Research Article Shortest-Path Optimization of Ship Diesel ...

Research ArticleShortest-Path Optimization of Ship Diesel Engine Disassemblyand Assembly Based on ANDOR Network

Deng-Zhi Chen1 Chen Wei 2 Guo-Ling Jia 3 and Zhi-Hua Hu 2

1Merchant Marine College Shanghai Maritime University Shanghai 201306 China2Logistics Research Center Shanghai Maritime University Shanghai 201306 China3School of Highway Changrsquoan University Xirsquoan Shaanxi Province 710054 China

Correspondence should be addressed to Guo-Ling Jia jglchdeducn

Received 28 August 2019 Revised 20 November 2019 Accepted 13 January 2020 Published 18 February 2020

Academic Editor Dimitri Volchenkov

Copyright copy 2020 Deng-Zhi Chen et al -is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Ship diesel engine disassembly and assembly (SDEDA) is essential for ship inspection andmaintenance and navigation safety-eSDEDA consists of various machinery parts and operations It is crucial to develop a system of SDEDA operations to improve theefficiency of disassembly and assembly (DampA) Considering the ldquoANDrdquo and ldquoORrdquo relations (modeled as links) among the DampAoperations (modeled as nodes) an ldquoANDORrdquo network is developed to extend a specialized graph model for the DampA sequencingproblem in the context of education and training -en we devised a mixed-integer linear program (MILP) to optimize theSDEDA sequence based on the ANDOR network Considering the flow balance in the ANDOR network we developed exactalgorithms and random search algorithms using breadth-first branch cut and depth-first strategies to minimize the cost of theshortest path that represents an optimal sequence of DampA operations To the best of our knowledge it is the first try to formulatethe DampA operations by an extended network model Numerical experiments show that the proposed algorithms are practical forsolving large-scale instances with more than 2000 DampA operations -e breadth-first shortest-path algorithm outperforms theMILP solver from the perspective of solution quality and computing time and all developed algorithms are competitive in terms ofcomputing time

1 Introduction

A diesel engine is ship equipment that is essential fornavigation and various shipping operations [1] Ship dieselengine consists of a wide variety of machinery parts that areinterconnected and mutually constrained A single part isconnected to several connecting components and is a pre-constraint of multiple parts Ship diesel engine disassemblyand assembly (DampA) (simplified as SDEDA) operations arecomplicated It requires the operators to be aware of thepartsrsquo connections When repairing or replacing specificparts the operator develops a disassembly plan followingconsideration of the predisassembly conditions of the partssubsequent disassembly constraints and the state of theparts [2] Besides it is essential to establish a reasonable andefficient part DampA operational system to reduce redundant

operations and improve equipment maintenance efficiencyNotably different from general DampA operations that areconducted at specialized workshops or even factories theSDEDA is generally handled on ships in ocean shipping-eskills of the seafarer operators are so crucial at such occa-sions that the DampA operations must be optimized and thuswe try to standardize the optimal SDEDA processes foreducation purposes In the context of education andtraining typical test scenarios include finding an optimialsequence of disassemble sequence or assembling some partsof an engine with minimal steps

-e SDEDA process includes operations of DampAmaintenances and overhauls A widely used diesel engine(the type number is 6135) is taken as an example in this studydue to the following reasons this diesel engine is general andwidely used in the shipping industry it is a basic

HindawiComplexityVolume 2020 Article ID 2919615 15 pageshttpsdoiorg10115520202919615

configuration for the labs in maritime universities and so wecan use it for experimental studies -e disassembly processof this diesel engine involves 509 possible operations of 60parts when we disassemble all these parts through variouspaths Generally we use 47 machinery tools to remove thediesel enginersquos block components or parts replace or cleanthe piston inject the oil and handle the inner circulatingwater pipes Due to the complexity of the equipmentstructure the disassembly process needs to strictly follow theprocedural principles ldquofrom top to bottomrdquo ldquofrom theoutside to the insiderdquo and ldquofirst removing last installingrdquoWe conclude these principles according to the positions andthe sequences of operating the parts In real operations theorder of DampA of parts is usually determined and guided byexperienced operators So DampA efficiency is affected by theexperiences of the operators -erefore we aim at devel-oping a system of reasonable DampA operations to optimizethe operationsrsquo sequences to improve the efficiency andaccuracy of SDEDA [3]

-e main problems faced by SDEDA are as follows firstwith the rapid development of the shipping industry thescale of waterborne transportation continues to expandwhich in turn leads to the aggravation of the maintenancework of ship diesel engines Meanwhile the aging problemsin ships stimulate the increment of maintenance costs -eincreasing amount of upgraded maintenance tasks andworkload continuously requires improving maintenanceefficiency Second modern ship engines are big and con-figured with complex electromechanical systems In theDampA operations the illegal activity will give rise to un-imaginable damages or loss to the engines It is not evenpossible for the operators to quickly locate the faultycomponents which affects maintenance efficiency as well Inthe case of time-sensitive requirements the optimized DampAsequence and skilled operations have direct impacts on theship repairing and operational costs

We organize the remainder of the paper as followsSection 2 presents related studies on machinery DampASection 3 introduces the methods used to model the DampAoperational network Section 4 devises the shortest-pathmodel for DampA sequence optimization Section 5 describesthe algorithms for the shortest-path optimization based onthe ANDOR network Section 6 gives numerical studies toshow the effectiveness of the proposed models and algo-rithms -e remarks and conclusion summarize the findingsand indicate future directions in Section 7

2 Related Studies

-e research on SDEDA mainly concentrates on DampAtechnology and tools First we can classify the DampA tech-nology research as a virtual and real type In terms of realDampA Hu et al reviewed assembly representation methodssequence generation methods and assembly line balancingmethods -ey discussed the operational complexity of theassembly system and the role of the human operator fromthe perspective of product types and disassembly andremanufacturing are challenging in the presence of a largenumber of product types [4] Zhu et al established an

SDEDA database for DampA ship management ship repairand ship craft teaching [5] -e database has variousfunctions (such as browsing query display addition dele-tion and modification) and can provide services such asDampA preparation DampA methods operation proceduresand disassembly precautions Tan et al studied the disas-sembly process of offshore oil and gas platforms consideredthe risks and costs of offshore operations adopted the re-verse installation method to minimize the elevator timedesigned the Alowast algorithm and optimized the DampA processof the components [6] Chang et al believed that the in-tegration of upscale manufacturing equipment and main-tenance services is not sufficient to ensure functionalavailability [7] -erefore they established an integratedproduct-service network model based on complex networkand operational readiness -e model incorporates func-tional units structural module units and service executionactivities to reveal modeling processes based on function-ality structure service network and network dependencies-e DampA technology used in the real process can be appliedin practical directly but needs more cost So Qing et al usedCatia and Mayarsquos modeling techniques to build an engine-overhaul plant simulation platform to avoid the disadvan-tages of real operation [8] Hong and Qi-Long used a Petrinet to obtain a general disassembly modeling method andexpressed the disassembly process in an orderly manner [9]Apart from single real or virtual technology Chen et alproposed a combination of virtual and practical assemblydisassembly [1] -e DampA of the crankshaft connecting rodpiston parts was taken as an example to introduce thecontents and steps of combined DampA Feng considered thesustainability issue of DampA in the context of product re-covery [10] -e DampA sequencing problem may incur un-certainties that make the problem even challenging [11]

Second there are some research studies which focus onthe selection and design of DampA equipment sequencingplanning and decision-making support systems Gungorbelieves that DampA design is before product maintenance andremanufacturing and the most critical issues are the choiceof connectors [12] Nahas formulated the machine type asdecision variables to establish an optimization design modelof the DampA manufacturing network and proposed an op-timization method based on the proxy algorithm [13]Starting from the overall structure of the process tree Xieet al proposed a process sequence sorting strategy to dividethe processes into internal processes and external ones andoptimize the scheduling sequence [14] Pellegrinelli et alstudied motion planning and scheduling methods to reducethe cycle time of mission planning -ese methods involvetrajectory selection task sequence and task assignment [15]

Among these related studies DampA operation optimi-zation emerges as the primary research stream in the lit-erature as studied in Table 1 We reviewed 19 journal papersby using the querying keywords disassembly and assemblyWe use four dimensions to examine the research charac-teristics of these studies In the ldquoDampArdquo dimension we canfind that 12 studies focus on ldquoDisassemblyrdquo and six studiesfocus on ldquoAssemblyrdquo while only one handles DampA simul-taneously In the ldquoIssuesrdquo dimensions 14 papers target at the

2 Complexity

ldquoSequencingrdquo topic while other studies investigate differentaspects of sequencing and its system In the column ofldquoModelling featuresrdquo graph-based models are dominant inthis research field Precedent graphs are baselines of almostall studies while ldquoANDORrdquo graphs are delicate onesconsidering the relations between an operation and itssuccessors Most papers describe the modeling results as acomparison base of the algorithms Some studies utilize thenetwork generation process [24ndash26] and some studies de-scribe the models by the ideal hierarchy structures [29 30]We can group the algorithms into four categories as studiedin the last dimension in Table 1 First intelligent algorithmsare dominant including genetic algorithm scatter searchand ant colony optimization Second the reviewed studiesuse experience-based heuristics widely eg multistage anditerative algorithms-ird the scholars increasingly concernthe exact algorithms due to its computing performancemainly including graph algorithms Fourth some scholarsdeveloped mathematical programs to describe the modelsformally and possibly be solved optimally by on-the-shelfmixed-integer linear program (MILP) solvers

-e end line of Table 1 describes the characteristics offour dimensions for this study -e issues studied in thispaper are kinds of sequencing problems We also use theANDOR graph as a basic model to formulate the com-plicated process of DampA However besides general DampAoperations we consider tools parts and backgrounds torevise the general DampA operations and so the network is anextended one Besides we also developed formal mathe-matical programs As for the solution algorithms MILPsolver graph traversal algorithms and heuristics are all usedbecause their strengths are differentWe extended the graph-based algorithms by considering the ANDOR relationships

In summary although the above research results offeruseful ideas and inspiration for the SDEDA a wide variety oftools and parts involved in the process contribute to the high

complication -e current procedures are still facing theproblems of time-consuming and requiring additionalstudies Because of these issues this paper establishes theANDOR network optimization procedures to investigatethem

-e contributions of this manuscript are as follows Firstof all the paper construct the ANDOR network for theequipment DampA process where the directed arc represents theprocess direction node means DampA operations the ldquoORrdquonode represents the optional process of the part and thepredecessor of the node describes the pre-DampA requirementsof the part Secondly we formulated a MILP to minimize thepath between two nodes Lastly the breadth-first search al-gorithm and search strategy are designed for the ANDORnetwork to optimize the shortest path between nodes

3 Methods

-e ANDOR network describes the logical relationship ofldquoANDrdquo and ldquoORrdquo in the connection between nodes and thenode that has these relationships is called ldquoANDrdquo or ldquoORrdquonode -e ldquoANDrdquo node indicates that the node can befinished only by completing all its precursors (nodes) Andthe ldquoORrdquo node means that we end a node as long as we endone of its successors in an ANDOR network [35] -eexisting studies can generally address the precedence andldquoANDrdquo relationship issues but not thoroughly discuss theldquoORrdquo relations in the developed solution methods [36]

In the complex context of SDEDA ANDOR networkG isused to describe the network of DampA operations G (V A)

defines a directed graph where V is a set of nodes repre-senting DampA operations consisting of ldquoANDrdquo ldquoORrdquo andcommon nodes A is a set of directed arcs indicating theprocess linking operation and one of its subsequent opera-tions An ldquoANDrdquo node indicates that the correspondingoperation can be performed only by finishing all its precursor

Table 1 Pioneering studies on DampA operations optimization

DampA Issues Modeling features Algorithm[16] D Sequencing Precedence graph Scatter search[17] D Sequencing Precedence graph Network flow[18] D Sequencing Precedence graph -ree-stage iterative procedure[19] D Sequencing ANDOR graph Iterative method[20] DampA Sequencing Precedence graph Genetic algorithm[21] D Sequencing ANDOR graph A two-phase algorithm[22] D Sequencing ANDOR graph Graph algorithm[23] D Sequencing Precedence graph Decision trees[24] A Sequencing Network and elimination Case-based reasoning algorithm[25] D Sequencing Network and elimination Efficient encoding and decoding strategy[26] A Sequencing Exploded view generation Hybrid conjugated algorithm[27] D Sequencing Descriptive model Hybrid ACO[28] D Sequencing Decision tool Descriptive[29] A Subassembly Hierarchy Graph algorithm[30] A Classification Hierarchy Ant colony optimization[31] A Solution space Precedence graph Ant colony optimization[32] D Line balancing Assignment model Hybrid genetic algorithm[33] A Graph generation ANDOR graph MILP[34] D Presentation Precedence graph Genetic algorithm DampA Sequencing ANDOR graph MILP graph algorithm heuristics

Complexity 3

operations And an ldquoORrdquo node means that we must conductat least one of the successor nodes For example at the pointof ldquochecking the connecting rod bearingrdquo (Figure 1) whetherto replace the connecting rod bearing is determined based onthe crack From the perspective of education and trainingoperators the choices of replacing rod bearing (T74) orcleaning rod bearing (T75) are both available -erefore theoperation of ldquochecking the connecting rod bearing bushrdquo(T48) is expressed as an ldquoORrdquo node inG as shown in Figure 1

In the ANDOR network the shortest path is a sequencebetween two specified nodes in the network such that theirconstituent nodes link with each other according to the ANDOR relations and the sum of the weights of their constituentarcs is minimal An ldquoANDrdquo node on the shortest path mayconnect with multiple nodes due to its ldquoANDrdquo relation AnldquoORrdquo node connects with one and only one of its successornodes-e shortest path is significant for the DampA operationsbecause it represents a sequence of assembling or dis-assembling parts of the engine with the minimum time costand operational cost Figure 2 shows an ANDOR networkconsisting of five ldquoANDrdquo node (a b d e g) one ldquoORrdquo node(c) one common node (f) eight arcs and a feasible shortestpath from node a to g as well where the square representcommon nodes the circles represents the ldquoANDrdquo node thediamond represents ldquoORrdquo nodes the dotted lines with arrowsindicates the directed arc and the solid lines with arrowindicates the directed arcs through which the shortest pathpasses-e shortest path between the node a and the node g isformed as follows We construct the shortest path by startingfrom the destination node g and then connect all the pre-cursors of node g covering node b and f Next as node d ande are the successor nodes of the OR node c we add only one ofthem to the shortest path such as node d -en we add thenodes a and c to the shortest path because they are theprecursors of node b and d Finally we connect node c and itsprecursor node a -is shortest path needs to pass through atleast five nodes and six arcs from node a to reach point gSimilarly (a b c e f g) constitutes another shortest pathwith five nodes and six arcs from node a to g

4 Model

We established an MILP ((1)ndash(12)) to minimize the arc costsof the shortest path according to the balance of inflow andoutflow in the path as well as ANDOR logic relationshipbetween the nodes by using the notations as follows

Sets

VA a set of ldquoANDrdquo nodesVR a set of ldquoORrdquo nodesVT a set of common nodesV 1 n a set of nodes V VA cupVR cupVT

A (i j) | i j isin V1113864 1113865 the set of arcs linking the nodes inV

Parameters

s an original node of the shortest path s isin V

d sestination of the shortest path d isin V

Cij the real number time cost for arc (i j) (i j) isin A

Ii integer in-degree of node i in the network i isin V

IMi integer the required minimum in-degree of node

i if node i is in the shortest path i isin V

IMi

1 i isin VT

Ii i isin VA cupVR1113896

Variables

xij isin 0 1 xij 1 if arc (i j) is in the shortest pathotherwise xij 0 (i j) isin Aui isin 0 1 ui 1 if node i is on the shortest pathotherwise ui 0

minf 1113944(ij)isinA

Cijxij (1)

which subjects to

1113944(is)isinA

xsi ge 1 (2)

1113944(id)isinA

xid IMd (3)

us 1 (4)

ud 1 (5)

M middot ui ge 1113944(ij)isinA

xij foralli isin V M |V|(6)

ui le 1113944(ij)isinA

xij foralli isin V(7)

M middot ui ge 1113944(ji)isinA

xji foralli isin V M |V|(8)

ui le 1113944(ji)isinA

xji foralli isin V(9)

xji ge 1 + M middot ui minus 1( 1113857 foralli isin VA

(j i) isin A M |V|

(10)

1113944(ij)isinA

xij ge 1 + M middot ui minus 1( 1113857 foralli isin VR M |V|

(11)

xij isin 0 1

ui isin 0 1

foralli j

(12)

Constraint (1) minimizes the cost of the shortest path (2)ensures that the out-degree of the initial node in the shortestpath is not less than one (3) indicates that the in-degree of theend node is equal to its requiredminimum in-degree (4) and (5)suggest that the shortest path must contain an origin and adestination node (6) suggests that if the out-degree of the node i

in the shortest path is greater than 1 the node i is included in theshortest path (7) indicates that if the out-degree of the point i inthe shortest path is 0 the node i is excluded from the shortestpath similarly (8) indicates that if the in-degree of the node i is

4 Complexity

greater than 1 the node i is included in the shortest path and (9)suggests that if the in-degree of the node i is 0 the node i isexcluded from the shortest path (6) to (9) constitute the flowbalance of outflow and inflow of the nodes in the shortest pathFlow balance constraint indicates that the outflows and inflowsof a node should be equal for the shortest path they shouldequal one Constraint (10) guarantees that the in-degree of theldquoANDrdquo node is not less than its minimum in-degree Constraint(11) ensures that the out-degree of the ldquoORrdquo node in the shortestpath is not less than 1 indicating the ldquoORrdquo node must select atleast one successor In (12) the decision variables x and u mustbe 01 integers

Notably in themodel for the investigated DampA problemwe use s and d to represent the original and target part in asequence of DampA operations Generally s is a virtual originwhen we try to sequence the parts for removing d graduallyd is a virtual origin when we try to sequence the parts forassembling them into a whole from s

5 Algorithms

In the ANDOR network there exist three types of nodesnamely common ldquoANDrdquo and ldquoORrdquo nodes A typical node

requires that we complete one of its precursors an ldquoANDrdquonode requires that we complete all of its precursors an ldquoORrdquonode requests that the algorithm travels one of its successorsIn the shortest path in the ANDOR network one ANDnode connects with multiple nodes We cannot directlyapply the traditional breadth and depth search algorithmsof the shortest path to the ANDOR Network -ereforewe proposed the following three optimization strategiesfor searching the shortest-path search in the ANDORNetwork

51 Breadth-First Search Based on ANDOR RelationsSome of the nodes in the ANDOR network may have bothldquoANDrdquo and ldquoORrdquo links with precursor nodes In the ANDOR network one node can be a node of type ldquoANDrdquo andldquoORrdquo simultaneously according to the required number ofits precursors and the required number of its candidatesuccessors -e coupling of ldquoANDrdquo and ldquoORrdquo relations in asingle node increases the computing complexity of theshortest path -erefore we developed Algorithm 1 to de-termine the branches of choices from OR nodes and markthe conflict nodes that excluded each other from the shortest

ANDORnetwork model

ldquoORrdquonodeT48

T74

T75

T48 checkconnecting rod bearing

T74 replaceconnecting rod

bearing

T75 clean connectingrod bearing

Crack

Figure 1 -e ldquoORrdquo node representing an operation of selectable successor operations in DampA operations

c

a

bd e

f

g

(a)

c

a

bd e

g

f

(b)

Figure 2 (a) ANDOR network and (b) the shortest path from a to g (solid line)

Complexity 5

path We removed the redundant nodes that are not nec-essarily in the path from the origin node to the destinationnode

Algorithm 2 is a breadth-first shortest-path algorithmwith the ANDOR network G Algorithm 2 starts the search

by initializing one path containing the destination nodeand recording the destination as the new-added node in thepath -en the algorithm adds all the precursors of thenew-added node to the path and logs the precursors asnew-added nodes During the process of adding precursors

Input

G (V A) original networks origin node of the shortest pathd destination of the shortest path

Sets

Vor a set of nodesVde a set of deleted nodesAde a set of deleted arcsAadd a set of new-added arcsBi a sub-set of ldquoORrdquo nodesVOS set of nodes that have successor relationships with node sVDP set of nodes that have precursor relationships to nodes pVN set of nodes in the cleaned networkAN set of arcs in the cleaned networkVO set of OR nodes in VNb a branch of an OR node consisted of nodesBi set of branches of OR node i Bi b1 b2 1113864 1113865VC

i set of nodes that are excluded from a path if node i is in the path

Output

Glowast (VN AN) the network starting from node s and ending in node dVC

i set of conflict nodes of node iBi branches of OR node i

Process

Step 1 find the successor nodes to which can be reached by a route from s denoted as VOSVOS i | (s i) isin A or (j i) isin A j isin VOS i isin V1113864 1113865

Step 2 find the precursor nodes from which the destination d can be reached by a route denoted as VDPVDP i | (i d) isin A or (i j) isin A j isin VDP i isin V1113864 1113865

Step 3 select the common nodes in both VOS and VDP denoted as VN VN VOS capVDPStep 4 select the arcs among the nodes of VN to form AN AN (i j) | (i j) isin A i j isin VN1113864 1113865Step 5 for v in VO

Step 51 select the successors of v denoted as VS

Step 52 for vs in VS

Step 521 add the nodes having a successor of vs denotes as bVvs generate bvs V1 V2 1113864 1113865 where V1 contains the nodes that are

successors of vs V2 contains the nodes that are successors of nodes in V1Step 522 for vN in bV

vs

Step 5221 if vN exists in all bVvs vs isin VS

set vT vb

go to Step 52Step 53 for vs in VS

Step 531 for vb in reverse (bvs ) reverse (Set) means reversely visit the elements in SetStep 5311 if vT notin vb

remove vb from bvs

elsego to Step 531

Step 532 update bNvs bN

vs i | i isin vb vb isin bvs1113864 1113865

Step 54 for vs in VS

Step 541 for vN in bNvs

Step 542 VCvN⟵Uvs lowast(bN

vs lowast) vslowast isin VS vs ne vslowast

Step 6 output Glowast (Vlowast Alowast) VCi

ALGORITHM 1 Network cleaning and Branches Preprocessing

6 Complexity

when a node vi to be added conflicts the nodes already inthe path p a new path is generated from p so that the newpath contains node vi and excludes the nodes conflicted bynode vi To increase the efficiency of the search of path withminimal cost we cut the paths with costs higher than thecurrent minimal cost in the algorithm After all the pathshave added the precursors of their new-added nodes Al-gorithm 2 selects the path with the minimum cost as theshortest path

Figure 3 illustrates the generation of a new path duringthe search for Algorithm 2 Algorithm 2 starts the search byadding the precursors v1 v41113864 1113865 of the destination v5 andobtains the path containing nodes v5 v1 v41113864 1113865 -en thealgorithm adds the precursors v2 v31113864 1113865 of node v4 andconstructs a path ( v5 v1 v4 v21113864 1113865) firstly However node v3 isforbidden to be added to the path v5 v1 v4 v21113864 1113865 since v2 andv3 belong to different branches of the ldquoORrdquo node Next anew path v5 v1 v4 v31113864 1113865 is generated by adding the node v3 to

Input

V a set of nodes in the network G

A a set of arcs in the network GCij cost of arcs (i j) (i j) isin As origin node of the shortest pathd destination of the shortest pathVC

i set of nodes that are excluded from the path p if p contains node i

Sets

P the path sets p1 p2 1113864 1113865 in which pi contains the nodes of the path from node s to dVF

i a set of forbidden nodes for the path pi VF VF1 VF

2 1113864 1113865VN

i a set of the newly added node to the path pi VN VN1 VN

2 1113864 1113865mi binary variable mi 1 if path pi is completed 0 otherwise M m1 m2 1113864 1113865

Output

plowast set of nodes in the shortest pathf the cost of the shortest path plowast

Process

Step 1 initialize p1 d m1 0 VFi empty VN

i d c1 0Step 2 set f 2 middot 1113936(ij)isinACij

Step 3 while existmi 0 pi isin P

Step 31 select the first path pi that satisfies mi 0 pi isin P

Step 32 if ci gtf

Step 321 set mi 1Step 322 go to Step 3Step 33 if VN

i s or VNi empty

Step 331 set f ci

Step 332 set plowast⟵pi

Step 333 set mi 1Step 334 go to Step 2Step 34 for vN in VN

i Step 341 select the precursor nodes of v denoted by VPre

Step 342 for vPre in VPreStep 3421 select VC

vPre (the conflict nodes of vPre ) denoted by VC

Step 3422 set vC⟵VC cappi

Step 3423 if vC emptyStep 34231 add vPre to pi pi⟵pi cup vPre1113864 1113865

Step 34232 delete vN in VNi V

Ni ⟵VN

i vN1113864 1113865

Step 34233 add vPre to VNi VN

i ⟵VNi cup vPre1113864 1113865

Step 34234 set ci⟵ ci + 1113936visinpiCvPre v

elseStep 34235 generate a new path p|P|+1 pi cup vPre1113864 1113865VC

Step 34236 set m|P|+1 0 VN|P|+1 VN

i cup vPre1113864 1113865VC VF|P|+1 VF

i cupVC

Step 34237 set c|P|+1⟵ ci minus 1113936visinpiCvCv + 1113936visinp|P|+1

CvPre v

Step 34238 add p|P|+1 to P

Step 34239 set c|P|+1 0Step 4 output plowast and f

ALGORITHM 2 Breadth-first shortest-path algorithm

Complexity 7

path v5 v1 v41113864 1113865 and removing the nodes conflicted by nodev3-en Algorithm 2 will expand the path v5 v1 v4 v21113864 1113865 anda new path ( v5 v1 v4 v31113864 1113865) into feasible paths linking theoriginal node and destination and calculate their costs

52 Node Cut-Off Search Based on Precursor Algorithm 3searches the shortest path by cutting off redundant branchesof OR nodes based on a full-linked network G First

Algorithm 3 selects all the nodes that have precursor rela-tionship of the destination and adds the arcs among theselected nodes to the path denoted by G then Algorithm 3reserves one branch of each OR node in G and cuts out otherbranches to form a feasible path p connecting the originalnode and destination finally the algorithm calculates the arccosts in p and outputs p and its cost

Figure 4(a) shows a full-linked network connecting theorigin node s and the destination d as a result generated

v1

v2 v3

v5

v4

OR

(a)

v2 v3

v5

v4v1

OR

(b)

Figure 3 Algorithm 2 generates paths which selects the branches of an ldquoORrdquo node (a) A constructing path v5 v1 v4 v21113864 1113865 and (b) a newconstructing path v5 v1 v4 v31113864 1113865

Input

s origin noded destination nodeV a set of nodes in the network GA a set of arcs in the network GCij cost of arc (i j) (i j) isin A

Sets

Bi set of branches of OR node i i isin VVPre

i set of precursor nodes of node i VPrei j | (i j) isin A i isin V1113864 1113865

p the shortest path represented by the nodes in the shortest path

Output

p the shortest path pf cost of path p

Process

Step 1 initialize p d Step 2 select the precursor nodes of the nodes in p denoted as VPre VPre j | (j i) isin A j notin p i isin p1113864 1113865Step 3 while VPre neemptyStep 31 add VPre to p p pcupVPre

Step 32 update VPre VPre j | (j i) isin A j notin p i isin p1113864 1113865Step 4 select all the OR nodes in p denoted as VOStep 5 for v in VO

Step 51 select the branch b with minimal cost in BvStep 52 select the nodes of other branches denoted by VB

Step 53 remove the nodes in VB from path p p⟵pVB

Step 6 calculate the cost f of the arcs (i j) in p i j isin p

Step 7 output the path p and the cost f

ALGORITHM 3 Node cut-off search based on the precursor

8 Complexity

from Step 1 to Step 3 of Algorithm 3 -e network G isconstructed by initializing from destination d and recur-sively adding all the precursors of the nodes in the networkin which solid arrow lines denote the linked arc -ere existsone OR node (denoted as OR in Figure 4) in G As the resultsof the cutting process from Step 4 to Step 5 of Algorithm 3 afeasible shortest path is obtained by cutting off the redun-dant branches of node OR as shown in Figure 4(b)-e arcs(OR v3) (v3 v2) (v2 v1)1113864 1113865 denote the cut-off branch andare represented by dotted arrow lines in Figure 4(b)

53 Random Depth-First Search -e random depth-firstsearch initializes the destination as the first node in the pathand adds the precursors of the nodes in the path until thepath includes the origin node and its successors Whenadding new nodes that belong to different branches of asingle OR node the algorithm randomly selects one nodeaccording to a predetermined threshold value Algorithm 4iterates multiple times to generate various paths and choosethe path with the minimal cost as the solution Algorithm 4presents the search processes

Figure 5 displays the random selection of nodes amongdifferent branches of a single OR node When Algorithm 4adds one node (v3) to the path containing conflict nodes (v2)we generate a random number (α) and a threshold value βand then compare the results when using them in the al-gorithm If αle β the algorithm reserves the existing node(v2) in the path and excludes the node (v3) from the pathotherwise the algorithm eliminates the current node (v2) outand adds the node (v3) to the path

6 Numerical Study

Taking the diesel engine (type number 6135) as an examplewe establish the ANDOR network for its DampA according tothe predecessor and subsequent relationship of componentand then develop the shortest steps to disassemble andassemble two specific parts We used the Matlab 2018a forthe coding of the shortest-path planning model and thesearch algorithm And the model is solved by Gurobi 725(httpswwwgurobicom) We execute the program in the

environment of the 64-bit Windows 7 operating system in acomputer with Intel Core i7-5500U dual-core CPU 8GBRAM

61 Network Construction As for the single node in theANDOR network the parts and component operations ofthe diesel engine are defined through the following attri-butes parts or components to be disassembled such asinstrument boxes water supply valves and return pipestools to be used such as inner diameter gauges torquewrenches and particle adsorption tools specific actionsperformed such as the circle assembly visual inspectionand wiping specific scenarios conducting performance suchas the water supply line area control panel and fuel supplyarea For a given power facility and workspace the abovefour attributes uniquely identify an operation Figure6showsthe ANDOR network of DampA operations for the dieselengine where the diamond node represents the ldquoORrdquo node-e network has 394 common nodes 115 ldquoORrdquo nodes and1143 directed arcs

Figure 7 is the result of conceptualizing the ANDORnetwork by a real-world case using the diesel engine (typenumber 6135) Our team took about one year to constructand verify this diagram with specialized operators in our laband the cooperative companies Because we need to find allpossible successors of operation when it is determined wemust try all possibilities of DampA methods As studied in theabove paragraph we denote all four categories of infor-mation for every node -en we coded the diagram intostructured text tables corresponding to the four groups Sowe named this diagram a conceptualized ANDOR networkfor the DampA operations because we denoted the nodes andarcs with the four categories of information We also addedannotations to the nodes and arcs -en we used Algo-rithm 1 to convert the conceptualized network to a struc-tured network -e ldquoORrdquo nodes are in green color

To test the effectiveness of the mathematical program-ming model and the search algorithms we generate the datasets of ANDOR networks in which the number of nodesranges from 10 to 5000 and the number of arcs ranges from10 to 8000 Using the above network as a base we generated

s

ORv3

v1

d

v2

(a)

v3

v1v2

s

OR

d

(b)

Figure 4 Algorithm 3 cuts off redundant branches of the OR node (a) a full-linked network connecting s and d and (b) cut-off one branchof node OR

Complexity 9

the test data sets by removing nodes or inserting nodes to theexisting networks by similar methods in the literature[24ndash26]

62 Results andDiscussion In the following we conduct theexperiments on the generated data sets by using the MILPmodel Algorithms 2ndash4 We used Gurobi 725 an on-shelfsolver of mathematical programs to solve the MILP model-e run time of the MILP solver for solving an instance once

is limited to 3600 seconds -e number of iterations ofAlgorithm 4 for one example is 100

Table 2 presents the experimental results of the modeland the search algorithm-e computing time (CT) includesthe code compiling time and the solving time As an indi-cator for comparing the results between the proposed al-gorithms and the MILP model a gap between the results iscalculated by Gap (fAlgorithm minus fMILP)fMILP middot 100 For theinstances with more than 2000 nodes the MILP solvercannot return an optimal result before the run time

Input

V a set of nodes in the network G

A a set of arcs in the network GCij cost of arcs (i j) (i j) isin As origin node of the shortest pathd destination of the shortest pathVC

i set of nodes that are excluded from the path p if p contains node iβ a given threshold value for choosing the node in branches of the ldquoORrdquo nodeN the maximal number of iterations

Sets

P the path sets p1 p2 1113864 1113865 in which pi contains the nodes of the path from node s to dVF the set of forbidden nodesVN the set of new-added nodes to path p

Output

plowast set of nodes in the shortest pathf the cost of the shortest path plowast

Process

Step 1 initialize i 1 f 1113936(ij)isinACij

Step 2 while ilt N

Step 21 initialize pn d VF empty VN d

Step 22 while VN neemptyStep 221 for vN in VNStep 2211 select the precursor nodes of v denoted by VPre

Step 2212 for vPre in VPreStep 22221 select VC

vPre(the conflict nodes of vPre ) denoted by VC

Step 22222 if VC cappi emptyadd vPre to p p⟵pcup vPre1113864 1113865

delete vN in VNVN⟵VN vN1113864 1113865

add vPre to VN VN⟵VN cup vPre1113864 1113865

elserandomly generate a value α α isin [0 1]

if αgt βadd vPre to p p⟵pcup vPre1113864 1113865

delete the conflict nodes of vPre in p p⟵pVC

delete the conflict nodes of vPre in VNVN⟵VNVC

add vPre to VN VN⟵VN cup vPre1113864 1113865

elsego to Step 221

Step 23 calculate the cost ci of arcs among the nodes of pi

Step 24 if ci ltf

Step 241 set f ci

Step 242 set pi as the best path plowast plowast⟵pi

Step 3 output plowast and f

ALGORITHM 4 Random depth-first search

10 Complexity

limitation and then the objective value at the terminationtime is recorded as a result

-e MILP model can obtain the optimal results for theinstances within 1500 nodes under the run time limitationand for the example with more than 2000 nodes near-optimal results are generated by the solver with terminationconditions -e execution time of the MILP model increasesrapidly when the number of nodes rises driven by the timefor handling the increasing number of the variables andconstraints Algorithm 2 generates the result close to theMILP solver and outperforms the MILP solver Further-more Algorithm 2 requires much less computing time toobtain the solution although we observed some fluctuationsin the computing time when the number of nodes and arcschanges Algorithm 3 has advantages against the MILP

solver and other algorithms from the perspective of com-puting time and it takes less than four seconds to solve thelargest instance However the gaps in the results of Algo-rithm 3 are higher than other methods and the gaps growmuch when the scale of the problem expands Algorithm 4can find the optimal solutions for the instances of less than100 nodes and it outperforms Algorithm 3 in the view of theresultant values Compared with Algorithm 2 Algorithm 4spends less time to solve the problem according to theconfiguration of the iteration number although they use asimilar search strategy

-e experimental results show that the complete dis-assembly of the diesel engine requires a minimum of 954steps as shown in Figure 8 Figures 6 and 9 present theoptimization results for the 11 and 52 nodes

v2v1

v1

v3

v2 v3

v1 v2 v3

OR

v

OR

v

OR

v

α le β

α gt β

Figure 5 Branches of an ldquoORrdquo node in Algorithm 4 according to α and β

3

1

6

7

9 10 11

8

4 5

2

Figure 6 ANDOR network of the DampA operations for the diesel engine

Complexity 11

Figure 7 -e ANDOR network of disassembly operations for the diesel engine

Figure 8 -e shortest path of a network of 10 nodes and 15 edges

12 Complexity

7 Remarks and Conclusions

-ere are strict pre- and postrelationships between theoperation of parts and components of the ship diesel engineDampA process and some of them need to be selected byexperienced judgments Although the process manualstipulates the DampA steps precautions and component

installation sequence the actual DampA of specific parts oftenrelies on manual experience due to the wide variety of partsand the complicated DampA steps

-is paper first establishes the ANDOR network forthe operation based on the predecessor relationship ofthe node and the subsequent selection of the judgmentnode Secondly we developed the mathematical program

Table 2 Comparison between different algorithms

Node ArcMILP solver Algorithm 2 Algorithm 3 Algorithm 4

f CTs f CTs Gap () f CTs Gap () f CTs Gap ()11 15 11 045 11 008 000 11 001 000 11 007 00020 31 25 076 25 006 000 25 001 000 25 004 00030 46 15 123 15 002 000 38 001 15333 15 001 00043 65 16 221 16 004 000 37 001 13125 45 002 1812552 77 47 306 47 007 000 62 001 3191 47 003 00064 98 54 442 54 004 000 72 000 3333 54 002 00072 105 16 557 16 001 000 72 000 35000 46 001 1875083 126 21 722 21 001 000 76 000 26190 25 001 190590 146 112 846 112 008 000 119 000 625 112 003 000101 163 129 1057 129 007 000 135 000 465 129 006 000204 310 80 4226 80 004 000 207 001 15875 118 002 4750303 472 42 9292 42 003 000 335 003 69762 214 002 40952401 631 356 16285 356 021 000 504 002 4157 448 011 2584501 797 79 25459 79 007 000 628 014 69494 79 006 000602 957 516 36741 516 031 000 780 003 5116 679 024 3159701 1103 413 49812 413 063 000 863 013 10896 533 026 2906802 1260 697 65240 697 063 000 971 017 3931 762 037 933901 1453 614 82342 614 099 000 1165 093 8974 672 049 9451005 1604 853 102483 853 116 000 1313 019 5393 943 062 10551504 2387 1007 230260 1007 348 000 1825 087 8123 1514 313 50352000 3168 1314 360000 1186 468 -974 2517 209 9155 1686 214 28312501 3984 1925 360000 1869 428 -291 3076 224 5979 2208 347 14703002 4768 744 360000 738 146 -081 3764 232 40591 1298 135 74463504 5565 869 360000 802 280 -771 4396 608 40587 1461 144 68124003 6366 950 360000 861 247 -937 4969 790 42305 3393 160 257164500 7118 2066 360000 1921 408 -702 5389 1992 16084 2795 246 35295003 7944 968 360000 881 369 -899 6131 3604 53337 1332 260 3760

3

21

24

31 32 343543

36373940

454644

38

33

30

22

8

23

6

25 12

27 29 28

56

26

1

5

15

47

49505148

52 53556061626364

54

10

2

4

169

1314414218192011 17

7575859

(a)

3

21

24

3132343543

36373940

45 4644

38

33

30

22

8

23

6

25 12

27 29 28

575859

56

26

1

5

15

47

49505148

525355606162636454

10

2

4

169

1314414218192011 17

7

(b)

Figure 9 -e shortest path of the ANDOR network with 64 nodes and 98 edges (a) integer-programming model optimization results and(b) precursor-based ldquoORrdquo node cut-off search

Complexity 13

and designed the heuristics algorithms to optimize theshortest path between the nodes Considering the ldquoANDrdquorelationship between nodes and the selective successor of theldquoORrdquo node the shortest-path search and optimizationmethod of the OR network is proposed

Taking a typical ship diesel engine as an example wetested the effectiveness of the model and algorithm forapplication Based on the designed ANDOR networkcovering multiple nodes and arcs we compared the opti-mization efficiency of the planning model and algorithms-e results show that the breadth-first shortest-path algo-rithm can achieve solutions close to the optimal onesreturned by solving the mathematical program -ereforethe method is useful for solving SEPDA problems As forfuture research we will study various network traversalsearch algorithms network evaluation methods DampA se-quence evaluation and data-driven and intelligent DampAevaluation and optimization methods Additionally we willextend the studies on general DampA sequencing problems byconsidering new features in marine diesel engine DampAproblems for generality

Data Availability

-e data files are available in the Github repository (httpsgithubcomzhihuah0115SDEDA)

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e National Natural Science Foundation of China (no71871136) Science and Technology Commission ofShanghai Municipality (no 17DZ2280200) and ShanghaiMaritime University Graduate Innovation Fund (no2015ycx076) partially supported this study

References

[1] Y-H Chen W-J Wang F-X Zhu Y-L Li and X-W ZhaoldquoResearch on virtual disassembly and assembly of ship powerequipment and its applicationrdquo China Water Transportvol 2014 pp 17-18 2014 in Chinese

[2] J-H Hu D-B Hu and J-B Xiao ldquoResearch on compre-hensive evaluation method of crewrsquos post operation abilityrdquoComputer and Digital Engineering vol 45 pp 1287ndash12932017 in Chinese

[3] Y-W Zhang X-L Sun Y-W Ding and P-T Sun ldquoDesignof intelligent diagnosis system for marine power equipmentrdquoChinese Journal of Ship Research vol 13 pp 140ndash146 2018 inChinese

[4] S J Hu J Ko L Weyand et al ldquoAssembly system design andoperations for product varietyrdquo CIRP Annals vol 60 no 2pp 715ndash733 2011

[5] F-X Zhu W-J Wang J-S Lu Y-L Li B-J Wu andY-G He ldquoDevelopment and application of ship powerequipment disassembly databaserdquo Journal of Zhejiang Ocean

University (Natural Science) vol 34 pp 461ndash464 2015 inChinese

[6] Y Tan Y Song X Liu X Wang and J C P Cheng ldquoA BIM-based framework for lift planning in topsides disassembly ofoffshore oil and gas platformsrdquo Automation in Constructionvol 79 pp 19ndash30 2017

[7] F Chang G Zhou X Xiao C Tian and C Zhang ldquoAfunction availability-based integrated product-service net-work model for high-end manufacturing equipmentrdquo Com-puters amp Industrial Engineering vol 126 pp 302ndash316 2018

[8] Z Qing Z Yan G Qing and Z Hong-Li ldquoSimulation re-search on rapid assembley and disassembly of aeroenginebased on motion capture equipmentrdquo Computer Simulationvol 35 pp 257ndash262 2018

[9] G Hong and W Qi-Long ldquoResearch on disassembly andinstallation process modeling method for virtual maintenancetasksrdquo Manufacturing Automation vol 37 pp 35ndash38 2015

[10] Y Feng Y Gao G Tian Z Li H Hu and H Zheng ldquoFlexibleprocess planning and end-of-life decision-making for productrecovery optimization based on hybrid disassemblyrdquo IEEETransactions on Automation Science and Engineering vol 16no 1 pp 311ndash326 2019

[11] G Tian M Zhou and P Li ldquoDisassembly sequence planningconsidering fuzzy component quality and varying operationalcostrdquo IEEE Transactions on Automation Science and Engi-neering vol 15 no 2 pp 748ndash760 2018

[12] A Gungor ldquoEvaluation of connection types in design fordisassembly (DFD) using analytic network processrdquo Com-puters amp Industrial Engineering vol 50 no 1-2 pp 35ndash542006

[13] N Nahas M Nourelfath and M Gendreau ldquoSelecting ma-chines and buffers in unreliable assemblydisassemblymanufacturing networksrdquo International Journal of ProductionEconomics vol 154 pp 113ndash126 2014

[14] Z Xie X-H Zhang Y-L Gao and Y Xing ldquoTime-selectiveintegrated scheduling algorithm considering the compactnessof serial processesrdquo Journal of Mechanical Engineering vol 54no 6 pp 191ndash202 2018

[15] S Pellegrinelli A Orlandini N Pedrocchi A Umbrico andT Tolio ldquoMotion planning and scheduling for human andindustrial-robot collaborationrdquo CIRP Annals vol 66 no 1pp 1ndash4 2017

[16] B Gonzalez and B Adenso-Dıaz ldquoA scatter search approachto the optimum disassembly sequence problemrdquo Computersamp Operations Research vol 33 no 6 pp 1776ndash1793 2006

[17] A J D Lambert ldquoExact methods in optimum disassemblysequence search for problems subject to sequence dependentcostsrdquo Omega vol 34 no 6 pp 538ndash549 2006

[18] S C Sarin H D Sherali and A Bhootra ldquoA precedence-constrained asymmetric traveling salesman model for disas-sembly optimizationrdquo IIE Transactions vol 38 no 3pp 223ndash237 2006

[19] A J D Lambert ldquoOptimizing disassembly processes sub-jected to sequence-dependent costrdquo Computers amp OperationsResearch vol 34 no 2 pp 536ndash551 2007

[20] Y-J Tseng H-T Kao and F-Y Huang ldquoIntegrated assemblyand disassembly sequence planning using a GA approachrdquoInternational Journal of Production Research vol 48 no 20pp 5991ndash6013 2010

[21] Y-S Ma H-B Jun H-W Kim and D-H Lee ldquoDisassemblyprocess planning algorithms for end-of-life product recoveryand environmentally conscious disposalrdquo InternationalJournal of Production Research vol 49 no 23 pp 7007ndash70272011

14 Complexity

[22] R Edmunds M Kobayashi and M Higashi ldquoUsing con-straint-satisfaction to optimise disassembly sequences gen-erated from ANDOR informationrdquo International Journal ofProduction Research vol 50 no 15 pp 4105ndash4126 2012

[23] N Ghoreishi M J Jakiela and A Nekouzadeh ldquoA non-graphical method to determine the optimum disassembly planin remanufacturingrdquo Journal of Mechanical Design vol 135no 2 2013

[24] R B Hadj I Belhadj M Trigui and N Aifaoui ldquoAssemblysequences plan generation using features simplificationrdquoAdvances in Engineering Software vol 119 pp 1ndash11 2018

[25] Y Ren C Zhang F Zhao H Xiao and G Tian ldquoAnasynchronous parallel disassembly planning based on geneticalgorithmrdquo European Journal of Operational Researchvol 269 no 2 pp 647ndash660 2018

[26] M V A R Bahubalendruni A Gulivindala M KumarB B Biswal and L N Annepu ldquoA hybrid conjugated methodfor assembly sequence generation and explode view genera-tionrdquo Assembly Automation vol 39 no 1 pp 211ndash225 2019

[27] H-E Tseng C-C Chang S-C Lee and Y-M HuangldquoHybrid bidirectional ant colony optimization (hybridBACO) an algorithm for disassembly sequence planningrdquoEngineering Applications of Artificial Intelligence vol 83pp 45ndash56 2019

[28] M-L Bentaha A Voisin and P Marange ldquoA decision toolfor disassembly process planning under end-of-life productqualityrdquo International Journal of Production Economicsvol 219 pp 386ndash401 2020

[29] Y Wang and J Liu ldquoSubassembly identification for assemblysequence planningrdquo Be International Journal of AdvancedManufacturing Technology vol 68 no 1ndash4 pp 781ndash793 2013

[30] S Li Y Liu J Wang and H Zeng ldquoAn intelligent interactiveapproach for assembly process planning based on hierarchicalclassification of partsrdquoBe International Journal of AdvancedManufacturing Technology vol 70 no 9ndash12 pp 1903ndash19142014

[31] H Wang Y Rong and D Xiang ldquoMechanical assemblyplanning using ant colony optimizationrdquo Computer-AidedDesign vol 47 pp 59ndash71 2014

[32] C B Kalayci O Polat and S M Gupta ldquoA hybrid geneticalgorithm for sequence-dependent disassembly line balancingproblemrdquo Annals of Operations Research vol 242 no 2pp 321ndash354 2016

[33] A J D Lambert ldquoGeneration of assembly graphs by sys-tematic analysis of assembly structuresrdquo European Journal ofOperational Research vol 168 no 3 pp 932ndash951 2006

[34] J R Li L P Khoo and S B Tor ldquoA novel representationscheme for disassembly sequence planningrdquoBe InternationalJournal of Advanced Manufacturing Technology vol 20 no 8pp 621ndash630 2002

[35] S Tao and Z S Dong ldquoScheduling resource-constrainedproject problem with alternative activity chainsrdquo Computersamp Industrial Engineering vol 114 pp 288ndash296 2017

[36] G Tian Y Ren Y Feng M Zhou H Zhang and J TanldquoModeling and planning for dual-objective selective disas-sembly using and or graph and discrete artificial bee colonyrdquoIEEE Transactions on Industrial Informatics vol 15 no 4pp 2456ndash2468 2019

Complexity 15