research article applying fuzzy multiobjective integrated...

Research ArticleApplying Fuzzy Multiobjective Integrated Logistics Model toGreen Supply Chain Problems

Chui-Yu Chiu,1 Yi Lin,2 and Ming-Feng Yang3

1 Department of Industrial Engineering and Management, National Taipei University of Technology, No. 1, Section 3,Chung-Hsiao East Road, Taipei 10643, Taiwan

2 College of Management, National Taipei University of Technology, No. 1, Section 3, Chung-Hsiao East Road, Taipei 10643, Taiwan3Department of Transportation Science, National Taiwan Ocean University, Keelung City 202, Taiwan

Correspondence should be addressed to Yi Lin; [email protected]

Received 19 January 2014; Revised 12 June 2014; Accepted 13 June 2014; Published 7 July 2014

Academic Editor: Ricardo Perera

Copyright © 2014 Chui-Yu Chiu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The aim of this paper is attempting to explore the optimal way of supply chain management within the domain of environmentalresponsibility and concerns. The background of this research involves the issue of green supply chain management (GSCM) andthe concept of the multiobjective integrated logistics model. More specifically, in this paper, we suggest the fuzzy multiobjectiveintegrated logistics model with the transportation cost and demand fuzziness to solve green supply chain problems in the uncertainenvironment which is illustrated via the detailed numerical example. Results and the sensitivity analysis of the numerical exampleindicate that when the governmental subsidy value increased the profits of the reverse chain also increased.The finding shows thatthe governmental subsidy policy could remain of significant influence for used-product reverse logistics chain.

1. Introduction

In today’s highly competitive global market, preferableenvironmental concerns and reserved considerations areacknowledged as having high potential to impact the benefitsof the supply chain management. Both academicians andpractitioners tend to find an optimal way to keep businesscompetition with more environmental concerns. Hence, themanufacturers have to consider carefully many aspects thatgovern their performance in order to ensure end user satisfac-tion [1]. In recent years considerable concern has been arisingover the issues of environmental pollution accompanyingindustrial development in the operational process of thesupply chain management research. Environment protectionis becoming a vital issue for enterprises, government, andnonprofit organizations because of stronger public awareness.Indeed, the green supply chain management has emerged asan approach to balance these competitive requirements [2].

This paper is an attempt to fill the gap in the existing liter-ature of GSCM,much of which focuses on themanufacturingchain, reverse logistics chain, chain members, cash flow, andso forth. However, major issues of uncertainty and real-world

applications have not been many researches attentions. Inview of this gap, we consider the fuzzy demand and trans-portation cost more closely in the real-world situation.

2. Literature ReviewIn reality, the environment of global market is complicatedand uncertain; therefore, some researchers have been devot-ing themselves to research the supply chain managementwith the aspect of uncertainty. Petrovic et al. [3] appliedfuzzy set to handle uncertain demands and external rawmaterial problems and to deal with linguistic expressions anduncertain issues. Giannoccaro et al. [4] also proposed fuzzysets theory to the uncertainties associated with both marketdemand and inventory costs. In this paper, center of gravityis proposed to convert the fuzzy number into a crisp number.

As a result of increasing challenges in highly competitiveglobal supply chain environment, both academicians andpractitioners have increasing interests of finding the optimalway to remain competitive, andmanufacturers have also beenseeking to deliver to their customers high-quality products inthe right time at the right price [1]. Drzymalski and Odrey [5]

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014, Article ID 767095, 12 pageshttp://dx.doi.org/10.1155/2014/767095

2 Journal of Applied Mathematics

proposed that each entity within a supply chain is also dif-ferent in its constraints, operations, and objectives, resultingin varying performance measures within each organization.Hence, supply chain modeling has been becoming crucialas companies face more complicated and global interactionsand increased customer expectations. When an item movesthrough more than one step before reaching the final cus-tomer, the terms “multilevel” or “multiechelon” productionand distribution supply chain are also synonymous with suchsupply chains [6–8]. Initial multiechelon inventory theorywas introduced by Clark and Scarf [9] as a way of proving theoptimality of a base stock policy for the pure serial inventorysystem and developed an efficient decomposing method tocompute the optimal base stock ordering policy. In addi-tion, some researchers considered a strategic supply chaindesign problem with three echelons, multiple commodities,and technology selection [10]. And then, Disney et al. [11]proposed the research on a coordination scheme in a two-echelon supply chain which involves sharing details of leadtimes, replenishment rules, and demand patterns and tuningthe replenishment rules to exploit the supply chain’s coststructure. Yazlali and Erhun [12] noted a single-product dual-supply problemunder a periodically reviewed, finite planninghorizon. As we mentioned in the earlier section, with thepromotion of environmental consciousness in recent years,the logistics and supply chain managers have to balanceefforts to reduce costs and innovate while maintaining goodenvironmental (ecological) performance [13].The enterprisesalso have to take more applicable measures to improvereverse logistics. Indeed, the green supply chainmanagement(GSCM) has appeared as an approach to balance thesecompetitive requirements [2].

Recently, greening the supply chain has become the vitalissue. Many organizations, universities, and governmentsheld conferences of supply chain management with envi-ronmental thinking. The purpose of these conferences wasto demonstrate and exchange the green technology, greenknowledge, and green research. It means that the field ofgreen supply chain management has been becoming moreand more important in both academic research and practicein the real market [14]. Also, there have been a number ofstudies that have developed and implemented how to greenthe supply chain. For example, Hsu et al. [15] applied theDecision-Making Trial and Evaluation Laboratory (DEMA-TEL) approach to select the green suppliers in green supplychain management. Pishvaee et al. [16] created the model tominimize the environmental impacts and costs in the greensupply chain. And then, Trappey et al. [17] designed thegreen production planning and discussed how to minimizea product’s carbon footprint.

However, due to the imprecision of the informationrelated to parameters, the deterministic models are inappro-priate for obtaining an effective solution for supply chainimplications. In uncertainty, the method to carry out thisstudy is applying the fuzzy set theory, which provides away to obtain feasible answers to overcome the naturaldifficulties. There have been a number of studies that haveinvestigated the implications of the fuzzy set theory. The

fuzzy decision-making concept, introduced by Bellman andZadeh [18] as a way of handling imprecise data, proposed themost suitable fuzzy decision analysis procedure in the fuzzyenvironment. Afterwards, Zimmermann [19] combined thefuzzy sets theory, the traditional linear programming, andthe fuzzy decision-making and linear membership functionas the modified method and it became a new academicdirection.

In fuzzymultiobjective programming aspect, the paper byZimmermann [20] provided the fuzzy goals of the decision-maker with the fuzzy decisions. Bellman and Zadeh [18]noted in their research that the linear membership functionsand the fuzzy decisions can be adopted to convert theproblem to be solved into an ordinary single-goal math-ematical programming (Max 𝐿) problem. Then, Li et al.[21] and Kumar et al. [22] developed a fuzzy mixed integergoal programming approach for supplier evaluation andselection model. Furthermore, Kumar et al. [23] and Amidet al. [24] extended their research and developed a fuzzymultiobjective integer programming model to deal withthe different weights in various criteria. Numerous studiesnoted that the fuzzy multiobjective programming decisionmodels remained consistently under different situations [25–28].

3. Model Formulation

The purpose of this section is to establish a mathematicalmodel. In this work, we modified the integrated logisticsmodel which is indicated by Sheu et al. [29]. We use thelinearmultiobjective programmingmodel into the integratedlogistics operational problems of green supply chainmanage-ment.The objective of our proposedmodel is tomaximize thetotal profit function with respect to general manufacturingchain and the reverse chain. Also, we consider the fuzzydemand and transportation cost and adopt the triangularfuzzy number to represent these variables [29].

3.1. Assumptions. The assumptions of this research are asfollows.

(1) Only single product is considered in the proposedmodel.

(2) The time-varying quantity of product demands fromend customers in any given time interval is given.

(3) Shortages are not allowed.

(4) There is a given return ratio, referring to the pro-portion of the quantity of used products returnedfrom end customers and through the reverse logisticschain.

(5) The time horizon is infinite.

(6) Facility capacities associated with chain members ofthe proposed integrated logistics system are known.

(7) The lead time is known in both the general and thereverse supply chains.

Journal of Applied Mathematics 3

Raw material

WholesalersManufacturers

End customers

Retailers

Collecting pointsRecycling plantsDisassembly plantsFinal disposal

Secondary material market

RMF

Raw materials Products

Products

Products

Products

Used products

Used products

Used products

Used products

Used products

Revenue

Revenue

Revenue

RevenueRevenueRevenueRevenue

RevenueRevenueRevenue

RevenueRevenue

Revenue

Revenue

Reusable materials

Reusable raw

materials

Wastes

Recycling fee

Subsidy

Physical flows Manufacturing chainMoney flows Reverse chain

Products

suppliers (m1)

(m2) (m3) (m4)

(m5)

(r1)(r2)(r3)

(r4)

(r5)

Figure 1: Conceptual framework for integrated logistics control across a green supply chain.

(8) Pollution such as heavy metal pollution, toxic pol-lution, and water pollution is not considered in thisgreen supply chain.

Amathematicalmodel was developed to seek equilibriumsolutions with the target of maximizing the systematic netprofit which aggregated from the chain-based net profitsassociated with the respect of the manufacturing supplychain and the reverse logistics chain. Figure 1 illustrates theconceptual framework for integrated logistics control acrossa green supply chain.

As we can see in Figure 1, there are two groups in thegreen supply chain system: (1) manufacturing supply chainand (2) used-product reverse supply chain. In addition, thetypical 5-layermanufacturing supply chain is proposed; theselayers are given as follows: raw material suppliers (𝑚1 forshort), manufacturers (𝑚2 for short), wholesalers (𝑚3 forshort), retailers (𝑚4 for short), and end customers (𝑚5

for short). Also, the typical 5-layer used-product reversesupply chain is proposed as well with its layers given asfollows: collecting points (𝑟1 for short), recycling plants(𝑟2 for short), disassembly plants (𝑟3 for short), secondarymaterial market (𝑟4 for short), and final disposal (𝑟5 forshort).Themathematical formulation of our proposedmodelis indicated below. All notations of the proposed model arelisted in the appendix.

3.2. Manufacturing Chain. According to the aforementionedassumptions, objective optimization models are formulatedto seek the maximum net profit of the general supply chainand the reverse supply chain.

MP and RP are measured by subtracting the correspond-ing aggregate costs from the respective aggregate revenuesand costs, as expressed, respectively, in (1) and (2) as follows:

Max MP

= MTR −MC = MTR

− (MPC +MMC +MIC +MTC +MRC +MLC) .

(1)

As in (1), the total cost of manufacturing chain consists ofsix parts: raw material procurement, manufacturing, inven-tory, transportation, recycling fees paid to the EPA, and laborcost.

3.3. Reverse Chain. Consider the following

Max RP = RTR − RC = (RR + RS)

− (RTCC + RTTC + RIC + RTC + RFC + RLC) .

(2)

Similarly, in (2), the total cost of the reverse chain iscomposed of six parts: the cost of collecting used prod-ucts, transitional treatment, inventory, transportation, finaldisposal, and labor cost. Besides, there are two sources ofrevenue in the reverse chain: the general revenue and thesubsidies from EPA.

From the proposed integrating logistics system archi-tecture as shown in Figure 1, the objective functions arecomposed of (1) manufacturing chain-based net profit (MP)


maximization and (2) reverse chain-based net profit (RP)maximization. And our target is to maximize the totalrevenue in the supply chain system as shown below:

Max Total Revenue = MP + RP = (MTR −MC)

+ (RTR − RC) .

(3)

3.4. Revenues. MTR = Profit oriented from the raw materialflows + Profit oriented from the physical flows of the man-ufactured product in any given distribution channel of themanufacturing chain:

∑

∀𝑡

{

{

{

[ ∑

∀𝑚1

∑

∀𝑚2

𝑅𝑚1,𝑚2 (𝑡) × 𝑄

𝑚1,𝑚2 (𝑡)]

+[

[

4

∑

𝑖=2

5

∑

𝑖+1

∑

∀𝑚𝑖

∑

∀𝑚𝑗

𝑅𝑚𝑖,𝑚+1 (𝑡) × 𝑄

𝑚𝑖,𝑚+1 (𝑡)]

]

}

}

}

.

(4)

RR = Refund obtained by end customer for returning theused product + Revenue associated with the used-productcollection for selling the collected unprocessed used productto other reverse chains’ members + Revenue from sellingthe processed used product to another member in the samereverse chain + Revenue of the secondary material marketfor selling the processed used raw materials to the layer ofmanufacturing of the given manufacturing chain:

∑

∀𝑡

{

{

{

[

[

3

∑

𝑗=1

∑

∀𝑚5

∑

∀𝑟𝑗

𝑅𝑚5,𝑟𝑗 (𝑡) × 𝑄

𝑚5,𝑟𝑗 (𝑡)]

]

+ [

[

3

∑

𝑗=2

∑

∀𝑟1

∑

∀𝑟𝑗

𝑅𝑟1,𝑟𝑗 (𝑡) × 𝑄

𝑟1,𝑟𝑗 (𝑡)]

]

+ [

[

3

∑

𝑗=2

∑

∀𝑟𝑗

∑

∀𝑟𝑗+1

𝑅𝑟𝑗,𝑟𝑗+1 (𝑡) × 𝑄

𝑟𝑗,𝑟𝑗+1 (𝑡)]

]

+ [∑

∀𝑟4

∑

∀𝑚2

𝑅𝑟4,𝑚2 (𝑡) × 𝑄

𝑟4,𝑚2 (𝑡)]

}

}

}

.

(5)

RS = Subsidies associated with the reverse chains that areoriented from the reverse flows of the returned used productstransported to the layer of disassembly plants for governmentsubsidies:

∑

∀𝑡

{

2

∑

𝑖=1

∑

∀𝑟𝑖

∑

∀𝑟3

EPO × 𝑄𝑟𝑖,𝑟3 (𝑡)} . (6)

As wementioned in the earlier section, the revenues frommanufacturing chain were composed of raw material andphysical flows. And the revenues from the reverse chain wereconstituted of the regular returned used-product flows andsubsidies.

3.5. Costs of Manufacturing Chain. The costs of manufac-turing chain are composed of procurement, manufacturing,inventory, transportation, recycle, and labor cost. In this part,the detailed discussions ofmanufacturing chain are presentedas follows.

MPC = Initialized cost of raw materials + Procurementcost oriented from raw material suppliers and secondarymaterial market +Manufactured-product procurement costsin any distribution channels of manufacturing chain:

∑

∀𝑡

{

{

{

[∑

∀𝑚1

𝐶𝑅(𝑡) × 𝑄

𝑅(𝑡)]

+ [ ∑

∀𝑚1

∑

∀𝑚2

𝐶𝑃

𝑚1,𝑚2(𝑡) × 𝑄

𝑚1,𝑚2 (𝑡)

+∑

∀𝑟4

∑

∀𝑚2

𝐶𝑃

𝑟4,𝑚2(𝑡) × 𝑄

𝑟4,𝑚2 (𝑡)]

+[

[

3

∑

𝑖=2

4

∑

𝑖+1

∑

∀𝑚𝑖

∑

∀𝑚𝑗

𝐶𝑃

𝑚𝑖,𝑚𝑖+1(𝑡) × 𝑄

𝑚𝑖,𝑚𝑖+1 (𝑡)]

]

}

}

}

.

(7)

MMC = Manufacturing cost of all manufactured prod-ucts:

∑

∀𝑡

{∑

∀𝑚2

𝐶𝑀

(𝑡) × 𝑄𝑀

(𝑡)} . (8)

MIC = Inventory cost of raw materials oriented fromraw material suppliers and manufactures + Inventory cost ofproducts in any chain member of the manufacturing chain:

∑

∀𝑡

{[

2

∑

𝑖=1

∑

∀𝑚𝑖

𝐶IR𝑚𝑖

(𝑡) × 𝑄IR𝑚𝑖

(𝑡)]+[

4

∑

𝑖=2

∑

∀𝑚𝑖

𝐶𝐼

𝑚𝑖(𝑡) × 𝑄

𝐼

𝑚𝑖(𝑡)]} .

(9)

MTC ≅ Transportation cost of raw materials transportedfrom suppliers to manufactures + Transportation cost ofproducts transported in any chain member of the manufac-turing chain:

∑

∀𝑡

{

{

{

[ ∑

∀𝑚1

∑

∀𝑚2

𝐶𝑇𝑚1,𝑚2 (𝑡) × 𝑄

𝑚1,𝑚2 (𝑡)]

+[

[

4

∑

𝑖=2

5

∑

𝑖+1

∑

∀𝑚𝑖

∑

∀𝑚𝑗

𝐶𝑇𝑚𝑖,𝑚𝑖+1 (𝑡) × 𝑄

𝑚𝑖,𝑚𝑖+1 (𝑡)]

]

}

}

}

.

(10)

MRC = Recycling fees of the products:

∑

∀𝑡

∑

∀𝑚2

𝐹 × 𝑄𝑀

(𝑡) . (11)

MLC = Labor cost of any member in the manufacturingchain:

∑

∀𝑡

{

4

∑

𝑖=1

∑

∀𝑚𝑖

𝐶𝐿

𝑚𝑖× 𝑄𝐿

𝑚𝑖(𝑡)} . (12)


3.6. Costs of Reverse Chain. The costs of the reverse chainare composed of collected returned used products, transi-tional treatment procedures, inventory, transportation, finaldisposal, and labor cost. Andwewill discuss the reverse chainin this section.

RTCC =The amount of used products collected from theend customer to the members of the reverse chain:

∑

∀𝑡

{

{

{

3

∑

𝑗=1

∑

∀𝑚5

∑

∀𝑟𝑗

𝐶𝐶

𝑚5,𝑟𝑗(𝑡) × 𝑄

𝑚5,𝑟𝑗 (𝑡)

}

}

}

. (13)

RTTC = The transitional treatment procedures executedpotentially in all the reverse chain layers, except the finaldisposal:

∑

∀𝑡

{

{

{

4

∑

𝑗=1

∑

∀𝑟𝑗

𝐶TT𝑟𝑗

(𝑡) × 𝑄TT𝑟𝑗

(𝑡)

}

}

}

. (14)

RIC = The inventory cost of unprocessed used product+ Inventory cost of processed used product + Inventory costof processed used product that may be stored in disassemblyplant which is for final disposal and selling to the secondarymarket:

∑

∀𝑡

{

{

{

[

[

4

∑

𝑗=1

∑

∀𝑟𝑗

𝐶IT𝑟𝑗

(𝑡) × 𝑄IT𝑟𝑗

(𝑡)]

]

+ [

[

4

∑

𝑗=1,𝑖 = 3

∑

∀𝑟𝑗

𝐶IT𝑟𝑗

(𝑡) × 𝐶IT𝑟𝑗

(𝑡)]

]

+ ∑

𝑟3

[𝐶𝐼

𝑟3,𝑟4(𝑡) × 𝑄

𝐼

𝑟3,𝑟4(𝑡) + 𝐶

𝐼

𝑟3,𝑟5(𝑡) × 𝑄

𝐼

𝑟3,𝑟5(𝑡)]

}

}

}

.

(15)

RTC ≅ The summation of transporting costs of anydistribution channels of the reverse chain, excluding thecollection costs that are oriented from the reverse flowsassociated with end customers:

∑

∀𝑡

{

{

{

[

[

3

∑

𝑗=2

∑

𝑟1

∑

∀𝑟𝑗

𝐶𝑇𝑟1,𝑟𝑗 (𝑡) × 𝑄


]

+ [

3

∑

𝑖=2

∑

𝑟𝑖

∑

∀𝑟𝑖+1

𝐶𝑇𝑟𝑖,𝑟𝑖+1 (𝑡) × 𝑄

𝑟𝑖,𝑟𝑖+1 (𝑡)]

+ [∑

∀𝑟3

∑

∀𝑟5

𝐶𝑇𝑟3,𝑟5 (𝑡) × 𝑄

𝑟3,𝑟5 (𝑡)]

+ [∑

∀𝑟4

∑

∀𝑚2

𝐶𝑇𝑟4,𝑚2 (𝑡) × 𝑄

𝑟4,𝑚2 (𝑡)]

}

}

}

.

(16)

RFC = Total amount of used products disposed in thelayer of final disposal:

∑

∀𝑡

{∑

∀𝑟5

𝐶𝐹(𝑡) × 𝑄

𝐹(𝑡)} . (17)

RLC = Labor cost of any member in the reverse chain:

∑

∀𝑡

{

{

{

5

∑

𝑟=1

∑

∀𝑟𝑗

𝐶𝐿

𝑟𝑗× 𝑄𝐿

𝑟𝑗(𝑡)

}

}

}

. (18)

3.7. Constraints. In this part, the detailed discussions ofthree constraints such as inventory constraints, demandconstraints, and return resource constraints are presented asfollows.

(i) Inventory Constraints. In order to reach the reality, we setsafety stock for every member in the two chains.

(a) For raw material suppliers,

𝑆𝑆IR𝑚1

≤ 𝑄IR𝑚1

(𝑡) = 𝑄IR𝑚1

(𝑡 − 1) + 𝑄𝑅(𝑡)

− ∑

∀𝑚2

𝑄𝑚1,𝑚2 (𝑡) ≤ 𝑆

IR𝑚1

∀ (𝑚1, 𝑡) .(19)

(b) For product manufacturers,

(1) for raw materials,

𝑆𝑆IR𝑚2

≤ 𝑄IR𝑚2

(𝑡) = 𝑄IR𝑚2

(𝑡 − 1)

+ [∑

∀𝑚1

𝑄𝑚1,𝑚2 (𝑡) + ∑

∀𝑟4

𝑄𝑟4,𝑚2 (𝑡)]

− 𝛾𝑟/𝑚

𝑚2× 𝑄𝑀

(𝑡) ≤ 𝑆IR𝑚2

∀ (𝑚2, 𝑡) ,

(20)

(2) for products,

𝑆𝑆𝐼

𝑚2≤ 𝑄𝐼

𝑚2(𝑡) = 𝑄

𝐼

𝑚2(𝑡 − 1) + 𝑄

𝑀(𝑡)

−

5

∑

𝑗=3

∑

∀𝑚𝑗

𝑄𝑚2,𝑚𝑗 (𝑡) ≤ 𝑆

𝐼

𝑚2∀ (𝑚2, 𝑡) .

(21)

(c) For wholesalers and retailers,

𝑆𝑆𝐼

𝑚𝑗≤ 𝑄𝐼

𝑚𝑗(𝑡) = 𝑄

𝐼

𝑚𝑗(𝑡 − 1)

+ [

𝑗−1

∑

𝑖=2

∑

∀𝑚𝑖

𝑄𝑚𝑖,𝑚𝑗 (𝑡)] − [

[

5

∑

𝑛=𝑗+1

∑

∀𝑚𝑛

𝑄𝑚𝑗,𝑚𝑛 (𝑡)

]

]

≤ 𝑆𝐼

𝑚𝑗∀ (𝑚𝑗, 𝑡) , 𝑗 = 3 or 4.

(22)

(d) For collecting points,

𝑆𝑆IT𝑟1

≤ 𝑄IT𝑟1

(𝑡) = 𝑄IT𝑟1

(𝑡 − 1) + [∑

∀𝑚5

𝑄𝑚5,𝑟1 (𝑡)]

− 𝑄TT𝑟1

(𝑡) ≤ 𝑆IT𝑟1

∀ (𝑟1, 𝑡) ,

𝑆𝑆IT𝑟1

≤ 𝑄IT𝑟1


(𝑡 − 1) + 𝑄TT𝑟1

(𝑡)

−

3

∑

𝑗=2

∑

∀𝑟𝑗

𝑄𝑟1,𝑟𝑗 (𝑡) ≤ 𝑆

IT𝑟1

∀ (𝑟1, 𝑡) .

(23)


(e) For recycle plants,

𝑆𝑆IT𝑟2

≤ 𝑄IT𝑟2


(𝑡 − 1)

+ [∑

∀𝑚5

𝑄𝑚5,𝑟2 (𝑡) + ∑

∀𝑟1

𝑄𝑟1,𝑟2 (𝑡)]

− 𝑄TT𝑟2


∀ (𝑟2, 𝑡) ,

𝑆𝑆IT𝑟2

≤ 𝑄IT𝑟2


(𝑡 − 1) + 𝑄TT𝑟2

(𝑡)

− ∑

∀𝑟3

𝑄𝑟2,𝑟3 (𝑡) ≤ 𝑆

IT𝑟2

∀ (𝑟2, 𝑡) .

(24)

(f) For disassembly plants,

𝑆𝑆IT𝑟3

≤ 𝑄IT𝑟3


(𝑡 − 1)

+ [∑

∀𝑚5

𝑄𝑚5,𝑟3 (𝑡) +

2

∑

𝑖=1

∑

∀𝑟𝑖

𝑄𝑟𝑖,𝑟3 (𝑡)]

− 𝑄TT𝑟3


∀ (𝑟3, 𝑡) ,

𝑆𝑆IT𝑟3,𝑟4

≤ 𝑄𝐼

𝑟3,𝑟4(𝑡) = 𝑄

𝐼

𝑟3,𝑟4(𝑡 − 1) + 𝛾

𝑟3,𝑟4

× 𝑄TT𝑟3

(𝑡) − ∑

∀𝑟4

𝑄𝑟3,𝑟4 (𝑡) ≤ 𝑆

𝐼

𝑟3,𝑟4∀ (𝑟3, 𝑡) ,

𝑆𝑆𝐼

𝑟3,𝑟5≤ 𝑄𝐼

𝑟3,𝑟5(𝑡) = 𝑄

𝐼

𝑟3,𝑟5(𝑡 − 1) + 𝛾

𝑟3,𝑟5

× 𝑄TT𝑟3

(𝑡) − ∑

∀𝑟5

𝑄𝑟3,𝑟5 (𝑡) ≤ 𝑆

𝐼

𝑟3,𝑟5∀ (𝑟3, 𝑡) .

(25)

(g) For secondary material markets,

𝑆𝑆IT𝑟4

≤ 𝑄IT𝑟4


(𝑡 − 1) + [∑

∀𝑟3

𝑄𝑟3,𝑟4 (𝑡)]

− 𝑄TT𝑟4


∀ (𝑟4, 𝑡) ,

𝑆𝑆IT𝑟4

≤ 𝑄IT𝑟4


(𝑡 − 1) + 𝛾𝑡𝑟𝑒

𝑡4× 𝑄𝑡𝑟𝑟4 (𝑡)

− ∑

∀𝑚2

𝑄𝑟4,𝑚2 (𝑡) ≤ 𝑆

IT𝑟4

∀ (𝑟4, 𝑡) .

(26)

(h) For final disposal locations,

𝑆𝑆IT𝑟5

≤ 𝑄IT𝑟5


(𝑡 − 1) + [∑

∀𝑟3

𝑄𝑟3,𝑟5 (𝑡)]

− 𝑄𝐹

𝑟5(𝑡) ≤ 𝑆

IT𝑟5

∀ (𝑟5, 𝑡) .

(27)

(ii) Demand Constraints. Consider the following

𝐷(𝑡) ≥

4

∑

𝑖=2

∑

∀𝑚𝑖

∑

∀𝑚5

𝑄𝑚𝑖,𝑚5 (𝑡) ≥ 0 ∀𝑡. (28)

(iii) Return Resource Constraints. Consider the following

𝑄RE

(𝑡) =

3

∑

𝑗=1

∑

∀𝑚5

∑

∀𝑟𝑗

𝑄𝑚5,𝑟𝑗 (𝑡) = 𝛽 × 𝐷(𝑡) ≥ 0 ∀𝑡. (29)

4. Treatment of the Fuzzy Formulation

In practice, Liang [30] noted that decision-makers are morefamiliar with estimating optimistic, pessimistic, and mostlikely parameters. The pattern of triangular distribution iscommonly adopted due to ease in defining themaximum andminimum limit of deviation of the fuzzy number of its centralvalue. Furthermore, according to the definition of Rom-melfanger [31], when knowledge of the distribution is limited,triangular distribution is appropriate for representing a fuzzynumber. And then, other studies also indicated that theprimary advantages of the triangular fuzzy number are thesimplicity and flexibility of the fuzzy arithmetic operations[31–35].

In order to discuss the fuzziness of the integrated logisticsmodel for the demand and transportation cost, there are somedefinitions stated as follows [34].

Definition 1. The fuzzy set 𝐵 = (𝑎, 𝑏, 𝑐), where 𝑎 < 𝑏 < 𝑐

is defined on 𝑅, is called the triangular fuzzy number, if themembership function of 𝐵 is given by

𝜇𝐵(𝑥) =

{{{{{{

{{{{{{

{

(𝑥 − 𝑎)

(𝑏 − 𝑎), 𝑎 ≤ 𝑥 ≤ 𝑏,

(𝑐 − 𝑥)

(𝑐 − 𝑏), 𝑏 ≤ 𝑥 ≤ 𝑐,

0, otherwise.

(30)

Definition 2. The fuzzy set [𝑎𝛼, 𝑏𝛼] defined on 𝑅, 0 ≤ 𝛼 ≤ 1,

is called an 𝛼-level fuzzy interval if the membership functionof [𝑎𝛼, 𝑏𝛼] is given by

𝜇[𝑎𝛼,𝑏𝛼] (𝑥) = {

𝛼, 𝑎 ≤ 𝑥 ≤ 𝑏,

0, otherwise.(31)

Definition 3. Let 𝐵 be a fuzzy set on 𝑅, and 0 ≤ 𝛼 ≤ 1; thenthe 𝛼-cut, 𝐵(𝛼), of 𝐵 consists of points x such that 𝜇

𝐵(𝑥) ≥ 𝛼;

that is, 𝐵(𝛼) = {𝑥 | 𝜇𝐵(𝑥) ≥ 𝛼}.

With (10) and (15), if the minimum acceptable mem-bership level 𝛼 is given, the corresponding auxiliary crispinequality expression of these two equations can be presentedas follows:

MTC ≅ ∑

∀𝑡

{

{

{

[𝑤1 ∑

∀𝑚1

∑

∀𝑚2

𝐶𝑡𝑝,𝛼

𝑚1,𝑚2(𝑡) × 𝑄

𝑚1,𝑚2 (𝑡)

+ 𝑤2 ∑

∀𝑚1

∑

∀𝑚2

𝐶𝑡𝑚,𝛼

𝑚1,𝑚2(𝑡) × 𝑄

𝑚1,𝑚2 (𝑡)

+ 𝑤3 ∑

∀𝑚1

∑

∀𝑚2

𝐶𝑡𝑜,𝛼

𝑚1,𝑚2(𝑡) × 𝑄

𝑚1,𝑚2 (𝑡)]


+ [

[

𝑤1

4

∑

𝑖=2

5

∑

𝑗=𝑖+1

∑

∀𝑚𝑖

∑

∀𝑚𝑗

𝐶𝑡𝑝,𝛼

𝑚𝑖,𝑚𝑗(𝑡) × 𝑄

𝑚𝑖,𝑚𝑗 (𝑡)

+ 𝑤2

4

∑

𝑖=2

5

∑

𝑗=𝑖+1

∑

∀𝑚𝑖

∑

∀𝑚𝑗

𝐶𝑡𝑚,𝛼


𝑚𝑖,𝑚𝑗 (𝑡)

+ 𝑤3

4

∑

𝑖=2

5

∑

𝑗=𝑖+1

∑

∀𝑚𝑖

∑

∀𝑚𝑗

𝐶𝑡𝑜,𝛼

𝑚𝑖,𝑚𝑗(𝑡)𝑄𝑚𝑖,𝑚𝑗 (𝑡)

]

]

}

}

}

,

RTC ≅ ∑

∀𝑡

{

{

{

[

[

𝑤1

3

∑

𝑗=2

∑

𝑟1

∑

∀𝑟𝑗

𝐶𝑡𝑝,𝛼


𝑟1,𝑟𝑗 (𝑡)

+ 𝑤2

3

∑

𝑗=2

∑

𝑟1

∑

∀𝑟𝑗

𝐶𝑡𝑚,𝛼


𝑟1,𝑟𝑗 (𝑡)

+𝑤3

3

∑

𝑗=2

∑

𝑟1

∑

∀𝑟𝑗

𝐶𝑡𝑜,𝛼



]

+ [𝑤1

3

∑

𝑖=2

∑

𝑟𝑖

∑

∀𝑟𝑖+1

𝐶𝑡𝑝,𝛼

𝑟𝑖,𝑟𝑖+1(𝑡) × 𝑄

𝑟𝑖,𝑟𝑖+1 (𝑡)

+ 𝑤2

3

∑

𝑖=2

∑

𝑟𝑖

∑

∀𝑟𝑖+1

𝐶𝑡𝑚,𝛼


𝑟𝑖,𝑟𝑖+1 (𝑡)

+𝑤3

3

∑

𝑖=2

∑

𝑟𝑖

∑

∀𝑟𝑖+1

𝐶𝑡𝑜,𝛼


𝑟𝑖,𝑟𝑖+1 (𝑡)]

+ [𝑤1∑

∀𝑟3

∑

∀𝑟5

𝐶𝑡𝑝,𝛼

𝑟3,𝑟5(𝑡) × 𝑄

𝑟3,𝑟5 (𝑡)

+ 𝑤2∑

∀𝑟3

∑

∀𝑟5

𝐶𝑡𝑚,𝛼

𝑟3,𝑟5(𝑡) × 𝑄

𝑟3,𝑟5 (𝑡)

+𝑤3∑

∀𝑟3

∑

∀𝑟5

𝐶𝑡𝑜,𝛼

𝑟3,𝑟5(𝑡) × 𝑄

𝑟3,𝑟5 (𝑡)]

+ [𝑤1∑

∀𝑟4

∑

∀𝑚2

𝐶𝑡𝑝,𝛼

𝑟4,𝑚2(𝑡) × 𝑄

𝑟4,𝑚2 (𝑡)

+ 𝑤2∑

∀𝑟4

∑

∀𝑚2

𝐶𝑡𝑚,𝛼

𝑟4,𝑚2(𝑡) × 𝑄

𝑟4,𝑚2 (𝑡)

+𝑤3∑

∀𝑟4

∑

∀𝑚2

𝐶𝑡𝑜,𝛼

𝑟4,𝑚2(𝑡) × 𝑄

𝑟4,𝑚2 (𝑡)]

}

}

}

.

(32)

Similarly, if the minimum acceptable membership level 𝛼is given, the constraint of demand is presented as follows:

𝑤1𝐷(𝑡)𝑝,𝛼

+ 𝑤2𝐷(𝑡)𝑚,𝛼

+ 𝑤3𝐷(𝑡)𝑜,𝛼

≥

4

∑

𝑖=2

∑

∀𝑚𝑖

∑

∀𝑚5

𝑄𝑚𝑖,𝑚5 (𝑡) ≥ 0 ∀𝑡.

(33)

The weights of 𝑤1, 𝑤2, and 𝑤3 (𝑤1 + 𝑤2 + 𝑤3 = 1)mustrepresent the weight of the most pessimistic, most likely, andmost optimistic values of the fuzzy variables. We set 𝑤2 =

4/6, 𝑤1 = 𝑤3 = 1/6, and 𝛼 = 0.5 for all formulations.However, in reality, the value 𝛼 and the relative weightingsamong three critical points can be adjusted subjectively basedon the experience and knowledge of decision-makers and/orexperts. The most likely values are used here because theyare generally the most important ones and, thus, should beassigned greater weights [30]. However, the most pessimisticand most optimistic values which provided the boundarysolutions of fuzzymarket demand for each destination are toopessimistic and optimistic, respectively, and, thus, should beassigned smaller weights [35].

For convenience, we will use fuzzy summation calcula-tion (FSC) to integrate all the experts’ optimistic, most likelyand pessimistic estimation values into one value, respectively.If 𝐴 is a parameter and 𝐴

𝑝, 𝐴𝑚, and 𝐴

𝑜 represent thefuzzy number of 𝐴’s optimistic, most likely and pessimisticestimation values. The formulation of integration is given asfollows [36, 37]:

𝐴𝑝= min {𝐴

𝑝

𝑘} ,

𝐴𝑚

= min {𝐴𝑚

𝑘} ,

𝐴𝑜= max {𝐴

𝑜

𝑘} .

(34)

4.1. Solving Procedure

Step 1. Based on (1)∼(27), we formulate the original fuzzymultiobjective linear programming model for the integratedlogistic problems.

Step 2. Based on (32) and (33), we provide the acceptableminimum membership level 𝛼 and then convert the fuzzyinequality constraints into crisp ones using the weightedaverage method.

Step 3. This step is to integrate all optimistic, most likelyand pessimistic estimation values into one value, respectively,according to (34).

Step 4. Final step is to solve the ordinary LP problem. If theDM is dissatisfied with the initial solutions, the model shouldbe adjusted until a preferred satisfactory solution is obtained.

5. Numerical Result

To illustrate the effectiveness of the models presented above,we examine a simplified numerical study. Sheu et al. [29] haveconducted a local operational case of awell-knownTaiwanesenotebook computer manufacturer which is one of the topthree domestic brands in Taiwan. This case study is based onthe logistics distribution channels and built a simplified inte-grated logistics network of the given notebookmanufacturersin the northern region of Taiwan. The collected historicaland interview survey data were used to estimate both theinput data such as annual sales and used-product returnsand primary parameters like logistics-induced operational


Table 1: Estimates of unit revenues.

Layer Unit revenue (US$)Manufacturing chain

(1) Raw material supplier 42(2) Manufacturer 485(3) Wholesaler 673(4) Retailer 873(5) End customer 2.5

Reverse chain(1) Collecting point 5.55(2) Recycle plant 7.8(3) Disassembly plant 10.85(4) Secondary material market 22.5Subsidy 8.7

Table 2: Estimates of manufacturing chain unit costs.

Layer Parameter Unit cost (US$)

(1) Raw material supplier𝐶𝑅 19.5

𝐶IR𝑚1

1.75𝐶𝐿

𝑚15

(2) Manufacturer

𝐶𝑃

𝑚1,𝑚224

𝐶𝑃

𝑟4,𝑚222.5

𝐶𝑀 115

𝐶𝐼

𝑚269.5

𝐶IR𝑚2

50𝐶𝐿

𝑚25

(3) Wholesaler𝐶𝑃

𝑚2,𝑚3531.5

𝐶𝐼

𝑚386.5

𝐶𝐿

𝑚35

(4) Retailer𝐶𝑃

𝑚3,𝑚4621.5

𝐶𝐼

𝑚4101.5

𝐶𝐿

𝑚45

costs for use in formulating the integrated logistics man-agement problem. With fuzzy formulations, the decision-maker can consider the environment under variable demandand transportation cost which are more close to the real.Details of the primary procedures in the numerical study andcorresponding results are presented below.

5.1. Parameter Settings. Based on Sheu et al. [29], the param-eters will be used as the average of Sheu’s data as shown inTables 1, 2, 3, and 4.

Because demand and transportation cost were fuzzynumbers, these were conducted with high-level decision-makers of the targeted notebook manufacturing enterpriseand its potential channel members, including the chainmembers in both the manufacturing and the reverse chains.These parameters will be estimated as optimistic, pessimistic,and most likely numbers and will be integrated by using thecenter of gravity method.

We invited five experts to estimate the demand andtransportation cost, while the last column is the data after

Table 3: Estimates of used-product reverse chain unit costs.

Layer Parameter Unit cost (US$)

(1) Collecting point

𝐶𝐶

𝑚5,𝑟11

𝐶TT 6.5

𝐶IT 0.45

𝐶IT 0.45

𝐶𝐿

𝑟13.5

(2) Recycle plant

𝐶𝐶

𝑚5,𝑟21.85

𝐶TT 2.85

𝐶IT 0.45

𝐶IT 0.45

𝐶𝐿

𝑟23.5

(3) Disassembly plant

𝐶𝐶

𝑚5,𝑟32.15

𝐶TT 1.75

𝐶IT 0.45

𝐶𝐼

𝑟3,𝑟41.8

𝐶𝐼

𝑟3,𝑟50.23

𝐶𝐿

𝑟33.5

(4) Secondary material market

𝐶𝐶

𝑟3,𝑟44.4

𝐶TT 2.05

𝐶IT 1.05

𝐶IT 1.6

𝐶𝐿

𝑟43.5

integrating into one number through fuzzy summationcalculation [36, 37]. In addition, Table 5 shows the otherparameters of the model.

In convenience, the initial inventory condition of eachmember in the manufacturing and the reverse chains wasgenerated here using a respective uniform distributionbounded by the range between 0 and the correspondinginventory capacity estimated.

5.2. Results. According to the corresponding regulations ofthe TaiwanEPA for 2005, the unit subsidy is set to be 10 (US$).The numerical results are summarized in Table 6.

Table 6 indicates the maximum profit of the manufactur-ing chain and the reverse chain.Whenwe aggregatemanufac-turing and reverse chains together, there will be some factorsinfluencing each other, so the maximum aggregate profit isnot the combination of the single profit of each chain.

Accordingly,manufacturers can be convincedmore easilyto coordinate all the chain members for the promotion ofGSCM. In addition, subsidy strategies also have a strongimpact on reverse logistics chain system. Due to the abovementions, we take the unit subsidy into further investigation.In practice, the unit subsidy may rely on the correspondingenvironmental protection regulations imposed by the EPA[29].

Figure 2 shows the sensitivity analysis of the unit subsidyparameter to investigate the potential effects of these param-eters on the performance of the reverse logistics chain.

In Figure 2, when the governmental subsidy valueincreased. This indicates that the governmental subsidy


Table 4: Inventory capacity.

(a) Manufacturing chain

𝑆IR𝑚1

𝑆IR𝑚2

𝑆𝐼

𝑚2𝑆𝐼

𝑚3𝑆𝐼

𝑚4

7000 5000 5000 500 100𝑆𝑆

IR𝑚1

𝑆𝑆IR𝑚2

𝑆𝑆𝐼

𝑚2𝑆𝑆𝐼

𝑚3𝑆𝑆𝐼

𝑚4

3500 2500 2500 250 50

(b) Reverse chain

𝑆IT𝑟1

𝑆IT𝑟1

𝑆IT𝑟2

𝑆IT𝑟2

𝑆IT𝑟3

𝑆𝐼

𝑟3,𝑟4𝑆𝐼

𝑟3,𝑟5𝑆IT𝑟4

𝑆IT𝑟4

𝑆IT𝑟5

500 500 1000 1000 2500 1500 500 1000 800 500𝑆𝑆

IT𝑟1

𝑆𝑆IT𝑟1

𝑆𝑆IT𝑟2

𝑆𝑆IT𝑟2

𝑆𝑆IT𝑟3

𝑆𝑆𝐼

𝑟3,𝑟4𝑆𝑆𝐼

𝑟3,𝑟5𝑆𝑆

IT𝑟4

𝑆𝑆IT𝑟4

𝑆𝑆IT𝑟5

250 250 500 500 1200 750 250 500 400 250

0

20000

40000

60000

80000

100000

120000

140000

160000

0 10 20 30 40

Sensitivity analysis

Reverse chain profits (US$)

Governmental subsidy value

Reve

rse c

hain

pro

fit (U

S$)

Figure 2: Numerical result of sensitivity analysis.

Table 5: Other parameters.

Return ratio (𝛽) 0.25Unit recycle fee (𝐹) 1.1Unit subsidy (𝑆) 10Used-product return 1538

Table 6: Numerical result.

Net profit (US$)Manufacturing chain 5,399,846Reverse chain 96,308Aggregate 5,454,023

policy remains as a critical determinant in influencing theperformance of used-product reverse chain.

6. Conclusion

With the encouragement of environmental consciousnessrecently, the issue of environmental protection has beenbecoming a trend of supply chain management. In addition,the enterprises also have to take more applicable measures

to improve the reverse logistics. Therefore, we formulateda fuzzy multiobjective integrated logistics model whichcoordinated the cross-functional product logistics flows andused-product reverse logistics flows with green supply chainconsideration.

The findings of the numerical result indicated that themaximum profit is $5,399,846 in the manufacturing chainand $96,308 in the reverse chain. And the results showedthat the maximum profit was up to $5,454,023 when weaggregated these two chains together. In addition, we foundthat when the governmental subsidy value increased, theprofit of the reverse chain also increased, the profit of thereverse chain also increased. The findings of this studyidentified that the governmental subsidy policy could remainof significant influence for used-product reverse logisticschain.

Nevertheless, this paper is not totally without merit. Weare hopeful that our experimental results are of great interestfor both application and scientific research.Most importantly,we will make every endeavor to cooperate with more real-world cases to acquire more perusable and actual data asour future works. Finally, the future research might usefullyextend the present use of the proposed models to examine


Table 7: Notations for our proposed model.

Manufacturing chain costMC Total costMIC Total inventory costMMC Total manufacturing costMPC Total raw material procurement costMTC Total transportation costMRC Total recycling fees paid from the manufacturing layer of a given manufacturing chain to the corresponding EPAMLC Labor cost

Manufacturing chain revenueMTR Total revenue

Reverse chain costRC Total costRTCC Total collection cost of corresponding used productsRFC Total final disposal cost of corresponding used productsRIC Total inventory costRTC Total transportation costRTTC Total transitional treatment cost of the corresponding used productsRLC Labor cost

Reverse chain revenueRTR Total revenueRR Total revenue oriented specifically from general vendor-buyer business operationsRS Total subsidies

Revenue

𝑅𝑚𝑖/𝑚𝑖+1

The generalized revenues from layer 𝑖 of the given manufacturing chain to layer 𝑖 + 1 of the given manufacturing chain(𝑖 = 2, 3, 4)

𝑅𝑚5/𝑟𝑗

The generalized revenues from end customers in layer 5 of the given manufacturing chain to layer 𝑗 of the given reverse chain(𝑗 = 1, 2, 3)

𝑅𝑟1/𝑟𝑗

The generalized revenues from the collecting points in layer 1 of the given reverse chain to layer 𝑗 of the given reverse chain(𝑗 = 2, 3)

𝑅𝑟𝑗/𝑟𝑗+1 The generalized revenues from layer 𝑗 of the given reverse chain to layer 𝑗 + 1 of the given reverse chain (𝑗 = 2, 3)

𝑅𝑟4/𝑚2

The generalized revenues from the second material market in layer 4 of the given reverse chain to the manufactures in layer 2of the given manufacturing chain

EPO The unit subsidy of environmental protection offered by EPACost

𝐶𝐶 Collecting cost of used product returned from end customer

𝐶𝐼 Inventory cost for storing products

𝐶IR Inventory cost for storing raw materials

CIT Inventory cost for storing used product that has been treated by a reverse logistics chain member𝐶

IT Inventory cost for storing used product that has not been treated by a reverse logistics chain member𝐶𝑀 Manufacturing cost of used product

𝐶𝑃 Procurement cost of physical flow 𝑖

𝐶𝑇 Transportation cost𝐶

TT Transitional treatment cost𝐹 Recycling fees charged by the corresponding EPA for manufacturing products𝐶𝐹 Unit cost of final disposal

𝐶𝐿 Hourly labor cost

𝐶𝑅 Raw material cost


Table 7: Continued.

Quantity𝑄𝐼 Quantity of inventory—decision variable

𝑄IR Quantity of raw materials inventory—decision variable

𝑄IT Quantity of inventory of used product that has been treated

𝑄IT Quantity of inventory of used product that has not been treated invent

𝑄𝐹 Quantity of final disposal—decision variable

𝑄𝑀 Manufacturing quantity—decision variable

𝑄𝑅 Raw materials quantity—decision variable

𝑄TT Transitional treatment quantity—decision variable

𝑄RE Quantity of used product that has been returned by end customers

𝑄𝐿 Quantity of labors—decision variable

𝑄𝑚𝑖,𝑚5

The generalized form of a decision variable referring to the physical flow quantity transported from layer 𝑖 given in themanufacturing chain to end customers in layer 5 given in the manufacturing chain (𝑖 = 2, 3, 4)

𝑄𝑚𝑖,𝑚𝑖+1

The generalized form of a decision variable referring to the physical flow quantity transported from layer 𝑖 given in themanufacturing chain to layer 𝑖 + 1 given in the manufacturing chain (𝑖 = 1, 2, 3, 4)

𝑄𝑚5,𝑟𝑗

The generalized form of a decision variable referring to the physical flow quantity transported from end customers in layer 5given in the manufacturing chain to layer 𝑗 given in the reverse chain (𝑗 = 1, 2, 3)

𝑄𝑟1,𝑟2

The generalized form of a decision variable referring to the physical flow quantity transported from collecting points in layer 1of the given reverse chain to recycling plants in layer 2 given in the reverse chain

𝑄𝑟1,𝑟3

The generalized form of a decision variable referring to the physical flow quantity transported from collecting points in layer 1of the given reverse chain to disassembly plants in layer 3 given in the reverse chain

𝑄𝑟2,𝑟3

The generalized form of a decision variable referring to the physical flow quantity transported from recycling plants in layer 2given in the reverse chain to disassembly plants in layer 3 of the given reverse chain

𝑄𝑟3,𝑟4

The generalized form of a decision variable referring to the physical flow quantity transported from disassembly plants inlayer 3 of the given reverse chain to final disposal in layer 4 given in the reverse chain

𝑄𝑟3,𝑟5

The generalized form of a decision variable referring to the physical flow quantity transported from disassembly plants inlayer 3 given in the reverse chain to final disposal in layer 5 of the given reverse chain

𝑄𝑟5,𝑚2

The generalized form of a decision variable referring to the physical flow quantity transported from final disposal in layer 5 ofthe given reverse chain to manufactures in layer 2 given in the manufacturing chain

Facility capacity𝑆 Safety stock𝑆𝐼 Facility capacity for inventory

𝑆IR Facility capacity for raw material inventory

𝑆IT Facility capacity for inventory that has already been treated

𝑆IT Facility capacity for inventory that has not been treated

Others𝛽 Predetermined used-product return ratio𝛾 A coefficient referring to the transformation𝐷 Demand of manufacturing chain end customer

more green supply chainmanagement aspects and solvemoreGSCM-related problems.

Appendix

See Table 7.

Conflict of InterestsThe authors declare that there is no conflict of interestsregarding the publication of this paper.

AcknowledgmentsThis paper was supported by theNational Science Committeeof Taiwan under Grant no. NSC 100-2410-H-019-004. Also,

the authors wish to thank the referees for those commentswhich provide a great help for authors to consider theirresearch more deeply.

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