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Advances in Theoretical and Applied Mathematics ISSN 0973-4554 Volume 11, Number 3 (2016), pp. 223-243 © Research India Publications http://www.ripublication.com

Environmentally Conscious Optimization of Closed Loop Supply Chain Network with Vehicle Routing

Santhosh Srinivasan and Shahul Hamid Khan

Department of Mechanical Engineering

Indian Institute of Information Technology Design and Manufacturing (IIITD&M)-Kancheepuram Chennai 600 127, Tamilnadu, India

E-mail: [email protected], [email protected]

Abstract

Product recovery and remanufacturing have become important business strategies to gain a competitive edge in business and also in the society. Parts from discarded products due to rapid technological advancement and post-consumer products before & after end-of-life (EOL) are recovered to reduce landfill waste and to have some economic advantage. Along with the forward supply chain, manufacturers concentrate on the reverse supply chain, bringing light to the importance of Close Loop Supply Chain (CLSC) network. Product recovery is made possible with the help of CLSC. This paper concentrates on multi-period, multi-product, and multi-echelon Closed Loop Green Supply Chain (CLGSC) network. A bi-objective (cost and emission) Mixed Integer Linear Programming (MILP) model has been formulated for the network and has been optimized using Goal Programming approach. Results are discussed and sensitivity analysis is carried out to show some managerial insights of the model. Keywords: Bi-Objective, CLGSC, Product Recovery, Goal Programming, Emission, Vehicle Routing.

1. INTRODUCTION Consumers are well aware of the dangers around them like the growing population, rapidly depleting natural resources and impact on our environment. In addition, the government has imposed several laws to protect the environment. Manufacturers have adopted Green as an important business strategy which increases their image in this competitive environment. Manufacturers are trying to use recycled and re-manufactured parts from post-consumer products or outdated products to reduce

224 Santhosh Srinivasan and Shahul Hamid Khan

landfill waste. Along with Green image, there are some economic advantages of recycling and re-manufacturing parts instead of disposing of them. Researchers and practitioners are keen on solving CLSC, Green Supply Chain (GSC), Remanufacturing, CO2 saving rate and Travelling Salesman Problem (TSP) models as Green has become more popular. Recapturing value from End-of-Use (EOU) and EOL product and related information from the customer to the manufacturer is known as Reverse Logistics (RL) (Rogers and Tibben-Lembke, 1998). Due to legislative, environmental and economic reasons, the importance of RL has amplified considerably in the last two decades (Ritichie et al., 2000). Value recovering as much as possible is the use of RL (EISaadany et al., 2013) and reduce the extraction of virgin materials and solid waste dumps. (Bonney and Jaber, 2011; Matar et al., 2014). Dell has developed an RL by which the products are refurbished or purchase fresh parts easily (Kumar and Craig, 2007). CLSC has two parts, Forward Logistics (FL) and Reverse Logistics. RL has become a fundamental part of Green Supply Chain Management. It exists in different industries including electronics, basic materials, and others. Increased customer's awareness and concern for the environment, the products that are not environmentally friendly are given less importance and it is used to fill warranty pools of sold products by refurbishing, and the remaining are sold in secondary markets (Krikke et al., 2004). Remanufacturing is a popular research topic among researchers and practitioners in developing countries due to resource scarcity (Rashid et al., 2013). Remanufactured products will result in fewer greenhouse emission over virgin manufacturing practices with less consumption of energy and cost (Sutherland et al., 2008). The researcher also interested in building the low-carbon supply chain. CO2 emission in the supply chain beyond single organization is reduced and visualized (Yamada, 2008). Many studies proposed by extending the classical Vehicle Routing Problem (VRP) and TSP objectives environmental and social impacts can be reduced (McKinnon & Piecyk, 2009; Sbihi & Eglese, 2007; Bektas & Laporte, 2011). As there is a need to extend the life of EOL products and to balance various environmental pressures, companies have to develop a system that avoids landfills (Rathore et al., 2011). The first sector to implement remanufacturing is the automobile sector (Seitz, 2007) for EOL vehicles with strategies like repair, reconditioning or reuse with warranties equivalent to a new product with better quality, new appearance, upgraded parts and original specifications (Ijomah, 2002 and Ijomah et al, 2007). Remanufacturing has become popular in other sectors especially in electronic industries where the EOL and a premature product is more. But in developing countries, remanufacturing is still in the initial stages and still struggling with remanufacturing implementation (Kannan et al., 2015). Integer Linear Programming (ILP), Mixed Integer Linear Programming (MILP) and Mixed Integer Non-Linear Programming (MINLP) are mostly used to model CLSC, GSC, and VRP. Models are optimized using Mathematical Programming Method, Simulation Method, Heuristic Method, Hybrid Method and Analytical Method. Multi-objective models are effectively solved using Mathematical Programming Methods. The outline of this report is as follows. Detailed literature review various CLSC with CO2 emission and TSP are presented in section 2. Problem definition is presented in

Environmentally Conscious Optimization of Closed Loop Supply Chain Network 225

section 3. Section 4, the mathematical model is presented. The data description, solution approach and results are presented as Computation Experiment in section 5. Section 6, presents the conclusion and future scope. 2. LITERATURE REVIEW In the past decade, many researchers worked on issues like wastage, shortages, unsatisfied customers and facility location, depletion of natural resources and environmental effect and tried to help optimizing this. For this, they considered real life problems and these problems are complex and hard to solve and the exact solution approach takes more CPU time to optimize it. An efficient search method needs to be employed to attain an optimal solution to reduce the CPU time. Meta-Heuristic methods helps us in achieving the best solution and reduces the CPU time. Some of their work are presented below as Closed Loop Supply Chain with CO2 emission and TSP. Kannan et al. (2009) designed CLSC network for a build-to-order environment using Genetic Algorithm (GA) and Particle Swarm Optimisation (PSO). Limitations and errors in the model, in data set and in the computational studies reported by Subramanian et al (2012). Kannan et al. (2010) developed GA, based on heuristics, to solve CLSC network model for making decisions on material procurement, production, distribution, recycling and disposal of a battery recycling. Paksoy et al. (2010) proposed multi-objective (minimize the forward logistics cost, minimize the reverse logistic cost, minimize total carbon-di-oxide emission and minimize purchasing cost) MILP for a CLSC network. Wang et al. (2011), modelled a supply chain network problem with environmental concerns. They made a decision regarding the environmental concern within the design stage itself and proposed a multi-objective optimization model that will capture the trade-off between the total cost and the environmental degradation in the form of carbon dioxide emission. Successfully implementation of the model can be done in planning the green supply chain management. Paksoy et.al. (2011) expressed their concerns as researchers in green supply chain management. They came up with the multi-objective problem in GSCN with reverse logistics. They aimed to minimize the total cost via minimizing the transportation cost in forward and the Reverse Logistics (RL), minimizing the CO2 emission, minimizing the total purchasing cost and maximizing the total profit. Winkler H. (2011) also expressed his concern in supply chain management. He emphasized on the integration of the production system with green manufacturing. He has mentioned the idea of greening and enlarging the production system on the supply chain level. Ozceylan et al. (2013 a) have developed an MILP model to optimize the production and distribution planning for a CLSC network, considering purchasing (raw material) and refurbishing (used-parts/products) costs to manage the realistic trade-off problem. For same model Ozceylan et al. (2013 b) addressed the fuzziness, capacities, demands, objective functions, land filling and the recovery rate are identified with uncertain parameters. Subramanian et al. (2013) proposed a comprehensive CLSC model optimized using a constructive heuristic based on VAM-TOC method and a


PBSA search heuristic. Jindal and Sangwan (2014) proposed CLSC framework in uncertain environment. Chaabane and Geramianfar (2015) presented a multi-objective, multi-product, multi-period and just in time inventory framework for sustainable supply chain optimization. Sustainability is measured on the basis of three performance criteria: cost, GHG emission, and service level. Jyoti Darbari et.al.(2015), developed a reverse network design with three objective economic, social and environmental development for EOL and EOU laptop under the fuzzy environment. Network design determines the percentage of product to be disassembled, remanufactured and disposed off. Also the author have implemented TSP between manufacturing facility and distribution center. Based on the above literature, it is identified that there is a research potential to make use of a closed-loop supply chain network with multi-parts/components under a time horizon with the incorporation of CO2 emissions and TSP. However, the integration of economic, environmental issues and social impact for multi-period is becoming critical, as most literature suggests. Since CLSC design and planning with environmental issues, social impact and TSP are NP-hard problems. Within an acceptable time, exact solvers cannot solve real size instances. Some researchers have attempted meta-heuristic algorithms such GA, PSO, Tabu Search (TS) and memetic algorithm. However, developing new methodologies which are capable of achieving better results regarding solution quality and time are required to ensure higher profit and lowers cost. This is the main motivation of this paper. The contributions of this paper are as follows. (1) developing a multi-objective, multi-period, and multi-part & product MILP model to optimize the integrated location-allocation-emission reduction planning for a CLGSC network with TSP between distribution hubs and retailers; (2) consider purchasing and reprocessing costs to manage the realistic trade-off problem; (3) results from the computational experiments used to analyse various performance components and some managerial insight for the proposed model through a sample problem instance. The next section presents a real life CLGSC design problem. The potential design of a supply chain is composed of suppliers, processing unit, assembling unit distribution hub, retailer, Sorting and dismantling center, and reprocessing unit as shown in Figure 1. 3. PROBLEM DEFINITION From the literature, the major objective framed was to design and optimize a multi-objective, multi-product, multi-period CLGSC network. A real life CLGSC network is presented in this section and it composed of suppliers, processing units, assembling units, distribution hubs, retailers, Sorting and dismantling units, and reprocessing units as shown in Figure 2. Vehicle routing is done between distribution hubs and retailers. Two products are used to flow in the CLGSC network. Two products are assembled with different parts and the detailed bill of the material is given in Figure 1.


Fig 1: Bill of Material Tree Diagram for Product 1 and Product 2

Some assumptions about the problem are 1) the demand for each product is deterministic and must be fully satisfied for multi-periods, 2) facilities capacities are limited and fixed in the network, all the costs are deterministic and known a prior, 3) collection, disposal and disassembly rates are known in prior, 4) the reprocessed part has the same quality as the new part, 5) only parts can be disposed or reprocessed, and 6) Wang and Hsu (2010) pointed the recovery amount is calculated as a percentage of customer demand. 4. MATHEMATICAL FORMULATION The objectives are to minimize the total supply chain cost and total supply chain emission.

Fig. 2: Proposed Closed Loop Supply Chain

Indices l Supplier p Processing Units a Assembling Units

Product 1

Part 1

(1)

Part 3

(2)

Part 4

(1)

Product 2

Part 2

(3)

Part 3

(2)

Part 4

(1)


n Distribution Hubs r Retailers c Customers x Reprocessing Units y Disposal Units i Raw Materials j Parts k Products m Time Period w Sorting and Dismantling Units (SD) q Cluster Variables QSm

ilp Quantity shipped from Supplier “l” to Processing Unit “p” for Raw Material

“i” in period “m” QPm

jpa Quantity shipped from Processing Unit “p” to Assembling Unit “a” for Part

“j” in period “m” QAm

kan Quantity shipped from Assembling “a” to Distribution Hub “n” for Product “k” in period “m”

QN mkdt

Quantity shipped from node "d" to "t" belonging to" q" cluster connected to "n" Distribution Hub in

period "m" QC m

krc Quantity shipped from Retailer “r” to Customer “c” for Product “k” in period “m”

QF mkcr Quantity shipped from Customer “c” to retailer “r” for Product “k” in period

“m” QR m

krw Quantity shipped from Retailer “r” to SD Unit “w” for Product “k” in period “m”

QY mjwy Quantity shipped from SD Unit “w” to Disposal Unit “y” for Part “j” in

period “m” QW m

jwx Quantity shipped from SD Unit “w” to Reprocessing Unit “x” for Part “j” in

period “m” QZ m

jwa Quantity shipped from SD Unit “w” to Assembling Unit “a” for Part “j” in

period “m” QX m

jxa Quantity shipped from Reprocessing Unit “x” to Assembling Unit “a” for

Part “j” in period “m” UPm

p If the Processing Unit “p” is open in period “m”, 1; otherwise, 0

UAma If the Assembling Unit “a” is open in period “m”, 1; otherwise, 0


UN mn If the Distribution Hub “n” is open in period “m”, 1; otherwise, 0

URmr If the Retailer “r” is open in period “m”, 1; otherwise, 0

UW mw If the SD Unit “w” is open in period “m”, 1; otherwise, 0

UX mx If the Reprocessing unit “x” is open in period “m”, 1; otherwise, 0

UY my If the Disposal Unit “n” is open in period “m”, 1; otherwise, 0

TSRqdtn If vehicle travel from node "d" to "t" belonging to" q" cluster connected to "n"

Distribution Hub, 1; otherwise, 0 TNRq

n If "n" Distribution Hub is connected to "q" Cluster, 1; otherwise, 0 Parameters CSm

il

Capacity of Supplier “l” in period “m”

CPmjp Capacity of Processing Unit “p” in period “m”

CAmka Capacity of Assembling Unit “a” in period “m”

CNmkn Capacity of Distribution Hub “n” in period “m”

CRmkr Capacity of Retailer “r” in period “m”

CW mjw Capacity of Sorting and Dismantling Unit “w” in period “m”

CX mjx Capacity of Reprocessing Unit “x” in period “m”

SI ij Stake of Raw Material “i" in Part “j”

SJ jk Stake of Part “j” in Product “k”

demmkc Demand of Customer “c” in period “m”

f op The fixed opening cost for Processing Unit “p”

f oa The fixed opening cost for Assembling Unit “a”

f on The fixed opening cost for Distribution Hub “n”

f ow The fixed opening cost for Sorting and Dismantling Unit “w”

f ox The fixed opening cost for Reprocessing Unit “x”

f oy The fixed opening cost for Disposal Unit “y”

f il The unit cost of purchasing of Raw Material “i" from supplier “l”

f jp The unit cost of processing of Part “j” in Processing Unit “p”

f ka The unit cost of assembling of Product “k” in Assembling Unit “a”

f kn The unit cost of sorting and packing for Product “k” in Distribution Hub “n”

f kw The unit cost of sorting and dismantling of Product “k” in SD Unit “w”

f jy The unit cost of disposal of Part “j” in Disposal area “y”


f jx The unit cost of reprocessing of Part “j” in Reprocessing Unit “x”

fe jp Emission while processing of Part “j” in Processing Unit “p”

feka Emission while of assembling of Product “k” in Assembling Unit “a”

fekw Emission while of sorting and dismantling of Product “k” in SD Unit “w”

fe jy Emission while disposal of Part “j” in Disposal area “y”

fe jx Emission while reprocessing of Part “j” in Reprocessing Unit “x”

TAkan The unit cost of shipping from Assembling Unit “a” to Distribution Hub “n” for Product “k”

TN kdt Shipping cost between the nodes "d" and "t" belonging to the "q" cluster connected to the "n" Distribution Hub for product "k"

TRkrw Shipping cost per unit from Retailer “r” to SD Unit “w” for Product “k”

TY jwy Shipping cost per unit from SD Unit “w” to Disposal Unit “y” for Product “k”

TW jwx Shipping cost per unit from SD Unit “w” to Reprocessing Unit “x” for Product “k”

TZ jwa Shipping cost per unit from SD Unit “w” to Assembling Unit “a” for Product “k”

TEAkan Shipping emission per unit from Assembling Unit “a” to Distribution Hub “n” for Product “k”

TEN knr Shipping emission per unit from Distribution Hub “n” to Retailer “r” for Product “k”

TERkrw Shipping emission per unit from Retailer “r” to SD Unit “w” for Product “k”

TEY jwy Shipping emission per unit from SD Unit “w” to Disposal Unit “y” for Product “k”

TEW jyx Shipping emission per unit from SD Unit “w” to Reprocessing Unit “x” for Product “k”

TEZ jwa Shipping emission per unit from SD Unit “w” to Assembling Unit “a” for Product “k”

TSP q Total number of nodes in the "q" cluster

EE td & Positive values that ensure no sub-routing in TSP η Percentage of demand, which is collected by Retailer from Customer λ Percentage of disassembled amount which is disposed υ Percentage of disassembled amount resend to Assembling Unit


Objective Functions

Min Total Cost Z1=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛++++

+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+++++

+

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

++

+++

∑∑∑∑∑∑

∑∑∑∑∑∑∑

∑∑

∑∑∑∑

fQXfQYfQRfQNfQAfQP

fQSUYfUXfUWfUNfUAfUPf

TZQZTWQW

TYQYTRQRQNTNTNRTSRTAQA

jxjxan

mjxajy

jwym

mjwykw

krwm

mkrwkn

knrm

mknrka

kanm

mkanjp

jpam

mjpa

ililpm

milp

my

ym

oy

mx

xm

ox

mw

wm

ow

mn

nm

on

ma

am

oa

mp

pm

op

jwajwam

mjwajwx

jwxm

mjwx

jwyjwym

mjwykrw

krwn

mkan

mkdtkdt

qn

kqdtn

qdtnkan

kanm

mkan

m

(01)

Min Total Emission Z2=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛++++

+

⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

+

++++

∑∑∑∑∑

∑∑

∑∑∑∑

feQXfeQYfeQRfeQAfeQP

TEZQZTEWQW

TEYQYTERQRTENQNTEAQA

jxjxan

m

jxajyjwym

m

jwykwkrwm

m

krwkakanm

m

kanjpjpam

m

jpa

jwajwam

mjwajwx

jwxm

mjwx

jwyjwym

mjwykrw

krwn

mkanknr

knrm

mknrkan

kanm

mkan

(02)

Constraints Capacity Constraints

mliCSQS mil

p

milp

,,,∀≤∑ (03)

mpjUPCPQP mp

mjp

a

mjpa

,,,∀≤∑ (04)

makUACAQA ma

mka

n

mkan

,,,∀≤∑ (05)

mnkUNCNQN mN

mkn

r

mknr

,,,∀≤∑ (06)

mrkURCRQCQR mr

mkr

c

mkrc

w

mkrw

,,, ∀≤+∑∑ (07)

mwjUWCWQZQWQY mw

mjw

a

mjwa

x

mjwx

y

mjwy

,,,∀≤++ ∑∑∑ (08)

mxjUXCXQX mx

mjx

a

mjxa

,,, ∀≤∑ (09)

mckdemQC mkc

r

mkrc

,,,∀≥∑ (10)

Flow balancing constraints

mapiSIQPQS ijj

mjpa

l

milp

,,,,( 0*) ∀=− ∑∑ (11)

mnajSJQAQXQZQP jkk

mkan

x

mjxa

w

mjwa

p

mjpa

,,,,( 0*)11∀=−++ ∑∑∑∑

−− (12)

mnkr

mknr

a

mkan QNQA ,,,0 ∀=−∑∑ (13)

mrkw

mkrw

c

mkrc

c

mkcr

n

mknr QRQCQFQN ,,,0 ∀=−−+ ∑∑∑∑ (14)

mwky

mjwyjk

r

mkrw QYSJQR ,,,( 0*) ∀=−∑∑λ (15)

mwka

mjwajk

r

mkrw QZSJQR ,,,( 0*) ∀=−∑∑υ (16)


mwkjx

mjwxjk

r

mkrw QWSJQR ,,,,)1{( 0*} ∀=−−− ∑∑λυ (17)

mxja

mjxa

w

mjwx QXQW ,,,0 ∀=−∑∑ (18)

Vehicle Routing Constraints

tdqnTSPt q

d

qdtnTSR ≠<∀=∑ ,,,,0 (19)

tdqnTSPt q

t

qdtnTSR ≠<∀=∑ ,,,,0 (20)

tdqnTSPt q

d

qtdn

d

qdtn TSRTSR ≠<∀=−∑∑ ,,,,0 (21)

tdqtd

qdtn

d

qn TSRTNR ≠∀=∑∑ ,,,1 (22)

1,1,,,1,,,1 ≠≠<=∀−=+− dtTSPtddqn qqqdtn

qtd TSPTSRTSPEE (23)

0,,,,,,,,, ≥QXQZQWQYQRQCQNQAQPQS mjxa

mjwa

mjwx

mjwy

mkrw

mkrc

mknr

mkan

mjpa

milp (24)

}1,0{,,,,,, =UYUXUWURUNUAUP my

mx

mw

mr

mn

ma

mp (25)

The objectives are to minimize total cost and total emission in the supply chain. The total cost objective has five components. Total transportation cost of CLGSC network is represented as the first component, the setup cost of different facilities in the chain as the second component, the logistics cost of the chain as the third component, raw material purchase cost of the chain as the fourth component and Reprocessing cost of the chain as the final component. Similarly, total emission has two components; total transportation emission of CLGSC network is presented in the first component and total logistics emission is presented in the second component. Constraints (03)-(09) ensure that the production and transportation amount must not surpass the capacity of all the facilities respectively. Constraint (10) ensures that demands fully satisfied for both the products. Constraints (11)-(18) are balance equations for the forward and reverse facilities. Constraints (19)-(23) are vehicle routing equations between Distribution Hubs and Retailers. Constraint (24) enforces the positivity of decision variables. Finally, Constraint (25) represents the binary variables. 5. COMPUTATIONAL EXPERIMENTS In this section, the result of a realistic proposed CLGSC network problem for random instances are illustrated. Computational properties and complexities of solving the problem are studied. Some insights are provided for the model based on different scenarios. 5.1. Description of data The network constitutes a sample problem of 5 suppliers, 3 processing units, 2 assembling units, 2 distribution hubs, 4 retailers, 2 SD units, 1 reprocessing unit, and 1 disposal unit. Five kinds of ram material have different utilization rate is supplied by suppliers, which in turn, are converted into four parts in processing units.


Table 1: Input Parameters

Parameters Intervals Parameters Intervals Capacity of Supplier 40000 Distance between Supplier to

Processing unit 200-300

Capacity of Processing unit

40000 Distance between Processing unit to Assembling unit

130-150

Capacity of Assembling unit

5000 Distance between Assembling unit to Distribution Hub

60-100

Capacity of Distribution hub

5000 Distance between Distribution Hub to Retailer

60-80

Capacity of Retailer 3000, 2000 Distance between Retailer and SD unit

60-80

Capacity of sorting and dismantling unit

3000 Distance between SD unit to Assembling Unit

140-200

Capacity of Reprocessing unit

10000 Distance between SD unit to Disposal Area

50-60

Capacity of Disposal area 4000 Distance between SD unit to Reprocessing unit

130-140

Raw material purchase cost

Uniform (6-10)

Distance between Reprocessing unit to Assembling unit

125-150

Processing cost Uniform (22-29)

Return Rate η 0.1

Assembling cost Uniform (12-14)

Disposal Rate λ 0.2

Storage cost at Distribution Hub

Uniform (2-3)

Recovery Rate υ 0.3

Sorting and Dismantling Cost

Uniform (11-13)

Emission at Processing unit Uniform (10-15)

Disposal cost Uniform (3-6)

Emission at Assembling unit Uniform (5-8)

Reprocessing cost Uniform (12-18)

Emission at Sorting and Dismantling unit

Uniform (5-8)

Distance between Retailers

60-80 Emission at Disposal unit Uniform (2-7)

Emission at Reprocessing unit Uniform (10-15)

These four parts are assembled into two products in assembling units. Road transportation is used for shipping products, parts, and raw materials from different facilities. The transportation cost and emission is given as 20 Rs per ton-Km and 20 g per ton-Km for a general truck. The fixed cost is found to be 200000 Rs, 100000 Rs, 50000 Rs, 75000 Rs, 75000 Rs and 50000 Rs for processing units, assembling units,


distribution hubs, sorting and dismantling units, reprocessing units, and disposal units respectively. The required parameter values are given in the Table 1. The MILP formulation (1)-(25) for sample instances will be computed on a PC with an Intel i7 2.54GHz processor with 8 GB RAM using CPLEX solver. The sample instance 2 has 801 (37 non-negative, 686 non-negative integers and 80 binary) variables and 576 constraints. 5.2. Solution Approach In this section, we will discuss the solution approach followed to solve the model. We have chosen Goal Programming approach to solve the model by a pre-emptive method which converts multiple objectives into a single goal to find an efficient solution. A pre-emptive method can be used when the model has several objectives with different priorities. Without degrading the higher priority objective by a lower priority objective all the objectives will be optimized. The higher priority objective will be solved and will be added as a constraint to the successive priority objective. For example, if Z1 and Z2 are the two objectives and Z1 has higher priority than Z2, then solve for Z1 first. Let Z1* be the optimal value of Z1. ie Z1= Z1*. Change the objective from Z1 to Z2, then re-optimize the model after adding Z1≤ Z1*. If the model turns to be infeasible then degrade the Z1* value by 5% and solve the model ie Z1 ≤ 1.05 Z1*. A Pareto frontier is formed by the value of Z1 and Z2 to obtain the alternative optimal solution for decision making. 5.3. Results and Discussions The total cost and emission found to be 16611334.6 Rs and 4607671.7 grams of CO2 for all periods which include transportation cost, setup cost, and logistics cost. Table 2 gives the cost performance criteria as a percentage of the objective 1 function value and emission performance criteria as a percentage of the objective 2 function value considering only Z1. Table 3 gives the cost performance criteria as a percentage of the objective 1 function value and emission performance criteria as a percentage of the objective 2 function value considering both Z1 & Z2. 5 suppliers, 2 processing units, 2 assembling units, 2 distribution hubs, 3 retailers, 1 sorting and dismantling unit, 1 reprocessing unit and 1 disposal unit is used in all the periods. Figure 3 show the Total Cost Vs the Total Emission curve. It is a Pareto frontier which can provide a portfolio of alternative optimal solutions. It clearly demonstrates the trade-off between the total cost and the total CO2 emission. When more facilities are opened the CO2 emission while transportation reduces and setup cost is increased. From Table 1 and Table 2, it is clear that Purchasing cost and Logistics cost dominates the Total cost. Setup cost and Reprocessing cost does not contribute more. Whenever the percentage of return product increases then Purchasing cost decreases and Reprocessing cost is increased. Figure 3 show the Cost and Emission Performance components considering both Z1 and Z2


Figure 3. Total Cost Vs Total Emission

Figure 4. Cost and Emission Performance components considering both Z1 and Z2

4595.0

4600.0

4605.0

4610.0

4615.0

4620.0

4625.0

4630.0

4635.0

16400.0 16600.0 16800.0 17000.0 17200.0 17400.0 17600.0 17800.0

Tot

al E

mis

sion

in K

g

Total Cost in Thousand RS


Table 2: Cost performance components and Emission performance components considering only Z1.

Cost Performance Components

Value (Rs)

Percentage of Total

Cost

Emission Performance Components

Value (grams)

Percentage of Total

Emission C1 Total Cost 16467644 100.00% P1 Total Emission 4631277 100.00% C2 Setup Cost 3600000 21.86% P2 Transportation

Emission 1777659 38.38%

C3 Transportation Cost

1777659 10.79% P3 Logistics Emission

2853617 61.62%

C4 Logistics Cost 4602064 27.95% C5 Purchasing

Cost 6339520 38.50%

C6 Reprocessing Cost

148400 0.90%

Table 3: Cost performance components and Emission performance components considering both Z1 and Z2.

Cost Performance Components

Value (Rs)

Percentage of Total

Cost

Emission Performance Components

Value (grams)

Percentage of Total

Emission C1 Total Cost 16611335 100.00% P1 Total Emission 4607672 100.00% C2 Setup Cost 3600000 21.67% P2 Transportation

Emission 1781935 38.67%

C3 Transportation Cost

1781935 10.73% P3 Logistics Emission

2825737 61.33%

C4 Logistics Cost 4567184 27.49% C5 Purchasing

Cost 6513815 39.21%

C6 Reprocessing Cost

148400 0.89%

5.4. Sensitivity Analysis Finally, we conducted a sensitivity analysis of the model with changes in demand for two products, changes in collection rate, changes in capacities of assembling unit and distribution hub, and changing the problem size.


Table 4: Minimum, maximum, and gap of total cost and total emission with change in demand

Demand Total Cost Total Emission Product 1 Product 2 Minimum Maximum Gap Minimum Maximum Gap

6K 4K 16467644 22554320 36.96% 4597266 6634318 44.31%6.3K 4.2K 17231986 23255543 34.96% 4872299 6895739 41.53%6.6K 4.4K 17996660 23916204 32.89% 5147475 7143332 38.77%6.9K 4.6K 18761860 24461429 30.38% 5422845 7350766 35.55%7.2K 4.8K 19527132 25006347 28.06% 5698251 7556954 32.62%

Table 4 show the result of sensitivity analysis when demand is changed. The total cost gap and the total emission gap decreases as demand increases. It means that when the demand is large, the utilization of facility is high which provide greater benefit in reducing the cost and emission. Table 5 show the result of sensitivity analysis when collection rate is changed. The total cost gap increases with increase in collection rate and the total emission gap reduce as the collection rate increases. It means that when the collection rate is more, the utilization of processing facility has become less and utilization of reprocessing facility is high which provide greater benefit in reducing the cost but on the other hand, emission has increased considerably because of increase in disposal emission and transportation emission. Table 5: Minimum, maximum, and gap of total cost and total emission with change in collection rate Collection Rate Total Cost Total Emission

Minimum Maximum Gap Minimum Maximum Gap 10% 16467644 22554320 36.96% 4597266 6634318 44.31%20% 15976064 21993394 37.66% 4660204 6660755 42.93%30% 14906086 21427373 43.75% 4722609 6682899 41.51%40% 14408075 20863597 44.80% 4782047 6706894 40.25%50% 13910658 20300827 45.94% 4840094 6731728 39.08%

Table 6: Minimum, maximum, and gap of total cost and total emission with change in capacity of Distribution hub and Assembling unit

Capacity Total Cost Total Emission Assembling

Unit Distribution

Hub MinimumMaximum Gap MinimumMaximum Gap

5000 5000 16467644 22554320 36.96% 4597266 6634318 44.31%5250 5250 16356443 22641170 38.42% 4562416 6665818 46.10%5500 5500 16245535 22728020 39.90% 4527566 6697317 47.92%5750 5750 16136744 22814869 41.38% 4492765 6728818 49.77%6000 6000 16026141 22834065 42.48% 4456708 6737183 51.17%


Table 6 show the result of sensitivity analysis when the capacity of assembling unit and distribution hub are changed. The total cost gap and total emission gap increases as the capacity of assembling unit and distribution hub is increased. It means that when the capacity of assembling unit and distribution hub is more, the utilization of facility is high which provide greater benefit in reducing the cost and emission. Table 7 shows the optimal and feasible solution for different problem size. Table 7: Optimal and feasible results and CPU time for different problem sizes considering both Z1 and Z2 Sl. No.

Problem size Product 1 Demand

Product 2 Demand

Total Cost(Rs)

Total Emission

(Kg)

CPU Time (sec)

l p a n r w x y

1 2 3 2 2 3 2 1 1 3000 2000 8542642 3048.2 2.01 2 5 3 2 2 4 2 1 1 6000 4000 16611334 4607.7 4.18 3 5 4 3 3 6 2 1 1 9000 6000 23459864 6154.8 5.23 4 7 4 3 3 8 2 1 1 12000 8000 31205685 7625.3 6.21 5 7 7 5 5 10 2 1 1 15000 10000 38965421 9145.7 6.56

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