Multi-objective optimization of green supply chain network ...transportation time of each...

Scientia Iranica E (2017) 24(6), 3355{3370

Sharif University of TechnologyScientia Iranica

Transactions E: Industrial Engineeringwww.scientiairanica.com

Multi-objective optimization of green supply chainnetwork designs for transportation mode selection

D.-C. Gonga,1, P.-S. Chenb;� and T.-Y. Lub

a. Department of Industrial and Business Management, Chang Gung University, Guishan District, Taoyuan City, 333, Taiwan,ROC.

b. Department of Industrial and Systems Engineering, Chung Yuan Christian University, Chung Li District, Taoyuan City, 320,Taiwan, ROC.

Received 10 November 2015; received in revised form 5 October 2016; accepted 29 October 2016

KEYWORDSSupply chain networkdesign;Green supply chain;Transportation mode;Multi-objectiveoptimization.

Abstract. This research considers both cost and environmental protection to design amulti-objective optimization model. With multi-period customer demands, the model cansolve a multi-plant resource allocation and production planning problem by focusing thedecisions on supplier selection, facility selection, production batches, transportation modeselection, and distribution of the materials and commodities of a green supply network.In this paper, four transportation modes, namely, road, rail, air, and sea, have theircorresponding transportation time, costs, and CO2 emissions. Based on multiple planningperiods, this research calculates the minimal total cost and total CO2 emissions basedon production and transportation capacity. Using numerical analyses, the results showthat, when the budget is su�cient, only production capabilities with � = 1:5 and 2.0are bene�cial for improving environmental protection; carbon dioxide emissions of bothproduction capacities are not signi�cantly di�erent. Furthermore, when the productionbatch size increases, total cost increases. Regarding transportation capacity, the resultsshow that, when the budget is su�cient, increasing transportation quantity limits will beslightly bene�cial for improving environmental protection.© 2017 Sharif University of Technology. All rights reserved.

1. Introduction

Global climate change has become a key topic andinternational trends have shifted toward increased reg-ulation of greenhouse gas emissions. In addition, eco-nomic globalization has linked the environment closely

1. Supply Chain Division, Chang Gung MemorialHospital-Linkou, Guishan District, Taoyuan City, 333,Taiwan, ROC

*. Corresponding author. Tel.: (886) 32654410;Fax: (886) 32654499E-mail addresses: [email protected] (D.-C. Gong);[email protected] (P.-S. Chen); [email protected](T.-Y. Lu)

doi: 10.24200/sci.2017.4403

to global supply chains. Production activities consumetremendous energy, with the manufacturing and trans-portation industries producing the most carbon diox-ide. Thus, corporations that wish to reduce greenhousegas emissions in their supply chain should begin withtheir manufacturing and transportation methods [1].

Beamon [2] de�ned a supply chain as \the networkstructure of raw material suppliers, manufacturers,wholesalers, retailers, and end customers involved inthe production and transportation of a product formedthrough integration." To enable e�ective, long-termoperations of the entire supply chain, the design ofSupply Chain Management (SCM) networks frequentlyinvolves strategic policy concerns that encompass ma-terial sources, plant location selections, plant produc-tion capabilities, and inventory management [3]. SCM

3356 D.-C. Gong et al./Scientia Iranica, Transactions E: Industrial Engineering 24 (2017) 3355{3370

networks also involve the selection of transportationroutes, which include raw material supply and trans-portation modes that begin at the supply end and�nish with the customers [4-6]. Melo et al. [7] dividedSCM network design according to the nature of productdemand and supply chain complexity into the followingfour categories: (a) single-stage or multi-stage supplychains; (b) single-product or multi-product supplychains; (c) single-period or multi-period planning; and(d) �xed demand or random demand.

Since 2000, SCM research topics have shiftedtoward multiple products. Rizk et al. [8] examined thedynamic production and transportation problems in-volving multiple products using a single plant locationand distribution center to plan production, transporta-tion, and inventory within a limited cycle. The studycontained di�erent transportation times and costs tosolve the values of decision variables with the objectiveof minimizing cost. Similar studies include Nishi etal. [9] who used Lagrangian decomposition to solve themulti-stage supply network problems of a single plantwith multiple products. Kanyalkar and Adil [10] incor-porated production capabilities and limited inventoryspace, and applied the heuristic method to maximizetarget pro�ts. Hugo and Pistikopoulos [11] developed amulti-supplier and multi-plant production transporta-tion network model of production investment choices toselect production technology investments that achievedthe target net present value and carbon emissionminimization.

In practice, product movement cannot beachieved by relying on only one transportation mode.Suitable transportation modes must be selected on thebasis of product weight, dimensions, product value, andurgency. Das and Sengupta [12] investigated numerousuncertain factors involved in international corporationstrategies and operations, including investment in rawmaterials, transit costs, duties, and changes in demandand transportation time. This two-stage mathematicalsolution model used pro�t maximization as the strate-gic dimension target to obtain supply chain networkdecisions (e.g., whether plants should enter production,product types, and quantity produced by each plant).The results were then used in the operations dimensionto explore cost minimization inventory strategies whentransportation times uctuated.

Sadjady and Davoudpour [13] discussed single-phase requirements and network planning of multipleproducts, and then used cost minimization to deter-mine the location of plants and distribution ware-houses and transportation modes. The Mixed Inte-ger Programming (MIP) model proposed by Sadjadyand Davoudpour incorporated transportation times,carrying costs, and facility setup costs of varioustransportation modes and used Lagrangian relaxationto obtain solutions.

Typically, supply chain network designs do nothave single objectives; decisions must frequently bal-ance di�erent and even mutually exclusive objectives.Researchers have focused on multiple-objective pro-gramming problems because actual situations requireful�lling two or more objectives simultaneously. Mul-tiple objectives require managers to balance numerousobjectives and use this balance as the basis of decisionmaking [14-16]. For example, cost is no longer theonly objective in supply chain design; other economicobjectives are responsiveness and service standards.As Melo et al. [7] indicated, in addition to the sup-ply chain network design, which involves plant siteselection, facility number and production capacity,and movement of raw materials and products betweenplants, increasing environmental social awareness hasadvanced environmental topics to the forefront in SCM.

Unlike typical supply chain design models, whichemphasize cost minimization, numerous scholars haverecently introduced environmental protection conceptsinto SCM to ensure that both economic and environ-mental protection factors are considered [14,17]. Wanget al. [18] used investment in equipment and plantscombined with costs and carbon dioxide emissions toyield innovative designs of multiple-objective supplychains. Hugo and Pistikopoulos [11] included theproduct Life Cycle Assessment (LCA) into decisioncriteria and proposed a multiple-objective MIP. Fer-retti et al. [19] used the aluminum supply chain inthe aluminum industry as an example to evaluate thein uence of the economy and environment. This math-ematical model incorporated the supply capabilities ofsuppliers, equipment depreciation, costs, and carbonemissions during the production and transportationprocess. The objective was to balance minimal totalcost and environmental protection requirements ofproducing the least amount of pollution. Choletteand Venkat [20] maintained that the design of supplychain networks had a direct correlation with energyconsumption and carbon emissions. They consideredthe wine making industry to explore the in uence ofplant and warehouse location, transportation modes,and inventory management strategies on carbon diox-ide emissions. Their results indicated that inventorymanagement and plant location could e�ectively reducecarbon dioxide emissions. Paksoy [21] proposed aproduction-transportation MIP model for three-stagesupply chain networks that considered the raw materialsources, transportation quantity limitations of rawmaterials, and transportation modes. Paksoy addedcarbon emission quotas to the supply chain networkplan. The results indicated that the design of supplynetworks could be used to reduce carbon dioxide emis-sions from industries. Chiu et al. [22] studied a 5-layersupply chain network problem with reverse logistics,which contained suppliers, manufacturers, wholesalers,

D.-C. Gong et al./Scientia Iranica, Transactions E: Industrial Engineering 24 (2017) 3355{3370 3357

retailers, and end customers. The authors calculatedtotal revenues and total cost of forward and reversesupply chain based on di�erent scenarios and, then,applied fuzzy summation calculations to calculate thevalue of each scenario.

Tables 1(a) and 1(b) summarize relevant refer-ences. Studies related to supply chains are divided into:(a) supply chain types, namely, Traditional SupplyChain (TSC) in Table 1(a) or Green Supply Chain(GSC) in Table 1(b); (b) factors such as capacity,inventory, and production; (c) demands (deterministicor stochastic); (d) transportation modes (single ormultiple) or product (single or multiple); (e) periods(single or multiple); and (f) other aspects.

In terms of the multi-transportation mode ofthe green supply chain network, Jamshidi et al. [23]considered multi-objective functions (minimal totalcost and minimal gas emissions) of the green sup-ply chain problem, which contained multiple cus-tomers, distribution centers, warehouses, manufac-turers, suppliers, and transportation modes. Al-e-Hashem et al. [24] studied a stochastic green supplychain problem, which contained multi-product, multi-transportation mode, multi-plant, multi-period, andlimitations of CO2 emissions. They formulated a two-stage stochastic optimization model and calculated itsexpected minimal total cost. Meanwhile, Fahimniaet al. [25] presented a green supply chain problemwhose objective function was to minimize total costs.The authors considered multiple products, suppliers,manufacturers, retailers, transportation modes, andplanning periods. They constructed an MIP model andapplied CPLEX to obtain the optimal solution. Coskunet al. [26] studied a green supply chain network thatconsisted of stores, carriers, distribution centers, andmanufacturers. They considered demand, capacity,and greenness expectations of manufacturers, carriers,distribution centers, and retailers to construct an MIPmodel and applied goal programming to solve theproposed model. Entezaminia et al. [27] integratedcollection and recycling centers into a green supplychain network; its features consisted of multi-period,multi-product, multi-transportation mode, and multi-site factors. For the green concept, they added thelimitations of CO2 emissions in both production andtransportation as constraints and added one objectivefunction. Although the studies discussed here con-sidered transportation capacity and CO2 emissions ofeach transportation mode, they did not consider thetransportation time of each transportation mode intheir supply chain network and nor did they investigatethe impact of transportation-mode selection decisionson the green supply chain network design. Addressingthis limitation is a strong motivation of the currentresearch.

Furthermore, the di�erence between Wang et

al. [18] and the current research is that Wang etal. [18] studied a supply chain network design prob-lem, namely, a one-time decision, to determine thenew locations and new investment levels of factoriesamong potential alternatives, in order to minimizetotal costs and CO2 emissions simultaneously. In theirmodel, they considered multiple products, suppliers,and customers, but they did not consider multipletransportation modes or multiple planning periods.Wang et al.'s [18] model is useful for helping companies,especially international/foreign companies, to decideon their factories' locations and investment levels priorto entering a new market, thereby creating a newsupply chain network. However, the current researchfocuses on determining multi-period decisions aboutproduction batches produced by each factory andtransportation modes used by each pair of supply chainpartners. Although the objective functions (total costand CO2 emissions) in both models (Wang et al. [18]and the current research) are similar, the detaileditems of the objective functions are di�erent. Inaddition, the model in the current research is usefulfor enabling manufacturers to decide on their optimalproduction batch-size plans among factories and trans-portation plans (modes) for an existing supply chainnetwork throughout the planning periods. For theconstraints of both models, Wang et al. [18] considered ow conservation, supplier capacity, order ful�llment,production capacity, environmental level, and non-negative and binary constraints whereas the currentresearch considers ow conservation, supplier capacity,order ful�llment, production capacity and productionbatch size, manufacturing and transportation time ofproducts, transportation capacity between suppliersand manufacturers and between manufacturers andcustomers, and non-negative and binary constraints.Although the methodologies used by both models(Wang et al. [18] and the current research) are thesame, the decisions and constraints in both proposedmodels are somewhat di�erent, leading to dissimilarobservations and conclusions in the two studies. Thisanalysis of the two models serves as the motivationbehind the current research.

This study develops a green supply network modelby taking into consideration supplier selection, plantbatch production, inventory management, selection ofmultiple transportation modes, and product delivery tocustomers. The purpose of the study is to investigatethe impact of production (plant batch sizes) andtransportation capacity (transportation modes) on themulti-period green supply chain network model. Thethree contributions of this research are described asfollows. First, when the budget is su�cient, onlyproduction capabilities with � = 1:5 and 2.0 are bene-�cial for improving environmental protection; carbondioxide emissions of both production capacities are


Table 1(a). Summary of papers of traditional supply chain network models.

Type Author Factors Demand Transportationmode

Product Period Other aspects

C I P D S S M S M S M

TSC Aliev et al. [4] }} } } } } } Fuzzy variables/parameters,and storage capacity

TSC Rizk et al. [8] }} } } } } }Machines, production sequence,setup time, and productionlead-time

TSC Kanyalkar andAdil [10] }} } } } } }

Shorter and longer time periods,storage space, and rawmaterial availability

TSC Das andSengupta [12] }} } } } } }

Strategic and operationalplanning models, minimumbreakeven level capacity, demandswith normal distributions, servicelevel, and safety stock

TSC Sadjady andDavoudpour [13] }} } } } } } Capacity levels of each

plant and warehouse

TSC Pyke and Cohen [35]}} } } } } } Batch size and reorder point

TSC Melkote andDaskin [36] } } } } } } Facility location

TSC Eksioglu et al. [37] } } } } } } None

TSC Farahani andElahipanah [38] }} } } } } }

Multi-objective function(total cost and total just-in-timedelivery), backorder,and storage capacity

TSC Selim et al. [39] }} } } } } }Fuzzi�ed aspiration level,workstations, overtime, backorder,storage capacity, andtransportation capacity

TSC Liang [40] }} } } } } }Fuzzy multi-objective function(total cost and total deliverytime), backorder, laborlevel, storage capacity,and total budget

TSC Al-E-Hashemet al. [41] }} } } } } }

Multi-objective function(total cost and totalcustomer satisfaction), workerskill levels, subcontractor, storagecapacity, and worker training

TSC Rezaei andDavoodi [42] }} } } } } }

Multi-objective function(total cost, total quality level,and total service level),with/without backorder,safety stock, andstorage capacity

TSC Liu andPapageorgiou [43] }} } } } } }

Multi-objective function(total cost, total ow time,and total lost sales),proportional and cumulative capacityexpansions, and capacity utilization

Note: Factors: Supplier/plant capacity (C), Inventory constraints/variables (I), and Production constraints/variables (P).Demand: Deterministic (D), and Stochastic (S). Transportation mode, Product, and Period: Single (S), and Multiple (M).


Table 1(b). Summary of papers of green supply chain network models.

Type Author Factors Demand Transportationmode

Product Period Other aspects

C I P D S S M S M S M

GSC Hugo andPistikopoulos [11] } } } } } }

Multi-objective function(total cost and total gasemission), capacityexpansions at each timeperiod, plant capital investmentcorrelation, and environmentalimpact assessment

GSC Cruz [17] } } } } }Multi-objective function(total cost and total gasemission), social responsibility,demand market price dynamics,and physical transaction level

GSC Wang et al. [18] }} } } } } }Multi-objective function(total cost and total gasemission) and investenvironmental level

GSC Ferretti et al. [19] }} } } } } } Pollution level of each pollutantand maximum allowed pollution level

GSC Paksoy [21] } } } } } } CO2 cost, emission quota penalty,and transportation capacity

GSC Chiu et al. [22] }} } } } } }

Minimization total pro�t offorward and reverse logistics;return resource constraints:most pessimistic, mostlikely, and mostoptimistic values

GSC Jamshidiet al. [23] }} } } } }

Multi-objective function(total cost and total gasemission), backorder,inventory level that consists ofdemands of customers with meanand standard deviation,and production lead-time

GSC Al-e-Hashemet al. [24] }} } } } } }

Backorder, overtime, CO2 limit,quantity discount function, andtransportation lead-time

GSC Fahimnia et al. [25]} } } } } } Minimization of total cost, CO2limit, and vehicle speed constraints

GSC Coskun et al. [26] } } } } } }

Multi-objective function(total income, total cost,total market penalty, totalmarket bonus, and total lost sales),lost sales, andgreenness expectation

GSC Entezaminiaet al. [27] }} } } } } }

Multi-objective function(total cost and total scoreof environmental criteria),recycling products, overtime,and CO2 limit

GSC This research }} } } } } }Multi-objective function(total cost and gas emission),lot-size, transportation lead-time,and transportation capacity

Note: Factors: Supplier/plant capacity (C), Inventory constraints/variables (I), and Production constraints/variables (P).Demand: Deterministic (D), and Stochastic (S). Transportation mode, Product, and Period: Single (S), and Multiple (M).


not signi�cantly di�erent. Second, when the produc-tion batch size increases, total cost increases. Third,regarding transportation capacity, when the budgetis su�cient, increasing transportation quantity limitswill be slightly bene�cial for improving environmentalprotection.

2. Problem description

This study considers the electronics industry as thesubject to investigate a three-stage multiple-productproduction-transportation network design that incor-porates suppliers, plants, and customers. Upstreamsuppliers are component or material vendors represent-ing di�erent supplier locations, production capabilities,and ordering costs. Midstream plants are primarilyresponsible for product manufacturing. Because plantmanufacturing capabilities are limited, plant selectionis required to ensure su�cient production and satisfycustomer demand. Downstream represents demandwhere customers present di�erent product demands atdi�erent times. After incorporating the transportationmodel, the �nal model structure is shown in Figure 1.

Plants are the core of the production trans-portation network. The objective of this study is todetermine the optimal production batches of a productfor each period, component's ordering quantity fromeach supplier, transported product quantity, productinventory, and transportation quantity correspondingto each transportation mode.

Plants must order components from suppliersbased on product requirements. However, suppliershave an upper limit to their supply capability foreach period. Suppliers are selected by considering theupper limit of transportation quantity, ordering costs,

component carrying costs, and carbon emissions forvarious transportation combinations.

This study only considers existing plants for plantselection. Electronic product production frequentlyrequires multiplied amounts of �xed production batchsize because of production technology or equipmentreasons. Thus, in a limited production situation, deci-sion selection involves whether plants should engage inproduction and when to setup and begin productionto ful�ll the requirements. Because plants are inbatch production, unsold products in each period areconverted to inventory and sold in the following period.

Consumer electronic products are usually manu-factured using core components and the general com-ponents, which can be easily substituted or are similar.This study uses the Bill Of Materials (BOMs) con-cept to describe product and component relationships.Because customer demands change in each period, sodoes the quantity ordered by each plant from suppliers.Thus, this study assumes that plants order componentsfrom suppliers in a lot-for-lot policy; consequently,component inventory or shortages are not considered.

Regarding the transportation dimension, freightforwarders typically assist in the planning of trans-portation mode selection and the delivery of transportcomponents and products. Sea and air transportationare the primary international transportation modes;road and rail are the main land transportation modes.Transportation departure points and endpoints aresuppliers to plants or plants to customers. The entiretransportation process (e.g., road, rail, air, or sea) canhave di�erent types of sequences to form compoundedtransportation modes. For example, a supplier inFukushima, Japan, uses road (or rail) to ship partsto the Fukushima airport or harbor. The parts are

Figure 1. Problem model diagram.


Table 2. Combinations of transportation modes between Fukushima and Wuhan.

Combinations oftransportation modes

Cost($/unit)

Carbon emissions(kg/unit)

Road-air-road 14.88 1.7117

Road-air-rail 10.817 1.5951

Road-sea-road 1.929 0.4043

Road-sea-rail 1.336 0.18221

Rail-air-road 14.76 1.5527

Rail-air-rail 10.697 1.4361

Rail-sea-road 1.831 0.27445

Rail-sea-rail 1.238 0.05236

then shipped by plane or ship to the Wuhan airportor harbor in China and then transported by road (orrail) to a Wuhan plant for manufacturing into the �nalproduct.

When selecting compound transportation modes,transportation costs and carrying costs are primaryconsiderations. Long transportation distances raise thetransportation costs paid by corporations. Each type oftransportation combination has its own transportationquantity upper limit. The eight possible transportationcombinations, which are applied in this study, cover arange of transportation times, costs, and carbon emis-sions. Example parameters for the transportation com-binations from Fukushima (Japan) to Wuhan (China)are presented in Table 2. Generally, transportationthat requires a long time (e.g., maritime shipping)has reduced unit transportation cost and unit carbonemission. These eight transportation combinations willbe incorporated in the analyses in Section 4, whichentail calculating and converting the transportationdistances to obtain the transportation times. Eachcombination corresponds to the transportation time,cost, and carbon emission parameters of one speci�cgroup. The combination formation reduces the symbolcomplexity of the variables as described in the followingsections.

3. Mathematical model and approach

3.1. Symbol de�nitionsGiven that supply chain network, G = (N;A), iscomposed of numerous nodes and arcs, N representsthe nodes in the network: Nodes are divided intosuppliers S, plants F , and customers C; thus, N =S [ F [ C. The connection between two nodesis called an arc, and represents one shipping lanecandidate for product ow. Each shipping lane consistsof multiple transportation combinations. Let '(i; j)be the transportation combinations from node i tonode j. For example, '(i; j) = 1 indicates that i to

j uses transportation combination 1 to transportationcargo and = f'(i; j) : (i; j) 2 Ag. If the originalG(N;A) from the shipping line perspective is con-verted to the transportation combination perspective,then the supply chain network can be represented byG(N; ). Detailed parameter and variable de�nitionsare provided in the following:

Notations:

Indices:t The index of time periods, and

t = 0; 1; 2; 3; :::; T 0r The index of components, and

r = 1; 2; 3; :::; R0p The index of products, and p =

1; 2; 3; :::; P 0

Sets: The set of transportation combinationsS The set of suppliersF The set of facilitiesC The set of customersR The set of componentsP The set of productsT The set of time periods

Parameters:fcti The occurring cost when supplier i is

selected at time period tfctj Setup cost of manufacturing products

at plant j at time period tpctjp Unit manufacturing cost of product p

at plant j at time period ttct'(i;j)r Unit transporting cost of component

r from supplier i to plant j usingtransportation combination '(i; j) attime period t


tct'(j;k)p Unit transporting cost of productp from plant j to customer k usingtransportation combination '(j; k) attime period t

hctjp Unit holding cost of product p at plantj at time period t

brp Amount of component r required byone unit of product p

dtkp Amount of product p required bycustomer k at time period t

usti Supply capacity of supplier i at timeperiod t

uf tj Production capacity of plant j at timeperiod t

usf t'(i;j) Transportation capacity oftransportation combination '(i; j)from supply i to plant j at time periodt

ufct'(j;k) Transportation capacity oftransportation combination '(j; k)from plant j to customer k at timeperiod t

qjp Batch size of product p at plant j

t'(i;j) Transporting time from supplieri to plant j using transportationcombination '(i; j)

t'(j;k) Transporting time from plant j tocustomer k using transportationcombination '(j; k)

gjp Required production capacity to makeone unit of product p at plant j

�r Required transportation capacity todeliver one unit of component r

�p Required transportation capacity todeliver one unit of product p

hr Unit holding cost of component r perperiod during transportation

hp Unit holding cost of product p perperiod during transportation

etjp CO2 emissions of manufacturing oneunit of product p at plant j at timeperiod t

et'(i;j)r CO2 emissions of transporting one unitof component r from supplier i to plantj using transportation combination'(i; j) at time period t

et'(j;k)p CO2 emissions of transporting one unitof product p from plant j to customerk using transportation combination'(j; k) at time period t

Decision variables:Xtjp Batches of product p manufactured at

plant j at time period t

Xt;t+t'(i;j)'(i;j)r Transportation quantities of

component r using transportationcombination '(i; j) from supplier i attime period t to plant j at time periodt+ t'(i;j)

Xt;t+t'(j;k)'(j;k)r Transportation quantities of product

p using transportation combination'(j; k) from plant j at time period t tocustomer k at time period t+ t'(j;k)

Y ti = 1; If supplier i takes orders at time periodt; Y ti = 0, otherwise

Y tj = 1; If plant j operates at time period t;Y tj = 0, otherwise

Dependent variables:

Itjp Inventory of product p kept at plant jat time period t

3.2. Mathematical modelObjective function 1:

Minimize costXi2S

Xt2T

fctiYti +

Xj2F

Xt2T

fctjYtj

+Xj2F

Xp2P

Xt2T

pctjpqjpXtjp

+X

'(i;j)2

Xr2R

Xt2T :t+t'(i;j)�T 0

tct'(i;j)rXt;t+t'(i;j)'(i;j)r

+X

'(j;k)2

Xp2P

Xt2T :t+t'(j;k)�T 0

tct'(j;k)pXt;t+t'(j;k)jkp

+X

'(i;j)2

Xr2R


hrt'(i;j)Xt;t+t'(i;j)'(i;j)r

+X

'(j;k)2

Xp2P


hpt'(j;k)Xt;t+t'(j;k)'(j;k)p

+Xj2F

Xp2P

Xt2T

hctjpItjp:

(1)

Eq. (1) consists of ordering cost charged by sup-pliers, setup cost at plants, production cost at plants,transportation cost of components and products, hold-ing cost while transporting components and products,and holding cost at plants.


Objective function 2:

Minimize CO2 emissions:Xj2F

Xp2P

Xt2T

etjpqjpXtjp

+X

'(i;j)2

Xr2R


et'(i;j)rXt;t+t'(i;j)'(i;j)r

+X

'(j;k)2

Xp2P


et'(j;k)pXt;t+t'(j;k)'(j;k)p :

(2)

Eq. (2) represents CO2 emissions incurred by produc-tion at plants, transportation from suppliers to plants,and transportation from plants to customers.

Subject to:Xj2'(i;j)

Xt;t+t'(i;j)'(i;j)r � ustiY ti ; 8i 2 S; 8r 2 R;

for ft : t+ t'(i;j) � T 0g; (3)

(X

i2'(i;j):t�t'(i;j)�0

Xt�t'(i;j);t'(i;j)r )=brp = qjpXt

jp;

8j 2 F;8r 2 R; p 2 P; 8t = T; (4)

I0jp = 0; 8j 2 F; 8p 2 P; (5)

It�1jp + qjpXt

jp�X

k2'(j;k):t+t'(j;k)�T 0Xt;t+t'(j;k)'(j;k)p =Itjp;

8j 2 F;8p 2 P; 8t = f1; 2; 3; :::; T 0g; (6)Xp2P

gjpqjpXtjp � uf tjY tj ; 8j 2 F; 8t 2 T; (7)

Xj2'(j;k):t�t'(j;k)�0

Xt�t'(j;k);t'(j;k)p = dtkp;

8k 2 C; 8p 2 P;8t 2 T; (8)

where dtkp = 0, if t < mini2S;j2F ft'(i;j) + t'(j;k)g.

Xr2R

�rXt;t+t'(i;j)'(i;j)r � usf t'(i;j);

8'(i; j) 2 : t+ t'(i;j) � T 0; 8t 2 T; (9)

Xp2P

�pXt;t+t'(j;k)'(j;k)p � ufct'(j;k);

8'(j; k) 2 : t+ t'(j;k) � T 0; 8t 2 T; (10)

Xtjp 2 Integer; 8j 2 F;8p 2 P; 8t 2 T; (11)

Xt;t+t'(i;j)'(i;j)r � 0;8'(i; j) 2 : i 2 S; j 2 F; 8r 2 R;

8t 2 T : t+ t'(i;j) � T 0; (12)

Xt;t+t'(j;k)'(j;k)p � 0;

8'(j; k) 2 : j 2 F; k 2 C; 8p 2 P;8t 2 T : t+ t'(j;k) � T 0; (13)

Itjp � 0; 8j 2 F; 8p 2 P;8t 2 T; (14)

Y ti 2 f0; 1g ; 8i 2 S;8t 2 T; (15)

Y tj 2 f0; 1g ; 8j 2 F; 8t 2 T: (16)

Eq. (3) represents the quantities of transporting com-ponents to plants being less than or equal to thequantities provided by each supplier at each timeperiod. Eq. (4) represents the number of componentsordered from suppliers being equal to the number ofproducts manufactured by each plant at each timeperiod. Eq. (5) represents the inventory at plant jbeing zero at time period 0. Eq. (6) represents owconservation of each product at each plant at eachtime period. Eq. (7) represents production capacityat each plant at each time period. Eq. (8) representsthe quantities transported to each customer being equalto the demand of each customer at each time period.Since this research assumes that there is no backorderfor each customer, the initial demands of each customerare set to 0. Eq. (9) represents the quantities ofcomponents transported from suppliers to plants beingless than or equal to the capacities of each transporta-tion mode between suppliers and plants at each timeperiod. Eq. (10) represents the quantities of productstransported from plants to customers being less thanor equal to the capacities of each transportation modebetween plants and customers at each time period.Eq. (11) represents the batch size of each product ateach plant at each time period, and must be an integer.Eqs. (12) and (13) represent transporting quantitiesfrom suppliers to plants and from plants to customers,and the values are non-negative. Eq. (14) representsthe amount of inventory, and the value is non-negative.Eqs. (15) and (16) represent the operating status ofeach supplier and each plant, and the values are binaryvariables.


3.3. Normalized normal constraint methodThe solution to multiple-objective decision problemsrequire determining the optimal solution set, not sim-ply a single optimal solution. The Normalized NormalConstraint (NNC) method is a highly e�ective methodof multiple-objective decision optimization that can beused to produce evenly distributed Pareto solutions.This study applies evenly distributed Pareto-optimalfronts to provide managers with improved decisions.The NNC method proposed by Messac et al. [28] isused to calculate a multiple-objective model. Thismethod does not require the calculation of the ini-tial weight of each objective to produce an evenlydistributed Pareto-optimal front. Figure 2 illustratesthe multiple-objective Pareto-optimal front and utopialine. When using the optimized solutions method ofthe secularization techniques, both local and globalsolutions are typically produced, thereby forming non-convex Pareto and discontinuous Pareto solutions [29].However, the NNC calculation method also produceslocal and global solutions and exhibits non-convexand discontinuous Pareto solutions [28,30]. Therefore,this study adopts the Pareto �lter algorithm proposedby Messac et al. [28] to �lter non-optimal solutionson the Pareto curve and obtain the optimal globalPareto solutions. Because of space, constraints pleasereferences Messac et al. [28] and Martinez et al. [31] fordetailed discussions on Pareto solution procedures andPareto �lters.

The NNC method consists of seven steps [28]:

- Step 1: Two anchor points, �1� = (�11; �12) and�2� = (�21; �22), are calculated (see Figure 2). InFigure 2, Objective 1 refers to total cost whereasObjective 2 refers to CO2 emissions. �11 is theminimal total cost of the problem (P1) with theobjective function in Eq. (1) subject to Eqs. (3) to

Figure 2. Utopia line and Pareto e�ciency frontier curve.

(16); �12 is the corresponding CO2 emissions calcu-lated by the same solution. �22 is the minimal CO2emissions of the problem (P2) with the objectivefunction in Eq. (2) subject to Eqs. (3) to (16); �21 isthe corresponding total cost calculated by the samesolution.

- Step 2: A normalization based on (�1�; �2�) isperformed because of the di�erent units (NT dollarsand kg) of Objectives 1 and 2. After running thenormalization, � is calculated by using Eq. (17):

�=��1(x)��1(x1�)�1(x2�)��1(x1�) ;

�2(x)��2(x2�)�2(x1�)��2(x2�)

�; (17)

where the Euclidean distance between �1� = (0; 1)and the origin = (0, 0) is 1; similarly, the Euclideandistance between �2� = (1; 0) and the origin = (0,0) is 1.

- Step 3: The utopia line vector (N = �2� � �1�),which is the direction from �1� to �2�, is calculated.

- Step 4: A normalized increment m is calculated. Inthis study, m is 30.

- Step 5: Utopia line points, Xj , using Eq. (18) aregenerated:

Xj =�

1m� 1

� �1�; (1� 1m� 1

)� �2��;

for j= 1; 2; � � � ;m� 1: (18)

- Step 6: Each Pareto-point problem, which is theproblem (P2), is solved with the objective functionin Eq. (2) subject to Eqs. (3) to (16) and thecorresponding Eq. (19):

N(�2 �Xj)T � 0; (19)

�2 is a point within the feasible region of P2, andthe optimal solution of P2 is the point of ��2.

- Step 7: The real value (�) of each Pareto point,��2, is calculated by calculating the inverse of thenormalization in Eq. (20):

� =[�1(�1(x2�)� �1(x1�)) + �1(x1�); �2(�2(x1�)

� �2(x2�)) + �2(x2�)]T : (20)

4. Case study and numerical analysis

This section presents how the study substitutes datainto the mathematical programming model to examinethe network design issues in green supply chains. Pa-rameter value changes are used to observe the responsestatus of the entire supply chain. The solution processuses ILOG CPLEX 12.4 to conduct calculations (usingan Intel Core i5-2400 CPU with a 3.10 GHz centralprocessor, 8 GB of memory, and the Windows 7Professional Edition operating system).


4.1. Case studyThis study extends the case company background usedby Wang et al. [18] and obtains the supplier sources,current plant locations, and customer locations byreviewing references (Figure 3). Assuming that themain sources for components are South Korea, Japan,and Thailand and the assembly plants are distributedin several cities in Taiwan and China, the assemblyplants would provide products to local customers.

The case supply chain network comprises threesuppliers, four plants, and four customers. To simplifyanalysis, three products and 12 planning horizon pe-riods are used in this study. Relevant data, such asthe product carbon emission coe�cients produced bythe plants, are obtained from sustainable developmentreports on products similar to the case company prod-ucts. The carbon emission coe�cients produced by thetransportation tools are collected using SimaPro 7.3.software. Transportation distances are measured ac-cording to Google Maps. Detailed numerical de�nitionsfor the parameters are presented in Table 3. These dataare used to obtain the optimal component order quan-tity, production batch, product delivery quantity, andplant location for various transportation combinationsand periods. The data in this example are used to setthe demand for the �rst two periods at zero to ensurethat supply shortages do not occur. A set amount ofinitial product inventory can also be assumed to satisfyinitial demand.

Because the ILOG CPLEX 12.4 involves usinga branch-and-bound search method in the internalsettings during the integer solution process, excessivefactors and data in the integer-programming model canoverload the memory, resulting in lacking solutions.Therefore, a 1% tolerance deviation is set when search-ing for the optimal integer solutions. Cordeau et al. [32]asserted that, in practice, a deviation exceeding 1%

Figure 3. Supply chain network of the case company.

Figure 4. Pareto e�ciency frontier curve.

frequently occurred in company data sources (e.g., esti-mations of costs, demands, and production capability);thus, a 1% variation is within the allowable range.

The optimal total cost and carbon emissioncombinations in the Pareto-optimal front curve areshown in Figure 4. The two terminal points areNT$862,269,800 and 4,985,400 kg, and $1,398,400,000and 4,738,968 kg, respectively. The �gure shows thebalance between total cost and carbon dioxide emis-sions. From a marginal utility perspective (e.g., usingthe farthest left point as the benchmark), the supplychain network design combination corresponding toNT$941,860,000 and 4,750,100 kg is recommended tocorporations. Increasingly stringent restrictions on car-bon dioxide generate rapidly increasing cost; however,these e�ects, which are produced by various factors,are di�cult to observe. Thus, in the next section,sensitivity analysis of several main factors is shownto understand how alterations in a variety of factorsin uence the supply chain network, and this researchexamines corporate-response decisions.

4.2. Sensitivity analysis4.2.1. Change in plant production capabilityTo understand how changes in plant production ca-pability a�ect decisions, this study adjusts the upperproduction limit � according to three values (� = 1:25,1.5, and 2.0) to obtain three groups of Pareto-optimalfronts. These three Pareto-optimal fronts are comparedwith those obtained using the original � = 1. Figure 5shows that when production capability increases, costsdecrease, resulting in a shift of the entire curve towardthe initial point. This indicates that, at the same cost,increased production capacities generate fewer carbondioxide emissions. In a �xed carbon dioxide emissionsituation, high production capacity reduces the totalcost because increasing plant production capabilityreduces the required number of transports, therebyreducing transportation costs and concurrent carbondioxide emissions. Fewer transports reduce the overall


Table 3. Parameter data set.

Parameters DescriptionsDemand dtkp = uniform (1d; 1:2d), and d is demand ratio

Cost

fcti = uniform (0:9�; 1:1�), and � is the ordering costfctj = uniform (0:9�; 1:1�), and � is the setup costpctjp = product price �!, ! is a ratio � 1

hctjp= product cost� � = product price� ! � � = product cost� �;and � = ! � � is a ratio � 1

BOM brp The number of required components of products 1, 2, and 3: (1, 2), (1,2), and (1,2)

Consumed capacitygjp The consumed production capacity of products 1, 2, and 3 is uniform (4, 5)�r The consumed transportation capacity of components 1 and 2 is (2, 2)�p The consumed transportation capacity of products 1, 2, and 3 is (3, 3, 3)

Capacity

usti = uniform (0:8�; 1:2�), and � is a constantuf ti = uniform (0:8�; 1:4�)� U , and � production utilization; U is a constant

usf t'(i;j) = uniform (0:8�; 1:4�)�A'(i;j), � is the ow utilization; A'(i;j) is a constantufct'(j;k) = uniform (0:8�; 1:4�)�A'(i;j), and A'(j;k) is a constant

CO2 emissionsetjp = uniform (0:9e; 1:2e), and e is the CO2 emissions for producing one product p

et'(i;j)r

= uniform (0:9wr; 1:2wr), and '(i; j) is the CO2 emissions fortransporting one component r by usingtransportation mode '(i; j); wr is the weight of the component r

et'(j;k)p

= uniform (0:9wp; 1:2wp), and '(j; k) is the CO2 emissions fortransporting one product p by using transportation mode '(j; k); wp isthe weight of the product p

Figure 5. Pareto e�ciency frontier curves of di�erentproduction capacity ratios.

transportation time; consequently, increased produc-tion yields a reduction in carbon dioxide emissions andthereby causes less harm to the environment. Thisphenomenon is similar to that described by Wang etal. [18]. Reduction in plant production capacity signi-�es that customer product demand must be supportedby production from other plants or additional setup

of production lines, thereby raising transportationcosts and carbon dioxide emissions produced duringtransportation.

Further, Figure 5 shows that when the budgetis su�cient (greater than 1 billion), only productioncapabilities with � = 1:5 and 2.0 are bene�cial forimproving environmental protection, but carbon diox-ide emissions of both production capacities are notsigni�cantly di�erent. When the budget is limited(less than 0.85 billion), increasing production capacityto � = 2:0 does improve environmental protection.Therefore, when international laws or the governmentset carbon dioxide emission limitations and the budgetis limited, increasing the production capability is afavorable decision.

4.2.2. Change in the upper limit of transportationquantity

Di�erent transportation tools have di�erent trans-portation quantity limits. To understand how trans-portation quantity changes in uence decisions, thisstudy adjusts the production capability rate � and setsthree values as the upper limit of the transportationquantity rate (i.e., � = 1:25, 1.5, and 2.0) to obtainthree groups of Pareto-optimal fronts. These three


Figure 6. Pareto e�ciency frontier curves of di�erentupper bound ratios of transportation capacities.

Pareto-optimal fronts are compared with that obtainedusing the original � = 1. Figure 6 shows that, exceptfor the � = 2:0 curve, the other three curves are thesame in the high carbon emission stage. Furthermore,both carbon emissions and total cost decrease whentransportation quantity increases. The researcherslearnt that when transportation quantity was limited,the limits of corporate component or product trans-portation raised because variations in transportationcosts resulted in high carbon dioxide emissions. Thus,raising the transportation improves the exibility of theentire supply chain.

Figure 6 shows that when the budget is su�cient(greater than 1 billion NT dollars), increasing trans-portation quantity limits will be slightly bene�cial forimproving environmental protection. When the budgetis limited (less than 0.9 billion NT dollars), increasingtransportation quantity limits is not bene�cial forimproving environmental protection. Therefore, trans-portation quantity limits is not a sensitive parameter.

4.2.3. Changes in production batch sizeTo understand the in uence of the size of plant pro-duction batches, this study adjusts production batchsize ratio � to compare � = 1:5 and � = 2:0 withthe original � = 1. Figure 7 shows that when thecarbon dioxide limit is 490,000 kg, plants with thesmall production batch size reduce the total cost.Figure 7 also shows that when the production batchsize increases, total cost increases. However, totalcosts are not signi�cantly di�erent for the productionbatch sizes � = 1:5 and � = 2:0. The possiblereason may be that when customer demands are knownand �xed, plants must produce more products dueto large production batch sizes. Therefore, when the

Figure 7. Pareto e�ciency frontier curves of di�erentproduction batch size ratios.

production batch sizes increase, ordering component,transportation, carrying, and total costs also increase.

In practice, companies prefer the large productionbatch sizes to small ones, because large productionbatch sizes can shorten the setup time of machines andbe easily scheduled in the production lines. Further,surplus products can be stored for the next-period cus-tomer demands. However, the large production batchsizes will increase the transportation and carrying costsand carbon dioxide emissions. There is a trade-o�between production preference (large production batchsizes) and total cost (small production batch sizes).Therefore, companies should determine appropriateproduction batch sizes based on their product char-acteristics, cost, and environmental factors. This topicmerits further research.

5. Conclusion

This study proposed a green supply chain networkmodel that involved calculating multi-phase, multiple-objective integer programming models. The supplychain network model also incorporated carbon emis-sions, including those produced during the transporta-tion process. The model used the selection of trans-portation type to reduce carbon emissions during thetransportation process. This model can be used bycorporations when considering localized environmentalin uences or globalized supply chain network designs.

Section 3 introduced the mathematical modeldeveloped in this study. Section 4 provided examples,sensitivity analysis results, and a discussion of manage-ment implications. Figure 5 indicated that productioncapability increases were bene�cial for improving envi-ronmental conditions. However, additional costs wererequired to increase production capability. When car-bon dioxide emissions were high, increasing productioncapability only slightly reduced the total cost. The


Pareto curve trends can serve as a reference for decisionmakers when determining the bene�ts for companiesgenerated by increasing production capability.

Lowering the upper transportation quantity limitrequired plants to order the necessary product-assembly components from additional suppliers (in-creasing the number of suppliers), thereby raising theordering costs. Similarly, the number of times the plantset up production also increased, generating setupproduction costs. Ordering components and transport-ing manufacturing products became complex, causing uctuations in transportation costs and increasingtotal costs. Figure 6 can be used as a reference fordecision makers when determining whether increasingthe upper transportation quantity limit would bene�tthe company.

Total costs rose when the production batch sizesincreased, because this production process required theordering of additional components. Thus, each timecomponents were ordered represented an increase intransportation and carrying costs. When productionmanagers plan multi-phase production activities, themanufactured multi-phase products from each pro-duction batch are stored in inventory to ensure thatcustomer demand in the following period is satis�ed.A large production batch size from the plant signi�esthat numerous products are available for storing intoinventory and ful�lling multi-period customer demand.Reducing the number of production setups reducessetup costs. However, the transportation and carryingcosts produced by the components raised costs. Thereis a trade-o� between production batch size and totalcost. Therefore, determining appropriate productionbatch sizes remains a challenging research topic.

Although this study used the electronics industryas the core, numerous factors were excluded from con-sideration when exploring overall supply chain planningin the production and delivery model. These factorscan be considered in future studies:

1. This study considered transportation time, but notthe product shortage costs resulting from delayeddeliveries subsequent to insu�cient production ca-pability or transportation delays [3]. Therefore,future studies should discuss the in uence of thesefactors on supply chain production and delivery;

2. This study also did not consider uctuating cus-tomer product demands [33,34]. Thus, productdemand uncertainty should be added to the modelto conform to actual situations.

Acknowledgement

This research was partially supported by Chang GungMemorial Hospital under Grant BMRPE93.

References

1. Trucost, \Carbon emissions - measuring the risks"(2009).

2. Beamon, B.M. \Supply chain design and analysis:Models and methods", International Journal of Pro-duction Economics, 55(3), pp. 281-294 (1998).

3. Melnyk, S.A., Narasimhan, R. and DeCampos, H.A.\Supply chain design: Issues, challenges, frameworksand solutions", International Journal of ProductionResearch, 52(7), pp. 1887-1896 (2014).

4. Aliev, R.A., Fazlollahi, B., Guirimov, B.G. andAliev, R.R. \Fuzzy-genetic approach to aggregateproduction-distribution planning in supply chain man-agement", Information Sciences, 177(20), pp. 4241-4255 (2007).

5. Badri, H., Ghomi, S.M.T.F. and Hejazi, T.H. \Atwo-stage stochastic programming model for value-based supply chain network design", Scientia IranicaTransaction E, Industrial Engineering, 23(1), pp. 348-360 (2016).

6. Mahmoodirad, A. and Sanei, M. \Solving a multi-stage multi-product solid supply chain network designproblem by meta-heuristics", Scientia Iranica, Trans-action E, Industrial Engineering, 23(3), pp. 1428-1440(2016).

7. Melo, M.T., Nickel, S. and Saldanha-da-Gama, F.\Facility location and supply chain management - Areview", European Journal of Operational Research,196(2), pp. 401-412 (2009).

8. Rizk, N., Martel, A. and D'Amours, S. \Multi-itemdynamic production-distribution planning in processindustries with divergent �nishing stages", Computers& Operations Research, 33(12), pp. 3600-3623 (2006).

9. Nishi, T., Konishi, M. and Ago, M. \A distributeddecision making system for integrated optimization ofproduction scheduling and distribution for aluminumproduction line", Computers & Chemical Engineering,31(10), pp. 1205-1221 (2007).

10. Kanyalkar, A.P. and Adil, G.K. \An integrated aggre-gate and detailed planning in a multi-site productionenvironment using linear programming", InternationalJournal of Production Research, 43(20), pp. 4431-4454(2005).

11. Hugo, A. and Pistikopoulos, E.N. \Environmentallyconscious long-range planning and design of sup-ply chain networks", Journal of Cleaner Production,13(15), pp. 1471-1491 (2005).

12. Das, K. and Sengupta, S. \A hierarchical processindustry production-distribution planning model", In-ternational Journal of Production Economics, 117(2),pp. 402-419 (2009).

13. Sadjady, H. and Davoudpour, H. \Two-echelon, multi-commodity supply chain network design with modeselection, lead-times and inventory costs", Computers& Operations Research, 39(7), pp. 1345-1354 (2012).


14. Yang, C.C. \A DEA-based approach for evaluatingthe opportunity cost of environmental regulations",Asia-Paci�c Journal of Operational Research, 30(2),p. 1250049 (1-17) (2013).

15. Forouzanfar, F., Tavakkoli-Moghaddam, R., Bashiri,M. and Baboli, A. \A new bi-objective model fora closed-loop supply chain problem with inventoryand transportation times", Scientia Iranica, Transac-tion E, Industrial Engineering, 23(3), pp. 1441-1458(2016).

16. Ramezani, M., Kimiagari, A.M. and Karimi, B. \Inter-relating physical and �nancial ows in a bi-objectiveclosed-loop supply chain network problem with un-certainty", Scientia Iranica, Transaction E, IndustrialEngineering, 22(3), pp. 1278-1293 (2015).

17. Cruz, J.M. \Dynamics of supply chain networks withcorporate social responsibility through integrated en-vironmental decision-making", European Journal ofOperational Research, 184(3), pp. 1005-1031 (2008).

18. Wang, F., Lai, X.F. and Shi, N. \A multi-objectiveoptimization for green supply chain network design",Decision Support Systems, 51(2), pp. 262-269 (2011).

19. Ferretti, I., Zanoni, S., Zavanella, L. and Diana, A.\Greening the aluminium supply chain", InternationalJournal of Production Economics, 108(1-2), pp. 236-245 (2007).

20. Cholette, S. and Venkat, K. \The energy and carbonintensity of wine distribution: A study of logisticaloptions for delivering wine to consumers", Journal ofCleaner Production, 17(16), pp. 1401-1413 (2009).

21. Paksoy, T. \Optimizing a supply chain network withemission trading factor", Scienti�c Research and Es-says, 5(17), pp. 2535-2546 (2010).

22. Chiu, C.Y., Lin, Y. and Yang, M.F. \Applying fuzzymultiobjective integrated logistics model to green sup-ply chain problems", Journal of Applied Mathematics,Article ID 767095, pp. 1-12 (2014).

23. Jamshidi, R., Fatemi Ghomi, S.M.T. and Karimi, B.\Multi-objective green supply chain optimization witha new hybrid memetic algorithm using the Taguchimethod", Scientia Iranica, Transaction E, IndustrialEngineering, 19(6), pp. 1876-1886 (2012).

24. Al-e-hashem, S.M.J.M., Baboli, A. and Sazvar, Z. \Astochastic aggregate production planning model in agreen supply chain: Considering exible lead times,nonlinear purchase and shortage cost functions", Eu-ropean Journal of Operational Research, 230(1), pp.26-41 (2013).

25. Fahimnia, B., Sarkis, J., Boland, J., Reisi, M. and Goh,M. \Policy insights from a green supply chain opti-misation model", International Journal of ProductionResearch, 53(21), pp. 6522-6533 (2015).

26. Coskun, S., Ozgur, L., Polat, O. and Gungor, A. \Amodel proposal for green supply chain network designbased on consumer segmentation", Journal of CleanerProduction, 110, pp. 149-157 (2016).

27. Entezaminia, A., Heydari, M. and Rahmani, D. \Amulti-objective model for multi-product multi-site ag-gregate production planning in a green supply chain:Considering collection and recycling centers", Journalof Manufacturing Systems, 40, pp. 63-75 (2016).

28. Messac, A., Ismail-Yahaya, A. and Mattson, C.A. \Thenormalized normal constraint method for generatingthe Pareto frontier", Structural and MultidisciplinaryOptimization, 25(2), pp. 86-98 (2003).

29. Logist, F., Houska, B., Diehl, M. and Impe, J.V.\Fast Pareto set generation for nonlinear optimalcontrol problems with multiple objectives", Structuraland Multidisciplinary Optimization, 42(4), pp. 591-603(2010).

30. Das, I. and Dennis, J.E. \Normal-boundary intersec-tion: A new method for generating the Pareto sur-face in nonlinear multicriteria optimization problems",SIAM Journal on Optimization, 8(3), pp. 631-657(1998).

31. Martinez, M., Sanchis, J. and Blasco, X. \Global andwell-distributed Pareto frontier by modi�ed normal-ized normal constraint methods for bicriterion prob-lems", Structural and Multidisciplinary Optimization,34(3), pp. 197-209 (2007).

32. Cordeau, J.F., Pasin, F. and Solomon, M.M. \Anintegrated model for logistics network design", Annalsof Operations Research, 144(1), pp. 59-82 (2006).

33. Rangel, D.A., Oliveira, T.K.d. and Leite, M.S.A. \Sup-ply chain risk classi�cation: Discussion and proposal",International Journal of Production Research, 53(22),pp. 6868-6887 (2015).

34. Wakolbinger, T. and Cruz, J.M. \Supply chain disrup-tion risk management through strategic informationacquisition and sharing and risk-sharing contracts",International Journal of Production Research, 49(13),pp. 4063-4084 (2011).

35. Pyke, D.F. and Cohen, M.A. \Performance character-istics of stochastic integrated production-distributionsystems", European Journal of Operational Research,68(1), pp. 23-48 (1993).

36. Melkote, S. and Daskin, M.S. \Capacitated facilitylocation/network design problems", European Journalof Operational Research, 129(3), pp. 481-495 (2001).

37. Eksioglu, S.D., Romeijn, H.E. and Pardalos, P.M.\Cross-facility management of production and trans-portation planning problem", Computers & OperationsResearch, 33(11), pp. 3231-3251 (2006).

38. Farahani, R.Z. and Elahipanah, M. \A genetic algo-rithm to optimize the total cost and service level forjust-in-time distribution in a supply chain", Interna-tional Journal of Production Economics, 111(2), pp.229-243 (2008).


39. Selim, H., Am, C. and Ozkarahan, I. \Collaborativeproduction-distribution planning in supply chain: Afuzzy goal programming approach", TransportationResearch Part E-Logistics and Transportation Review,44(3), pp. 396-419 (2008).

40. Liang, T.-F. \Fuzzy multi-objective production/dist-ribution planning decisions with multi-product andmulti-time period in a supply chain", Computers &Industrial Engineering, 55(3), pp. 676-694 (2008).

41. Al-e-hashem, S.M.J.M., Malekly, H. and Aryanezhad,M.B. \A multi-objective robust optimization model formulti-product multi-site aggregate production plan-ning in a supply chain under uncertainty", Interna-tional Journal of Production Economics, 134(1), pp.28-42 (2011).

42. Rezaei, J. and Davoodi, M. \Multi-objective modelsfor lot-sizing with supplier selection", InternationalJournal of Production Economics, 130(1), pp. 77-86(2011).

43. Liu, S.S. and Papageorgiou, L.G. \Multiobjective opti-misation of production, distribution and capacity plan-ning of global supply chains in the process industry",Omega-International Journal of Management Science,41(2), pp. 369-382 (2013).

Biographies

Dah-Chuan Gong is a Professor in the Departmentof Industrial and Business Management at Chang GungUniversity, Taiwan, ROC. He obtained a PhD degreefrom the School of Industrial and Systems Engineering,Georgia Institute of Technology, USA. His researcharea focuses on global logistics management, sustain-able supply chain management, production systemdesign, and operations research applications.

Ping-Shun Chen is an Associate Professor in theDepartment of Industrial and Systems Engineeringat Chung Yuan Christian University, Taiwan, ROC.He obtained a PhD degree from the Department ofIndustrial and Systems Engineering, Texas A&M Uni-versity, USA. His research area focuses on network pro-gramming or applications, supply chain management,healthcare applications, and system simulation.

Tzu-Yang Lu is a master student in the Departmentof Industrial and Systems Engineering at Chung YuanChristian University, Taiwan, ROC. His research areafocuses on analyses of the supply chain network design.

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