover course is shown in Figure 5
Step 5 The mutation of this study also adopts a single-pointmutationmethod and treats the delivery route of one supplieras a ldquosingle-pointrdquo of valueThemutationmethod is shown inFigure 6
Step 6 The new filial generation was generated through thegene evolution of Steps 3ndash5 if the optimal fitness functionvalue of the filial generation is higher than that of the parental
Figure 8 Particle swarm encoding for reverse logistics
generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation
Step 7 This study sets the iteration times as the terminationcondition for gene evolution
232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows
Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and
reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage
The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own
The Scientific World Journal 9
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Figure 8 Particle swarm encoding for reverse logistics
generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation
Step 7 This study sets the iteration times as the terminationcondition for gene evolution
232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows
Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and
reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage
The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own
The Scientific World Journal 9
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages
Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle
Step 10 The target value of each particle generated in Step 9is compared to receive Gbest
Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest
Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)
(1) PSOA IWM (Eberhart and Shi [61])
Vnew119894
= 119908Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
(20)
(2) PSOA VMM (Eberhart and Kennedy [43 63])
Vnew119894
= Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
) + 1198882
times rand () times (119904119894minus 119904
old119894
)
119904new119894
= 119904old119894
+ Vnew119894
if V119894gt Vmax V
119894= Vmax
else if V119894lt minusVmax V
119894= minusVmax
(21)
When the particle velocity was too extreme it could beguided to the normal velocity vector
(3) PSOA CFM (Clerc [62])
Vnew119894
= 119896 times ⟨Vold119894
+ 1198881times rand () times (119904
lowast
119894minus 119904
old119894
)
+1198882times rand () times (119904
119894minus 119904
old119894
)⟩
119904new119894
= 119904old119894
+ Vnew119894
119870 =2
2 minus 120593 minus radic1205932 minus 4120593
120601 = 1198881+ 1198882 120601 gt 4
(22)
Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula
Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes
3 Illustrative Example and Results Analysis
This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer
This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status
This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs
10 The Scientific World Journal
Siliconmaterial
Materialsfabrication
Waferfabrication Assembly Final
test Customer
Manufacturing unit
Demand unitForward route
Reverse route
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Figure 9 Typical supply chain network for semiconductor
transportation costs transportation time and product qual-ity were assumed to be equal
This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2
For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888
1= 205 119888
2= 205 pro-
posed byClerc [62] 1198881= 28 119888
2= 13proposed byZhang et al
[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888
1= 28 119888
2= 13 velocity = 50
and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5
For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8
Tables 6ndash8 show that all 1198670are rejected Finally the
Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as
(119909119894minus 119909119895minus radic(119896 minus 1) 119865
120572(119896minus1)(119899minus119896)radicMSE(
1
119899119894
+1
119899119895
)
119909119894minus 119909119895+ radic(119896 minus 1) 119865
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt
119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times
For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has
The Scientific World Journal 13
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Table 2 Experimental design results of GA with different groups of parameters
GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value
1000
10002 06 4565 6522 5858455
095 3691 5272 5864019
005 06 5888 8412 5820524095 6012 8588 5853552
20002 06 9907 14153 5857317
095 5849 8357 5791562
005 06 11126 15894 5788794095 9415 13451 5787604
2000
10002 06 5942 11212 5830374
095 5187 9788 5873883
005 06 9085 17142 5769888095 8987 16958 5802988
20002 06 8823 16649 5769203
095 7251 13681 5793471
005 06 15542 29372 5755047095 13379 25245 5769029
Table 3 Experimental design results of PSOA IWM with different groups of parameters
PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value
1000
1020 04 117 249 5816602
09 126 269 5853555
50 04 228 486 588147309 294 562 5935652
2020 04 345 521 5938588
09 271 577 5824685
50 04 576 1012 581133809 617 1121 5899211
2000
1020 04 296 489 6129503
09 238 521 5817566
50 04 469 924 584003409 510 1026 5851926
2020 04 473 931 5912584
09 502 1006 5803912
50 04 756 1888 573972109 1194 2234 5809798
better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems
Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure
that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would
14 The Scientific World Journal
Table 4 Experimental design results of PSOA CFM with different groups of parameters
PSOA CFMGeneration Particle Velocity 119888
1 1198882
Convergence time (S) Execution time (S) Objective function value
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes
return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage
4 Conclusion and Suggestion
Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market
The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical
The Scientific World Journal 17
Table 15 The third period transportation plan by PSOA IWM
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
Demand 250 300 400 300 350 400Bold data are the reverse transportation volumes
model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors
would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper
References
[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997
[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998
[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999
[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008
[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007
[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007
[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005
18 The Scientific World Journal
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006
[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011
[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992
[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001
[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988
[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003
[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998
[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000
[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997
[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001
[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997
[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999
[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998
[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995
[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001
[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005
[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001
[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004
[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005
[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006
[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005
[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009
[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012
[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010
[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011
[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012
[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013
[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013
[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013
[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013
[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010
[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007
[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007
[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012
[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995
The Scientific World Journal 19
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953
[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007
[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005
[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007
[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010
[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012
[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012
[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012
[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012
[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012
[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013
[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012
[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005
[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006
[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002
[58] W A McCall Measurement Macmillan New York NY USA1939
[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010
[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988
[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the
7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998
[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999
[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995
[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999
[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953