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\title{Optimization of Supply Chain Network Perspective Environmental Impact based on Fuzzy Mathematical Programming}
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\begin{document}

             \author[1]{Md.  Shakil}

             \author[2]{Subrata  Talapatra}

             \affil[1]{  Khulna University of Engineering and Technology (KUET)}

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\date{\small \em Received: 15 December 2013 Accepted: 5 January 2014 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


Supply chain management (SCM) is concerned with a complex business relations network that contains interrelationships between various entities, such as suppliers, manufacturers, distribution centers and customers. SCM integrates these entities and manages their interrelationships through the use of information technology to meet customer expectation effectively along the entire value chain. Thus, one of the vital issues in supply chain management is the design of the value chain network.In this paper, a multi objective fuzzy mathematical programming model is developed to optimize the supply chain networking under inherent uncertainty of input data. The proposed model is able to optimize the environmental impacts beside the traditional cost minimization objective to make a fair balance between them. The model determines the fuzzy capacities of the facilities and the design of the network con?guration with a minimum total cost. A real case is used to demonstrate the significance and applicability of the developed fuzzy optimization model as well as the usefulness of the proposed solution approach. The developed model is solved by a professional software package (LINDO), and the computational results are discussed.

\end{abstract}


\keywords{optimization, fuzzy, supply chain network design, environmental impact and model formulation.}

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\let\tabcellsep& 	 	 		 \par
supply chain. In general, supply chain network design includes determining the locations, numbers and capacities of network facilities and the aggregate material flow between them. Since the end-of-life (EOL) products have significant impact on environment, a considerable part of literature is dedicated to EOL product management. This has created a need to develop models for reverse supply chain (logistics) network design. Reverse supply chain network design problem addresses the number of collection, recovery, recycling and disposal centers needed, their location and capacities and material flows between them.\par
In the last several years, many studies have been proposed and much research has been performed on the design and optimization of supply chain networks. In one study, Pirkul and Jayaram an \hyperref[b0]{[1]} studied a multi-commodity, multi-plant, capacitated facility location problem and proposed an efficient heuristic solution to the problem. In the capacitated plant and warehouse location model, customers typically demand multiple units of different products that are distributed to customer outlets from open warehouses that receive these products from several manufacturing plants. The objective function of the model minimizes the sum of the fixed cost of establishing and operating the plants and the warehouses plus the variable cost of transporting units of products from the plants to the warehouses and distributing the products from the warehouses to the customer, to satisfy the multiple demands of the customers. Recently Ilgin and Gupta et al. \hyperref[b1]{[2]} present a comprehensive review on environmentally conscious manufacturing and product recovery; below we have surveyed some relevant papers on environmental supply chain network design. Timpe and Kallrath \hyperref[b2]{[3]} considered a multi-site, multi-product production network and presented a general mixed integer linear programming model that combines aspects related to production, distribution and marketing and involves production sites (plants) and sales points. Cakra vastia et al. \hyperref[b3]{[4]} developed an analytical model of the supplier selection process in designing a supply chain network. The constraints on the capacity of each potential supplier are considered in the process. The objective of the supply chain is to minimize the level of customer Optimization of Supply Chain Network Perspective Environmental Impact based on Fuzzy Mathematical Programming Subrata Talapatra ? \& Md. Shakil ? dissatisfaction, which is evaluated by two performance 
\section[{I. Introduction}]{I. Introduction}\par
well-structured supply chain is an important strategic competency that enables firms to be competitive in today's marketplace. Along this important issue, the concern about environmental impact of business activities results in governmental legislations and environmentally conscious consumers. Environmental or green supply chain management can be defined as integrating environmental aspects into supply chain management covering both forward and reverse supply chains from product design to end-of-life management of used products. The ultimate goal is to consider environment in every decision making process across supply chain, especially the strategic level decisions. Supply chain optimization can help define, recommend, and set flexible supply chain strategies based on organization's operations, resources, and other capabilities. Optimization of supply chain network design, as the most important strategic decision in supply chain management, plays an important role in overall environmental and economic performance of the A criteria: (i) price and (ii) delivery lead time. The overall model operates at two levels of decision making: the operational level and the chain level. The operational level concerns decisions related to optimizing the manufacturing and logistical activities of each potential supplier, to meet the customer's requirements. At the chain level, all of the bids from potential suppliers are evaluated, and the final configuration of the supply chain is determined. The structure of the chain de pends on the product speci fic ations and on the customer's order size. An optimal solution in terms of the models for the two levels can be obtained using a mixed -integer programming technique \hyperref[b3]{[4,}\hyperref[b4]{5]} presented a multi-phase mathematical programming approach for effective supply chain design. Syarif et al. \hyperref[b5]{[6]} considered the logistic chain network problem formulate d by the 0-1 mixed integer linear programming problem. The design of the problem involves the choice of the facilities (plants and distribution center s) to be opened and the distribution network de sign, with the goal of satisfying the demand with minimum cost. For the solution method, the spanning tree-based genetic algorithm using Pr?fer number representation is proposed. Sanayeia et al. \hyperref[b6]{[7]} proposed an integrated approach of multi-attribute utility theory (MAUT) and linear programming (LP) for rating and choosing the best suppliers and defining the optimum order quantities among selected ones in order to maximize total additive utility. Javadi et al. \hyperref[b7]{[8]} developed a fuzzy multi-objective linear programming (FMOLP) model for solving the multi-objective no-wait flow shop scheduling problem in a fuzzy environment. The proposed model attempted to simultaneously minimize the weighted mean completion time and the weigh ted mean earliness. A numerical example demonstrated the feasibility of applying the proposed model to no-wait flow shop scheduling problem. The proposed model yielded a compromised solution and the decision maker's overall levels of satisfaction.\par
To overcome the literature gap, this paper proposes a practical, but tractable, multi-objective fuzzy mathematical programming model for optimization of supply chain networking perspective environmental impact problem that is able to (1) consider both economic and environmental objectives in the design of the supply chain network, (2) integrate the design of reverse and forward supply chain networks to avoid the sub-optimality's results from separated design of forward and reverse supply chains, (3) The model allows decision-makers to design the network configuration with the minimum total cost. (4) Handle the epistemic uncertainty in parameters in real cases results from unavailability or incompleteness and imprecise nature of input data. Also, this paper proposes an efficient solution approach that is able to generate both balanced and unbalanced solutions through making a reasonable tradeoff between environmental and economic objectives.\par
This paper is organized into eight sections. After the introduction, in which some supply chain models are described, the remainder of the paper is structured as follows. In Section 2, problem statement of the proposed supply chain network is introduced. This model is formulated in section 3 and developed an equivalent auxiliary crisp model in section 5. Implementation and evaluation of this proposed model is described in section 6, and section 7 represents the results and discussion. Conclusions are presented in Section 8. As well as finally appendix and references are attached. 
\section[{II. Problem Statement}]{II. Problem Statement}\par
The concerned integrated supply chain network in this paper is motivated by a real industrial case. The case is a supply chain network of Coca-Cola drinks in Bangladesh that supplies about 80\% of domestic demand. The manufacturer has one production plant with about 600 thousand production capacity per one year. In transportation system of supply chain networking consists of environmental impact like, carbon di oxide (co 2 ) that is responsible for the environmental disasters. To overcome this problem proposed a multi-echelon supply chain network that includes both forward and reverse networks is illustrated in Fig. \hyperref[fig_0]{1}. Through forward network the new products manufactured by plants (production centers) are distributed among customer zones. In the reverse network, the used products are shipped to recycling centers through collection/disassembly centers. All demands of customers must be satisfied and all of the returned products from customers must be collected. Also, a predefined percent of demand from each customer is assumed as returned products from corresponding customer. Unavailability or incompleteness of data in real world network optimization problems is an important challenge that imposes a high degree of uncertainty in such problem. The problem is concerned with the uncertain parameters are presented by fuzzy numbers described by their possibility distribution. The possibility distributions are estimated based on current insufficient data and the decision makers' knowledge. The main objective of this integrated supply chain under uncertain conditionincludes the material flow quantities between different facilities with respect to two conflicting objective functions: (1) minimization of total cost and (2) minimization of total environmental impact. ?? =index of candidate location for production centers, i=1, 2, 3, 4??.i j=index of fixed location of customer zones, j=1, 2, 3, 4??.j k=index of candidate location for collection centers, k=1, 2, 3, 4??.k l=index of existing glass recycling centers, l=1, 2, 3, 4??.l m=index of existing plastic recycling centers, m=1, 2, 3, 4??.m b) Parameters ?? ?? = demand of customer zone, j ?? ?? = rate of return percentage from customer zones, j ð??"ð??" ?? = fixed cost of opening production centers, i ð??"ð??" ?? = fixed cost of opening collection centers, k ?? ???? = transportation cost per product unit from plant, i to customer zones, j ?? ???? = transportation cost of per used product unit from customer zone, j to collection center, k ?? ???? = transportation cost of per glass part of used product unit from collection center, k to glass recycling center, l ? ???? = transportation cost of per plastic part of used product unit from collection center, k to plastic recycling center, m ?? ?? = manufacturing cost per unit of product at production center, i ?? ?? = processing cost for per unit of used product at collection center, k ?? ?? = processing cost for per glass part of used product unit at glass recycling center, l ?? ?? = processing cost for per plastic part of used product unit at plastic recycling center, m ?? ?? = maximum capacity of production center, i ?? ?? = maximum capacity of collection center, k ?? ?? = maximum capacity of glass recycling center, l ?? ?? = maximum capacity of plastic recycling center, m ???? ?????? = Environmental impact per production of one unit of product ?? ???? ?????? = environmental impact of shipping one unit of product from plant, i to customer zone, j ?? ???? ?????? = environmental impact of shipping one unit of used product from customer zone, j to collection center, k ?? ???? ?????? = environmental impact of shipping glass part of used product unit from collection center, k to glass recycling center, l ?? ???? ?????? = environmental impact of shipping plastic part of used product unit from collection center, k to plastic recycling center, m ???? ?????? = environmental impact per handling one unit of collected used product at collection centers ???? ?????? = environmental impact of recycling the glass part of one unit of used product ???? ?????? = environmental impact of recycling the plastic part of one unit of used product c) Variables ?? ???? = quantity of product shipped from plant, i to customer zone, j ?? ???? = quantity of used product shipped customer zone, j to collection center, k ?? ???? =+ ? ? (?? ?? + ?? ???? )?? ???? ?? ?? + ? ? (?? ?? + ?? ???? )?? ???? ?? ?? + ? ? (?? ?? + ?? ???? )?? ???? ?? ?? + ? ? (?? ?? + ? ?? ?? )?? ???? ?? ??\par
Here transportation costs between facilities are calculated by multiplying the transportation cost of one unit shipping per unit of distance.\par
For the second objective: minimizing the total environmental impact\par
The purpose of this supply chain network is to fulfill the customer demand by producing and distributing the product at forward network and the safe management of product by reverse network.\par
The purpose of using ECO-indicator is to estimate the environmental impact of different supply chain network configurations. Following ECO-indicators are considered for this supply chain network design.\par
? The production (pro)\par
? Transportation from production centers to customer zone (tpc)\par
? Transportation from customer zone to collection centers (tcc)\par
? Handling the used product at collection centers(col) ? Transportation from collection to glass recycling centers (tcs) ? Glass recycling center (src)\par
? Transportation from collection centers to plastic recycling centers (tcp)? Plastic recycling centers (src) Min w 2 = ? ? (???? ?????? + ???? ???? ?????? )?? ???? ?? ?? + ? ? (???? ?????? + ???? ???? ?????? )?? ???? ?? ?? + ? ? (???? ?????? + ???? ???? ?????? )?? ???? ?? ?? + ? ? (???? ?????? + ???? ???? ?????? )?? ???? ?? ?? 
\section[{IV. Constraints}]{IV. Constraints} 
\section[{Demand and return satisfaction constraints}]{Demand and return satisfaction constraints}\par
Here following constraints (3) and ( \hyperref[formula_4]{4}) ensure the demands of all customers are satisfied and the entire used products are collected from the customer zones.? ?? ???? ?? ? ?? ??\textbf{(3)}? ?? ???? ?? ? ?? ?? ?? ??\textbf{(4)}\par
a) Flow Balance Constraints\par
Here constraints (  {\ref 5}) and (  {\ref 6}) ensure the flow balance at collection centers. Two EOL options are considered in the proposed model, the collected used product should be sent to glass and plastic recycling centers. Therefore the total number of plastic and glass parts should be equal to recycling centers because they are disassembled from one used product.? ?? ???? ?? ? ? ?? ???? ?? (5) ? ?? ???? ?? ? ? ?? ???? ?? (6) ? ?? ???? ?? ? ?? ?? ?? ?? (8) ? ?? ???? ?? ? ?? ??\textbf{(9)}\par
? ?? ???? ?? ? ?? ?? \hyperref[b9]{(10)} Here constraints \hyperref[b7]{(8)} to \hyperref[b9]{(10)} are capacity constraints on production, collection and glass recycling and plastic recycling centers respectively. Also constraints \hyperref[b6]{(7)} and (  {\ref 8}) prohibit the units of new and used products from being transferred to production and collection centers which are not opened respectively. 
\section[{Decision variables constraints}]{Decision variables constraints}\par
The following constraints are related to the binary and non-negatively restrictions on the corresponding decision variables. ?? ?? , ?? ?? Ñ?"\{0,1\}\textbf{(11)}\par
V. Proposed Method This is a multi-objective probabilistic mixed integer programming model. To solve this model a two phase approach is proposed one is the method of Jimenez to convert the proposed model and the second Second objective function: minimization of total environmental impact First objective Function: minimization of total cost VI. Equivalent Auxiliary Crisp Model Jimenez et al. \hyperref[b8]{[9]} method is selected to develop this equivalent auxiliary crisp model as well as this triangular, trapezoidal and nonlinear ones in both symmetric and asymmetric functions. This method also computational efficient to solve fuzzy linear problems as it can preserve its linearity and do not increase the number of objective functions and inequality constraints. The detail of this method is given in Appendix.\par
Equivalent auxiliary crisp model can be formulated as follows:minw 1 = ? ( ð??"ð??" ?? ?????? +2ð??"ð??" ?? ?????? +ð??"ð??" ?? ?????? 4 )?? ?? ?? + ? ( ð??"ð??" ?? ?????? +2ð??"ð??" ?? ?????? +ð??"ð??" ?? ?????? 4 )?? ?? ?? + ? ? ( ?? ?? ?????? +2?? ?? ?????? +?? ?? ?????? +?? ???? ?????? +2?? ???? ?????? +?? ???? ?????? 4 ) ?? ?? ?? ???? + ? ? ( ?? ?? ?????? +2?? ?? ?????? +?? ?? ?????? +?? ???? ?????? +2?? ???? ?????? +?? ???? ?????? 4 ) ?? ?? ?? ???? + ? ? ( ?? ?? ?????? +2?? ?? ?????? +?? ?? ?????? +?? ???? ?????? +2?? ???? ?????? +?? ???? ?????? 4 ) ?? ?? ?? ???? + ? ? ( ?? ?? ?????? +2?? ?? ?????? +?? ?? ?????? +? ???? ?????? +2? ???? ?????? +? ???? ?????? 4 ) ?? ?? ?? ???? minw 2 = ? ? ????? ?????? + ???? ???? ?????? ??? ???? ?? ?? + ? ? ????? ?????? + ???? ???? ?????? ??? ???? ?? ?? + ? ? (???? ?????? + ???? ???? ?????? )?? ???? ?? ?? + ? ? ????? ?????? + ???? ???? ?????? ??? ???? ?? ?? Subject to, ? ?? ???? ?? ? ? ( ?? ?? ?????? +?? ?? ?????? 2 ) + (1-?)( ?? ?? ?????? +?? ?? ?????? 2 ) ? ?? ???? ?? ? ??? ? ?? ?? ?????? +?? ?? ?????? 2 ? + (1 ? ??)( ?? ?? ?????? +?? ?? ?????? 2 )? ??? ? ?? ?? ?????? +?? ?? ?????? 2 ? + (1 ? ??)( ?? ?? ?????? +?? ?? ?????? 2 )? ? ?? ???? ?? = ? ?? ???? ?? ? ?? ???? ?? = ? ?? ???? ?? ? ?? ???? ?? ??? ?? ??? ? ?? ?? ?????? +?? ?? ?????? 2 ? + (1 ? ??)( ?? ?? ?????? +?? ?? ?????? 2 )? ? ?? ???? ?? ??? ?? ??? ? ?? ?? ?????? +?? ?? ?????? 2 ? + (1 ? ??)( ?? ?? ?????? +?? ?? ?????? 2 )? ? ?? ???? ?? ???? ? ?? ?? ?????? +?? ?? ?????? 2 ? + (1 ? ??)( ?? ?? ?????? +?? ?? ?????? 2 )? ? ?? ???? ?? ???? ? ?? ?? ?????? +?? ?? ?????? 2 ? + (1 ? ??)( ?? ?? ?????? +?? ?? ?????? 2 )? ?? ?? , ?? ?? Ñ?"\{0,1\}\par
?? ???? , ?? ???? , ?? ???? , ?? ???? ? 0 
\section[{VII. Implementation and Evaluation}]{VII. Implementation and Evaluation}\par
The validity of the developed model as well as the usefulness of the proposed solution method is investigated via the data withdrawn from the case study. The manufacturer firm has nine customer zones. The firm is responsible to collect the used product from domestic customers therefore the return rate from the foreign customer is considered equal to zero. To estimate the possibility of distribution parameters first objective data is gathered and the firm managers determined three prominent values (most likely, most pessimistic and most optimistic) of triangular fuzzy numbers according to available data. The fuzzy data for demand and rate of return each customer is represented in table: 1 for the over three years.  
\section[{VIII. Results and Discussion}]{VIII. Results and Discussion}\par
Firm supplies products from different production centers to customer's zone as well as shipped using transportation by trucks. Products manufactured in production centers are directly dispatched to customer zone, and the manufacturer has to pay transportation costs. The firm assigns trucks with respect to the capacities of truck options and transports the products from the production center to the customer zone.\par
Table \hyperref[tab_5]{4}. presents the transportation cost form production center to customer zone; here trucks are used to transport the products. Table \hyperref[tab_16]{10}. Represents the transportation cost of product from collection center to plastic recycling center by using trucks in reverse supply chain networking. Table \hyperref[tab_19]{12}. Represents the environmental impact of shipping product from production center to customer zone, here environmental impact means the amount of carbon di oxide (CO 2 ) obtained from the trucks during transportation. Environmental impact per production of one unit of product, ???? ?????? =42 ? ?(???? ?????? + ?? ???? ?????? ) = 6155 ?? ?? Table \hyperref[tab_20]{13}. Represents the environmental impact of shipping one unit of product from customer zone to collection center, here environmental impact means the amount of carbon di oxide (CO 2 ) obtained from the trucks during transportation. Environmental impact of handling one unit of collected used product at collection center, ???? ?????? =32 ? ?(???? ?????? + ?? ???? ?????? ) = 5416 ?? ?? Table \hyperref[tab_21]{14}. Represents the environmental impact of shipping glass part from collection center to glass recycling center, here environmental impact means the amount of carbon di oxide (CO 2 ) obtained from the trucks during transportation. Environmental impact of recycling one unit of glass part, ???? ?????? =40 ? ?(???? ?????? + ?? ???? ?????? ) = 3197 ?? ?? Table \hyperref[tab_22]{15}. Represents the environmental impact of shipping plastic part from collection center to plastic recycling center, here environmental impact means the amount of carbon di oxide (CO 2 ) obtained from the trucks during transportation. The above solution represent the minimization of total cost is 0.1394333E+11; here no iteration is required to get the optimal solution. The optimal solution is obtained for the proposed supply chain networking contains of variables of production centers (X) is 10175.00 that shows that if a new production center is opened than cost will increase otherwise reduced amount is 10175.00. The variables (Y) represent the collection center that is obtained 15925.00, that presents if a collection center is opened than cost will increase amount of 15925.00 otherwise reduced.\par
Variables (Z) show the quantity of product shipped from production centers (i) to customer zone (j) that is obtained 15012.00 units for the minimization of cost.\par
Variables (W) shows the quantity of product shipped from customer zone (j) to collection center (k) that is obtained 10730.61 for the minimization of total cost. For the reverse flow variables (m) \& (n) presents the quantity of used product shipped from collection center (k) to glass recycling center (l) \& quantity of plastic part of used product shipped from collection center (k) to plastic recycling center (m) those are 43925.00 and 41375.00 reduced cost. Inequality constraint to transform it to equality slack and surplus values for the row 1,2,4,5 are 0.1394333E+11, 7281.000, 6736.500 and row 2 \& 3 presents the transportation cost of production center(i) to customer zone(j)\& customer zone (j) to collection center (k). The above solution represent the minimization of total environmental impact here environmental impact minimization means the reduction of carbon di oxide (CO 2 ) during the transportation of product from production center (i) to customer zone (j) and customer zone (j) to location centers (k) finally location centers (l) to glass or plastic recycle center(l or m) through trucks.\par
Here for the proposed supply chain networking problem only carbon di oxide (CO 2 ) is considered as an environmental impact others are neglected. The 2 nd objective function shows the minimization of environmental impact that is 0.9239886E+08 as well as no iteration is required to get the optimal solution. Variables (Z) show the quantity of product shipped from production centers (i) to customer zone (j) that is obtained 15012.00 units for the minimization of environmental impact. The variables (Y) represent the collection center that is obtained reduced 5416.000. A variable (M) is the quantity of glass part shipped from collection center (k) to glass recycling center (l) than the reduced amount of 3197.000. A variable (N) is the quantity of plastic part shipped from collection center (k) to plastic recycling center (m) than the reduced amount of 1510.000. A variable (W) is the quantity of used product shipped from customer zone (j) to collection center (k) amount of 10730.61.Inequality constraint to transform it to equality slack and surplus values for the row 1,4,5 are 0.9239886E+08, 7281.000, 6736.500 and dual prices are showing in row 1 \& 2. 
\section[{IX. Conclusion}]{IX. Conclusion}\par
Effective supply chain network design and optimization of the network are tasks that provide a competitive advantage to firms and organizations in today's highly intractable global business environment. In this study, design and optimization supply chain networking based on multi-objective fuzzy mathematical programming model, this consists of minimizing the total cost and environmental impact and determining the optimal physical shipment of product from production center to customer zone in forward flow and collection center to recycling center in reverse flow. The proposed fuzzy model includes the design of the network configuration with a minimum total cost and environmental impact under the fuzzy capacity constraints with triangular and trapezoidal member ship functions. The total cost involves the following: the transportation costs between production center and customer zone; customer zone to collection center and collection center to recycling center. To solve the proposed optimization model, an interactive fuzzy solution approach is developed based on the econstraint method and the possibility programming approach proposed by Jimenezet al. \hyperref[b8]{[9]}.The proposed hybrid solution approach is able to generate both balanced and unbalanced solutions and making a reasonable tradeoff between environmental and economic objectives. The effectiveness of the developed fuzzy optimization model as well as the usefulness of the proposed solution approach is investigated through a real industrial case. Finally, a sensitivity analysis developed to show the correlation between the objective function value and the constraints using LINDO 12 optimization software. \par
According to the ranking method of Jimenez \hyperref[b9]{[10]}, for any pair of fuzzy numbers 'a and b', the degree in which a is bigger than b can be de fined as follows. \par
When ? m (a,b)?? it will be said that a is bigger than, or equal to, b at least in degree of ? and it will be represented as a? ? b. Now, consider the following fuzzy mathematical programming model in which all parameters are defined as triangular or trapezoidal fuzzy numbers.\par
Min z= ? t x ST, ?? ?? ?? ? ?? ?? , i= 0,1,2???l;  \par
Eq. ( 17) can be rewritten as follows.\par
?(1 ? ??)?? \par
Also, Jimenez et al. \hyperref[b8]{[9]} showed that a feasible solution like x 0 is an acceptable optimal solution of the model \hyperref[b17]{(18)}   \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}2 =}\end{figure}
    \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.2669265033407572\textwidth}P{0.04354120267260579\textwidth}P{0.539532293986637\textwidth}}
\tabcellsep \tabcellsep 1, if a production center opened at location, ?? ?? ?? =? 0, otherwise\\
\tabcellsep \tabcellsep 1, if a collection center opened at location, ?? ?? ?? =? 0, otherwise\\
\tabcellsep \tabcellsep d) Objective Function\\
\tabcellsep \tabcellsep There are two objective functions are\\
\tabcellsep \tabcellsep considered:\\
\multicolumn{2}{l}{?? ???? = quantity of plastic part of used product shipped from collection center, k to plastic recycling center, m}\tabcellsep i. Minimization of total cost ii. Minimization of total environmental impact\\
Minw 1 =? ð??"ð??" ?? ??\tabcellsep ?? ?? + ? ð??"ð??" ??\end{longtable} \par
  {\small\itshape [Note: ?? ?? ?? + ? ? (?? ?? + ?? ???? )?? ???? ?? ??]} 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.85\textwidth}}
Optimization of Supply Chain Network Perspective Environmental Impact based on Fuzzy\\
Mathematical Programming\\
b) Capacity Constraint\\
? ?? ????\end{longtable} \par
  {\small\itshape [Note: ??? ?? ?? ?? ??]} 
\caption{\label{tab_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.85\textwidth}}
different kind of membership functions such as\\
model is based on mathematical concepts that is\\
expected interval and expected value of fuzzy numbers\\
and also explain a ranking method which can support\end{longtable} \par
 
\caption{\label{tab_2}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.18140243902439024\textwidth}P{0.19695121951219513\textwidth}P{0.09329268292682927\textwidth}P{0.09329268292682927\textwidth}P{0.16067073170731708\textwidth}P{0.062195121951219505\textwidth}P{0.062195121951219505\textwidth}}
Location(i)\tabcellsep \multicolumn{3}{l}{Fixed Cost, ?? ?? (Thousand) pes mos opt}\tabcellsep \multicolumn{3}{l}{Capacity, ?? ?? (Thousand) pes mos opt}\\
Khulna\tabcellsep 13300\tabcellsep 14500\tabcellsep 15300\tabcellsep 190\tabcellsep 200\tabcellsep 210\\
Rajshahi\tabcellsep 13500\tabcellsep 14700\tabcellsep 15400\tabcellsep 190\tabcellsep 200\tabcellsep 210\\
Narayongonj\tabcellsep 13600\tabcellsep 14800\tabcellsep 15500\tabcellsep 200\tabcellsep 210\tabcellsep 220\\
Chitagong\tabcellsep 13500\tabcellsep 14700\tabcellsep 15400\tabcellsep 165\tabcellsep 180\tabcellsep 195\\
Dhaka\tabcellsep 13000\tabcellsep 14000\tabcellsep 15000\tabcellsep 190\tabcellsep 200\tabcellsep 210\\
Rangpur\tabcellsep 13600\tabcellsep 14700\tabcellsep 15400\tabcellsep 190\tabcellsep 200\tabcellsep 210\\
Barisal\tabcellsep 13400\tabcellsep 14200\tabcellsep 15200\tabcellsep 165\tabcellsep 180\tabcellsep 195\\
Joshor\tabcellsep 0\tabcellsep 0\tabcellsep 0\tabcellsep 170\tabcellsep 190\tabcellsep 210\end{longtable} \par
 
\caption{\label{tab_3}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.18640350877192982\textwidth}P{0.18888888888888888\textwidth}P{0.0894736842105263\textwidth}P{0.0894736842105263\textwidth}P{0.16154970760233917\textwidth}P{0.06710526315789474\textwidth}P{0.06710526315789474\textwidth}}
Location, i\tabcellsep \multicolumn{3}{l}{Fixed cost, ?? ?? (Thousand) pes mos opt}\tabcellsep \multicolumn{3}{l}{Capacity, ?? ?? (Thousand) pes mos opt}\\
Khulna\tabcellsep 1700\tabcellsep 1740\tabcellsep 1780\tabcellsep 240\tabcellsep 245\tabcellsep 250\\
Rajshahi\tabcellsep 1750\tabcellsep 1790\tabcellsep 1830\tabcellsep 240\tabcellsep 245\tabcellsep 250\\
Chitagong\tabcellsep 1700\tabcellsep 1740\tabcellsep 1780\tabcellsep 250\tabcellsep 255\tabcellsep 260\\
Dhaka\tabcellsep 1680\tabcellsep 1720\tabcellsep 1740\tabcellsep 220\tabcellsep 225\tabcellsep 230\\
Narayongonj\tabcellsep 1780\tabcellsep 1830\tabcellsep 1880\tabcellsep 230\tabcellsep 235\tabcellsep 240\\
Rangpur\tabcellsep 1760\tabcellsep 1810\tabcellsep 1860\tabcellsep 220\tabcellsep 205\tabcellsep 210\\
Savar\tabcellsep 1740\tabcellsep 1780\tabcellsep 1820\tabcellsep 200\tabcellsep 205\tabcellsep 210\\
Barisal\tabcellsep 1720\tabcellsep 1750\tabcellsep 1780\tabcellsep 210\tabcellsep 215\tabcellsep 220\\
Joshor\tabcellsep 1730\tabcellsep 1770\tabcellsep 1810\tabcellsep 225\tabcellsep 230\tabcellsep 235\end{longtable} \par
 
\caption{\label{tab_4}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.038558467741935484\textwidth}P{0.06940524193548386\textwidth}P{0.09168346774193548\textwidth}P{0.09339717741935484\textwidth}P{0.08996975806451613\textwidth}P{0.09339717741935484\textwidth}P{0.09339717741935484\textwidth}P{0.09339717741935484\textwidth}P{0.09339717741935484\textwidth}P{0.09339717741935484\textwidth}}
\multicolumn{2}{l}{Production Customer Center, i}\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 5\tabcellsep 6\tabcellsep 7\tabcellsep 8\\
Zone, j\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep pes\tabcellsep 900\tabcellsep 1000\tabcellsep 900\tabcellsep 1000\tabcellsep 1100\tabcellsep 1100\tabcellsep 1000\tabcellsep 1000\\
1\tabcellsep mos\tabcellsep 1000\tabcellsep 1200\tabcellsep 1200\tabcellsep 1200\tabcellsep 1300\tabcellsep 1250\tabcellsep 1400\tabcellsep 1250\\
\tabcellsep opt\tabcellsep 800\tabcellsep 1100\tabcellsep 800\tabcellsep 1100\tabcellsep 1200\tabcellsep 1000\tabcellsep 1200\tabcellsep 1200\\
\tabcellsep pes\tabcellsep 1100\tabcellsep 1100\tabcellsep 1000\tabcellsep 1100\tabcellsep 1000\tabcellsep 1200\tabcellsep 1000\tabcellsep 1200\\
2\tabcellsep mos\tabcellsep 1200\tabcellsep 1350\tabcellsep 1100\tabcellsep 1250\tabcellsep 1400\tabcellsep 1250\tabcellsep 1300\tabcellsep 1400\\
\tabcellsep opt\tabcellsep 1150\tabcellsep 1200\tabcellsep 1200\tabcellsep 1300\tabcellsep 1200\tabcellsep 1300\tabcellsep 1200\tabcellsep 1100\\
\tabcellsep pes\tabcellsep 1200\tabcellsep 1200\tabcellsep 1100\tabcellsep 1100\tabcellsep 1200\tabcellsep 1400\tabcellsep 1000\tabcellsep 1500\\
3\tabcellsep mos\tabcellsep 1400\tabcellsep 1400\tabcellsep 1150\tabcellsep 1300\tabcellsep 1450\tabcellsep 1100\tabcellsep 1350\tabcellsep 1600\\
\tabcellsep opt\tabcellsep 1100\tabcellsep 1100\tabcellsep 1200\tabcellsep 1200\tabcellsep 1000\tabcellsep 1200\tabcellsep 1200\tabcellsep 1400\\
\tabcellsep pes\tabcellsep 1400\tabcellsep 1200\tabcellsep 1000\tabcellsep 1100\tabcellsep 1200\tabcellsep 1200\tabcellsep 1300\tabcellsep 1300\\
4\tabcellsep mos\tabcellsep 1500\tabcellsep 1500\tabcellsep 1200\tabcellsep 1350\tabcellsep 1500\tabcellsep 1150\tabcellsep 1400\tabcellsep 1500\\
\tabcellsep opt\tabcellsep 1300\tabcellsep 1300\tabcellsep 900\tabcellsep 1200\tabcellsep 1400\tabcellsep 1000\tabcellsep 1200\tabcellsep 1200\\
\tabcellsep pes\tabcellsep 1200\tabcellsep 1200\tabcellsep 1000\tabcellsep 1200\tabcellsep 1300\tabcellsep 1000\tabcellsep 1000\tabcellsep 1100\\
5\tabcellsep mos\tabcellsep 1350\tabcellsep 1550\tabcellsep 1300\tabcellsep 1400\tabcellsep 1500\tabcellsep 1200\tabcellsep 1500\tabcellsep 1700\\
\tabcellsep opt\tabcellsep 1100\tabcellsep 1100\tabcellsep 1200\tabcellsep 1100\tabcellsep 1400\tabcellsep 1100\tabcellsep 1300\tabcellsep 1200\\
\tabcellsep pes\tabcellsep 1200\tabcellsep 1400\tabcellsep 1300\tabcellsep 1200\tabcellsep 1400\tabcellsep 1200\tabcellsep 1200\tabcellsep 1300\\
6\tabcellsep mos\tabcellsep 1500\tabcellsep 1600\tabcellsep 1350\tabcellsep 1450\tabcellsep 1600\tabcellsep 1250\tabcellsep 1550\tabcellsep 1750\\
\tabcellsep opt\tabcellsep 1100\tabcellsep 1350\tabcellsep 1200\tabcellsep 1100\tabcellsep 1300\tabcellsep 1300\tabcellsep 1200\tabcellsep 1200\\
\tabcellsep pes\tabcellsep 1400\tabcellsep 1200\tabcellsep 1500\tabcellsep 1200\tabcellsep 1400\tabcellsep 1200\tabcellsep 1100\tabcellsep 1400\\
7\tabcellsep mos\tabcellsep 1600\tabcellsep 1700\tabcellsep 1400\tabcellsep 1500\tabcellsep 1250\tabcellsep 1300\tabcellsep 1600\tabcellsep 1600\\
\tabcellsep opt\tabcellsep 1300\tabcellsep 1300\tabcellsep 1300\tabcellsep 1100\tabcellsep 1500\tabcellsep 1000\tabcellsep 1200\tabcellsep 1300\\
\tabcellsep pes\tabcellsep 1500\tabcellsep 1400\tabcellsep 1400\tabcellsep 1300\tabcellsep 1000\tabcellsep 1000\tabcellsep 1000\tabcellsep 1200\\
8\tabcellsep mos\tabcellsep 1700\tabcellsep 1750\tabcellsep 1450\tabcellsep 1600\tabcellsep 1300\tabcellsep 1350\tabcellsep 1650\tabcellsep 1550\\
\tabcellsep opt\tabcellsep 1600\tabcellsep 1500\tabcellsep 1200\tabcellsep 1400\tabcellsep 1200\tabcellsep 1200\tabcellsep 1100\tabcellsep 1300\\
\tabcellsep pes\tabcellsep 1500\tabcellsep 1300\tabcellsep 1000\tabcellsep 1000\tabcellsep 1200\tabcellsep 1000\tabcellsep 1200\tabcellsep 1000\\
9\tabcellsep mos\tabcellsep 1650\tabcellsep 1400\tabcellsep 1500\tabcellsep 1250\tabcellsep 1350\tabcellsep 1400\tabcellsep 1400\tabcellsep 1600\\
\tabcellsep opt\tabcellsep 1400\tabcellsep 1200\tabcellsep 900\tabcellsep 1200\tabcellsep 1100\tabcellsep 1200\tabcellsep 1000\tabcellsep 1200\end{longtable} \par
 
\caption{\label{tab_5}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_6}Table 5 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.15159235668789808\textwidth}P{0.2328025477707006\textwidth}P{0.2328025477707006\textwidth}P{0.2328025477707006\textwidth}}
Production\tabcellsep pes\tabcellsep mos\tabcellsep opt\\
centers, i\tabcellsep \tabcellsep \tabcellsep \\
1\tabcellsep 10000\tabcellsep 10500\tabcellsep 11000\\
2\tabcellsep 10500\tabcellsep 12000\tabcellsep 12500\\
3\tabcellsep 11000\tabcellsep 11500\tabcellsep 10000\\
4\tabcellsep 10000\tabcellsep 12000\tabcellsep 11000\\
5\tabcellsep 11500\tabcellsep 12500\tabcellsep 13000\\
6\tabcellsep 12000\tabcellsep 11000\tabcellsep 14000\\
7\tabcellsep 11000\tabcellsep 10000\tabcellsep 15000\\
8\tabcellsep 10500\tabcellsep 11500\tabcellsep 12000\end{longtable} \par
 
\caption{\label{tab_7}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_8}Table 6 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.04181922196796339\textwidth}P{0.07877574370709382\textwidth}P{0.080720823798627\textwidth}P{0.08169336384439359\textwidth}P{0.08266590389016018\textwidth}P{0.080720823798627\textwidth}P{0.080720823798627\textwidth}P{0.080720823798627\textwidth}P{0.080720823798627\textwidth}P{0.07974828375286042\textwidth}P{0.08169336384439359\textwidth}}
\multicolumn{2}{l}{Collection}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{2}{l}{Center, k}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 5\tabcellsep 6\tabcellsep 7\tabcellsep 8\tabcellsep 9\\
Customer\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Zone, j\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep pes\tabcellsep 650\tabcellsep 800\tabcellsep 900\tabcellsep 650\tabcellsep 700\tabcellsep 650\tabcellsep 600\tabcellsep 700\tabcellsep 800\\
1\tabcellsep mos\tabcellsep 800\tabcellsep 900\tabcellsep 1000\tabcellsep 700\tabcellsep 600\tabcellsep 700\tabcellsep 800\tabcellsep 900\tabcellsep 1000\\
\tabcellsep opt\tabcellsep 700\tabcellsep 700\tabcellsep 800\tabcellsep 600\tabcellsep 800\tabcellsep 600\tabcellsep 700\tabcellsep 600\tabcellsep 900\\
\tabcellsep pes\tabcellsep 500\tabcellsep 700\tabcellsep 700\tabcellsep 600\tabcellsep 600\tabcellsep 700\tabcellsep 700\tabcellsep 800\tabcellsep 650\\
2\tabcellsep mos\tabcellsep 750\tabcellsep 800\tabcellsep 600\tabcellsep 650\tabcellsep 750\tabcellsep 800\tabcellsep 850\tabcellsep 900\tabcellsep 700\\
\tabcellsep opt\tabcellsep 600\tabcellsep 750\tabcellsep 800\tabcellsep 700\tabcellsep 700\tabcellsep 750\tabcellsep 800\tabcellsep 700\tabcellsep 600\\
\tabcellsep pes\tabcellsep 700\tabcellsep 700\tabcellsep 600\tabcellsep 700\tabcellsep 600\tabcellsep 700\tabcellsep 600\tabcellsep 750\tabcellsep 750\\
3\tabcellsep mos\tabcellsep 800\tabcellsep 600\tabcellsep 700\tabcellsep 900\tabcellsep 1000\tabcellsep 800\tabcellsep 700\tabcellsep 800\tabcellsep 900\\
\tabcellsep opt\tabcellsep 850\tabcellsep 750\tabcellsep 500\tabcellsep 750\tabcellsep 900\tabcellsep 900\tabcellsep 650\tabcellsep 700\tabcellsep 800\\
\tabcellsep pes\tabcellsep 900\tabcellsep 1000\tabcellsep 400\tabcellsep 800\tabcellsep 800\tabcellsep 800\tabcellsep 800\tabcellsep 700\tabcellsep 700\\
4\tabcellsep mos\tabcellsep 1000\tabcellsep 1200\tabcellsep 800\tabcellsep 900\tabcellsep 700\tabcellsep 600\tabcellsep 1000\tabcellsep 800\tabcellsep 900\\
\tabcellsep opt\tabcellsep 800\tabcellsep 900\tabcellsep 500\tabcellsep 850\tabcellsep 850\tabcellsep 900\tabcellsep 900\tabcellsep 600\tabcellsep 800\\
\tabcellsep pes\tabcellsep 700\tabcellsep 800\tabcellsep 600\tabcellsep 900\tabcellsep 900\tabcellsep 800\tabcellsep 700\tabcellsep 850\tabcellsep 1000\\
5\tabcellsep mos\tabcellsep 800\tabcellsep 900\tabcellsep 700\tabcellsep 650\tabcellsep 600\tabcellsep 700\tabcellsep 800\tabcellsep 900\tabcellsep 950\\
\tabcellsep opt\tabcellsep 600\tabcellsep 750\tabcellsep 750\tabcellsep 950\tabcellsep 800\tabcellsep 900\tabcellsep 900\tabcellsep 950\tabcellsep 800\\
\tabcellsep pes\tabcellsep 800\tabcellsep 800\tabcellsep 850\tabcellsep 700\tabcellsep 900\tabcellsep 700\tabcellsep 800\tabcellsep 700\tabcellsep 550\\
6\tabcellsep mos\tabcellsep 850\tabcellsep 950\tabcellsep 750\tabcellsep 900\tabcellsep 700\tabcellsep 600\tabcellsep 550\tabcellsep 500\tabcellsep 600\\
\tabcellsep opt\tabcellsep 700\tabcellsep 900\tabcellsep 800\tabcellsep 800\tabcellsep 800\tabcellsep 950\tabcellsep 900\tabcellsep 600\tabcellsep 700\\
\tabcellsep pes\tabcellsep 750\tabcellsep 800\tabcellsep 900\tabcellsep 700\tabcellsep 900\tabcellsep 700\tabcellsep 800\tabcellsep 700\tabcellsep 550\\
7\tabcellsep mos\tabcellsep 800\tabcellsep 900\tabcellsep 950\tabcellsep 900\tabcellsep 700\tabcellsep 600\tabcellsep 550\tabcellsep 500\tabcellsep 600\\
\tabcellsep opt\tabcellsep 700\tabcellsep 700\tabcellsep 800\tabcellsep 800\tabcellsep 800\tabcellsep 950\tabcellsep 900\tabcellsep 600\tabcellsep 700\\
\tabcellsep pes\tabcellsep 800\tabcellsep 900\tabcellsep 700\tabcellsep 1000\tabcellsep 750\tabcellsep 1000\tabcellsep 500\tabcellsep 600\tabcellsep 600\\
8\tabcellsep mos\tabcellsep 900\tabcellsep 950\tabcellsep 800\tabcellsep 850\tabcellsep 800\tabcellsep 700\tabcellsep 600\tabcellsep 650\tabcellsep 550\\
\tabcellsep opt\tabcellsep 700\tabcellsep 800\tabcellsep 750\tabcellsep 900\tabcellsep 700\tabcellsep 900\tabcellsep 700\tabcellsep 700\tabcellsep 700\\
\tabcellsep pes\tabcellsep 600\tabcellsep 700\tabcellsep 1100\tabcellsep 700\tabcellsep 750\tabcellsep 700\tabcellsep 500\tabcellsep 850\tabcellsep 650\\
9\tabcellsep mos\tabcellsep 900\tabcellsep 800\tabcellsep 1000\tabcellsep 800\tabcellsep 800\tabcellsep 800\tabcellsep 600\tabcellsep 900\tabcellsep 700\\
\tabcellsep opt\tabcellsep 500\tabcellsep 600\tabcellsep 900\tabcellsep 600\tabcellsep 650\tabcellsep 600\tabcellsep 550\tabcellsep 800\tabcellsep 600\end{longtable} \par
 
\caption{\label{tab_9}Table 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_10}Table 7 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{P{0.17761194029850746\textwidth}P{0.22835820895522388\textwidth}P{0.20298507462686566\textwidth}P{0.24104477611940298\textwidth}}
Collection\tabcellsep pes\tabcellsep mos\tabcellsep opt\\
center, k\tabcellsep \tabcellsep \tabcellsep \\
1\tabcellsep 1000\tabcellsep 1200\tabcellsep 1100\\
2\tabcellsep 800\tabcellsep 700\tabcellsep 1000\\
3\tabcellsep 900\tabcellsep 800\tabcellsep 1200\\
4\tabcellsep 1100\tabcellsep 1000\tabcellsep 900\\
5\tabcellsep 800\tabcellsep 700\tabcellsep 1000\\
6\tabcellsep 1100\tabcellsep 800\tabcellsep 1000\\
7\tabcellsep 1000\tabcellsep 900\tabcellsep 1200\\
8\tabcellsep 1100\tabcellsep 800\tabcellsep 1000\\
9\tabcellsep 1000\tabcellsep 900\tabcellsep 1200\end{longtable} \par
 
\caption{\label{tab_11}Table 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_12}Table 8 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8} \par 
\begin{longtable}{P{0.07928416485900217\textwidth}P{0.16594360086767895\textwidth}P{0.1511930585683297\textwidth}P{0.1511930585683297\textwidth}P{0.1511930585683297\textwidth}P{0.1511930585683297\textwidth}}
\multicolumn{2}{l}{Glass recycling}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep center, l\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\\
collection\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
center, k\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep pes\tabcellsep 500\tabcellsep 300\tabcellsep 900\tabcellsep 400\\
1\tabcellsep mos\tabcellsep 600\tabcellsep 400\tabcellsep 500\tabcellsep 300\\
\tabcellsep opt\tabcellsep 400\tabcellsep 200\tabcellsep 600\tabcellsep 500\\
\tabcellsep pes\tabcellsep 600\tabcellsep 400\tabcellsep 600\tabcellsep 400\\
2\tabcellsep mos\tabcellsep 700\tabcellsep 750\tabcellsep 650\tabcellsep 600\\
\tabcellsep opt\tabcellsep 650\tabcellsep 500\tabcellsep 700\tabcellsep 300\\
\tabcellsep pes\tabcellsep 450\tabcellsep 600\tabcellsep 700\tabcellsep 500\\
3\tabcellsep mos\tabcellsep 500\tabcellsep 550\tabcellsep 600\tabcellsep 700\\
\tabcellsep opt\tabcellsep 550\tabcellsep 700\tabcellsep 750\tabcellsep 600\\
\tabcellsep pes\tabcellsep 700\tabcellsep 800\tabcellsep 600\tabcellsep 500\\
4\tabcellsep mos\tabcellsep 650\tabcellsep 700\tabcellsep 800\tabcellsep 700\\
\tabcellsep opt\tabcellsep 600\tabcellsep 900\tabcellsep 700\tabcellsep 600\\
\tabcellsep pes\tabcellsep 500\tabcellsep 800\tabcellsep 700\tabcellsep 700\\
5\tabcellsep mos\tabcellsep 600\tabcellsep 500\tabcellsep 450\tabcellsep 300\\
\tabcellsep opt\tabcellsep 400\tabcellsep 700\tabcellsep 600\tabcellsep 800\\
\tabcellsep pes\tabcellsep 400\tabcellsep 400\tabcellsep 500\tabcellsep 700\\
6\tabcellsep mos\tabcellsep 450\tabcellsep 550\tabcellsep 650\tabcellsep 750\\
\tabcellsep opt\tabcellsep 300\tabcellsep 500\tabcellsep 550\tabcellsep 600\\
\tabcellsep pes\tabcellsep 500\tabcellsep 600\tabcellsep 900\tabcellsep 500\\
7\tabcellsep mos\tabcellsep 800\tabcellsep 750\tabcellsep 700\tabcellsep 850\\
\tabcellsep opt\tabcellsep 600\tabcellsep 700\tabcellsep 800\tabcellsep 300\\
\tabcellsep pes\tabcellsep 700\tabcellsep 650\tabcellsep 500\tabcellsep 200\\
8\tabcellsep mos\tabcellsep 900\tabcellsep 600\tabcellsep 300\tabcellsep 400\\
\tabcellsep opt\tabcellsep 800\tabcellsep 700\tabcellsep 600\tabcellsep 300\\
\tabcellsep pes\tabcellsep 400\tabcellsep 700\tabcellsep 500\tabcellsep 400\\
9\tabcellsep mos\tabcellsep 300\tabcellsep 450\tabcellsep 400\tabcellsep 500\\
\tabcellsep opt\tabcellsep 500\tabcellsep 800\tabcellsep 600\tabcellsep 600\end{longtable} \par
 
\caption{\label{tab_13}Table 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_14}Table 9 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9} \par 
\begin{longtable}{P{0.31875\textwidth}P{0.17708333333333334\textwidth}P{0.17708333333333334\textwidth}P{0.17708333333333334\textwidth}}
Glass\tabcellsep \tabcellsep \tabcellsep \\
recycling\tabcellsep pes\tabcellsep mos\tabcellsep opt\\
center, l\tabcellsep \tabcellsep \tabcellsep \\
1\tabcellsep 500\tabcellsep 600\tabcellsep 900\\
2\tabcellsep 800\tabcellsep 900\tabcellsep 700\\
3\tabcellsep 700\tabcellsep 450\tabcellsep 400\\
4\tabcellsep 600\tabcellsep 650\tabcellsep 500\end{longtable} \par
 
\caption{\label{tab_15}Table 9 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{10} \par 
\begin{longtable}{P{0.41157894736842104\textwidth}P{0.08052631578947368\textwidth}P{0.0894736842105263\textwidth}P{0.0894736842105263\textwidth}P{0.0894736842105263\textwidth}P{0.0894736842105263\textwidth}}
\multicolumn{2}{l}{Plastic recycling}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{2}{l}{center, m}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Collection\tabcellsep \tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\\
Center, k\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep pes\tabcellsep 300\tabcellsep 400\tabcellsep 400\tabcellsep 400\\
1\tabcellsep mos\tabcellsep 400\tabcellsep 300\tabcellsep 450\tabcellsep 500\\
\tabcellsep opt\tabcellsep 500\tabcellsep 500\tabcellsep 500\tabcellsep 300\end{longtable} \par
 
\caption{\label{tab_16}Table 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{11} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_17}Table 11 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{11} \par 
\begin{longtable}{P{0.085\textwidth}P{0.255\textwidth}P{0.255\textwidth}P{0.255\textwidth}}
m\tabcellsep pes\tabcellsep mos\tabcellsep opt\\
1\tabcellsep 500\tabcellsep 600\tabcellsep 700\\
2\tabcellsep 600\tabcellsep 650\tabcellsep 550\\
3\tabcellsep 500\tabcellsep 400\tabcellsep 450\\
4\tabcellsep 500\tabcellsep 650\tabcellsep 700\end{longtable} \par
 
\caption{\label{tab_18}Table 11 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{12} \par 
\begin{longtable}{P{0.16451612903225807\textwidth}P{0.05788530465949821\textwidth}P{0.05788530465949821\textwidth}P{0.1218637992831541\textwidth}P{0.21630824372759858\textwidth}P{0.05788530465949821\textwidth}P{0.05788530465949821\textwidth}P{0.05788530465949821\textwidth}P{0.05788530465949821\textwidth}}
Year 2014\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
IV Version I\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
( ) G Volume XIV Issue\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{5}{l}{?????? ) of shipping product from production center,}\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{3}{l}{i to customer zone, j}\tabcellsep \tabcellsep \tabcellsep \\
i\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 5\tabcellsep 6\tabcellsep 7\tabcellsep 8\\
j\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
1\tabcellsep 30\tabcellsep 32\tabcellsep 34\tabcellsep 30\tabcellsep 32\tabcellsep 36\tabcellsep 38\tabcellsep 40\\
2\tabcellsep 42\tabcellsep 35\tabcellsep 36\tabcellsep 38\tabcellsep 39\tabcellsep 40\tabcellsep 42\tabcellsep 45\\
3\tabcellsep 46\tabcellsep 47\tabcellsep 48\tabcellsep 39\tabcellsep 40\tabcellsep 46\tabcellsep 47\tabcellsep 48\\
4\tabcellsep 50\tabcellsep 52\tabcellsep 42\tabcellsep 46\tabcellsep 47\tabcellsep 48\tabcellsep 49\tabcellsep 50\\
5\tabcellsep 52\tabcellsep 53\tabcellsep 54\tabcellsep 55\tabcellsep 46\tabcellsep 48\tabcellsep 50\tabcellsep 52\\
6\tabcellsep 54\tabcellsep 32\tabcellsep 34\tabcellsep 36\tabcellsep 38\tabcellsep 40\tabcellsep 42\tabcellsep 45\\
7\tabcellsep 46\tabcellsep 48\tabcellsep 50\tabcellsep 52\tabcellsep 54\tabcellsep 46\tabcellsep 48\tabcellsep 50\\
8\tabcellsep 42\tabcellsep 46\tabcellsep 40\tabcellsep 38\tabcellsep 35\tabcellsep 45\tabcellsep 46\tabcellsep 48\\
9\tabcellsep 44\tabcellsep 48\tabcellsep 38\tabcellsep 36\tabcellsep 32\tabcellsep 40\tabcellsep 48\tabcellsep 46\end{longtable} \par
 
\caption{\label{tab_19}Table 12 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{13} \par 
\begin{longtable}{P{0.04516908212560387\textwidth}P{0.07801932367149758\textwidth}P{0.07801932367149758\textwidth}P{0.18067632850241547\textwidth}P{0.07801932367149758\textwidth}P{0.07801932367149758\textwidth}P{0.07801932367149758\textwidth}P{0.07801932367149758\textwidth}P{0.07801932367149758\textwidth}P{0.07801932367149758\textwidth}}
\tabcellsep \tabcellsep \tabcellsep \multicolumn{4}{l}{j to collection center, k}\tabcellsep \tabcellsep \tabcellsep \\
J\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\tabcellsep 5\tabcellsep 6\tabcellsep 7\tabcellsep 8\tabcellsep 9\\
k\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
1\tabcellsep 24\tabcellsep 26\tabcellsep 28\tabcellsep 30\tabcellsep 39\tabcellsep 32\tabcellsep 36\tabcellsep 38\tabcellsep 40\\
2\tabcellsep 26\tabcellsep 28\tabcellsep 30\tabcellsep 32\tabcellsep 34\tabcellsep 36\tabcellsep 38\tabcellsep 40\tabcellsep 38\\
3\tabcellsep 32\tabcellsep 36\tabcellsep 38\tabcellsep 44\tabcellsep 32\tabcellsep 24\tabcellsep 28\tabcellsep 30\tabcellsep 32\\
4\tabcellsep 34\tabcellsep 34\tabcellsep 40\tabcellsep 42\tabcellsep 34\tabcellsep 32\tabcellsep 30\tabcellsep 28\tabcellsep 34\\
5\tabcellsep 30\tabcellsep 28\tabcellsep 32\tabcellsep 36\tabcellsep 34\tabcellsep 35\tabcellsep 28\tabcellsep 30\tabcellsep 32\\
6\tabcellsep 36\tabcellsep 32\tabcellsep 38\tabcellsep 40\tabcellsep 36\tabcellsep 26\tabcellsep 32\tabcellsep 48\tabcellsep 38\\
7\tabcellsep 38\tabcellsep 34\tabcellsep 36\tabcellsep 38\tabcellsep 38\tabcellsep 32\tabcellsep 36\tabcellsep 46\tabcellsep 36\\
8\tabcellsep 36\tabcellsep 36\tabcellsep 34\tabcellsep 36\tabcellsep 36\tabcellsep 44\tabcellsep 38\tabcellsep 44\tabcellsep 32\\
9\tabcellsep 40\tabcellsep 38\tabcellsep 32\tabcellsep 36\tabcellsep 40\tabcellsep 42\tabcellsep 40\tabcellsep 42\tabcellsep 34\end{longtable} \par
 
\caption{\label{tab_20}Table 13 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{14} \par 
\begin{longtable}{P{0.1074712643678161\textwidth}P{0.18563218390804598\textwidth}P{0.18563218390804598\textwidth}P{0.18563218390804598\textwidth}P{0.18563218390804598\textwidth}}
l\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\\
k\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
1\tabcellsep 50\tabcellsep 48\tabcellsep 50\tabcellsep 52\\
2\tabcellsep 52\tabcellsep 46\tabcellsep 54\tabcellsep 54\\
3\tabcellsep 48\tabcellsep 44\tabcellsep 56\tabcellsep 55\\
4\tabcellsep 46\tabcellsep 42\tabcellsep 58\tabcellsep 42\\
5\tabcellsep 44\tabcellsep 44\tabcellsep 42\tabcellsep 44\\
6\tabcellsep 50\tabcellsep 46\tabcellsep 44\tabcellsep 46\\
7\tabcellsep 52\tabcellsep 48\tabcellsep 46\tabcellsep 48\\
8\tabcellsep 54\tabcellsep 50\tabcellsep 48\tabcellsep 50\\
9\tabcellsep 50\tabcellsep 52\tabcellsep 50\tabcellsep 52\end{longtable} \par
 
\caption{\label{tab_21}Table 14 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{15} \par 
\begin{longtable}{P{0.5342857142857143\textwidth}P{0.085\textwidth}P{0.0769047619047619\textwidth}P{0.0769047619047619\textwidth}P{0.0769047619047619\textwidth}}
m\tabcellsep 1\tabcellsep 2\tabcellsep 3\tabcellsep 4\\
k\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
1\tabcellsep 16\tabcellsep 18\tabcellsep 20\tabcellsep 22\\
2\tabcellsep 24\tabcellsep 18\tabcellsep 22\tabcellsep 24\\
3\tabcellsep 26\tabcellsep 20\tabcellsep 18\tabcellsep 16\\
4\tabcellsep 28\tabcellsep 18\tabcellsep 22\tabcellsep 18\\
5\tabcellsep 30\tabcellsep 28\tabcellsep 18\tabcellsep 18\\
6\tabcellsep 32\tabcellsep 26\tabcellsep 20\tabcellsep 20\\
7\tabcellsep 34\tabcellsep 24\tabcellsep 16\tabcellsep 22\\
8\tabcellsep 32\tabcellsep 22\tabcellsep 20\tabcellsep 24\\
9\tabcellsep 18\tabcellsep 20\tabcellsep 18\tabcellsep 18\\
\multicolumn{5}{l}{Environmental impact of recycling one unit of plastic product, ???? ?????? =20}\\
\multicolumn{4}{l}{? ?(???? ?????? + ?? ???? ?????? ) = 1510}\tabcellsep \\
??\tabcellsep ??\tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_22}Table 15 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{16} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_23}Table 16 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{16} \par 
\begin{longtable}{P{0.6118131868131867\textwidth}P{0.03502747252747253\textwidth}P{0.04903846153846154\textwidth}P{0.03502747252747253\textwidth}P{0.03502747252747253\textwidth}P{0.04903846153846154\textwidth}P{0.03502747252747253\textwidth}}
l, m\tabcellsep pes\tabcellsep ?? ?? mos\tabcellsep opt\tabcellsep pes\tabcellsep ?? ?? mos\tabcellsep opt\\
1\tabcellsep 100\tabcellsep 150\tabcellsep 200\tabcellsep 180\tabcellsep 150\tabcellsep 200\\
2\tabcellsep 200\tabcellsep 150\tabcellsep 180\tabcellsep 180\tabcellsep 200\tabcellsep 250\\
3\tabcellsep 190\tabcellsep 200\tabcellsep 250\tabcellsep 220\tabcellsep 180\tabcellsep 250\\
4\tabcellsep 230\tabcellsep 250\tabcellsep 180\tabcellsep 240\tabcellsep 250\tabcellsep 180\\
\multicolumn{7}{l}{Simplifications of the constraints are obtained by developing a program using Code blocks programming}\\
software:\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
minw 1 = Constraints,\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
?? ???? ? 15012\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
?? ???? ? 10730.61\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
?? ???? ? 13860 or ?? ???? ? 0\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
?? ???? ? 18639 or ?? ???? ? 0\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
?? ???? ? 7281\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
?? ???? ? 6736.5\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_24}Table 16 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{17} \par 
\begin{longtable}{P{0.584375\textwidth}P{0.265625\textwidth}}
Symbol\tabcellsep Modified\\
\tabcellsep Symbol\\
?? ??\tabcellsep X\\
?? ??\tabcellsep Y\\
?? ????\tabcellsep Z\\
?? ????\tabcellsep W\\
?? ????\tabcellsep M\\
?? ????\tabcellsep N\end{longtable} \par
 
\caption{\label{tab_25}Table 17 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_28}}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US)} 			\footnote{Optimization of Supply Chain Network Perspective Environmental Impact based on FuzzyMathematical Programming} 			\footnote{© 2014 Global Journals Inc. (US)Global Journal of Researches in Engineering} 		 		\backmatter  			 
\subsection[{Appendix}]{Appendix}\par
The Jimenez et al. \hyperref[b8]{[9]} method is based on the definition of the ''expected interval'' and the ''expected value'' of a fuzzy number. Assume that ? is a triangular fuzzy number. The following equation can be defined as the membership function of ?.\par
Here ?? ?????? , ?? ?????? ?????? ?? ?????? are the three prominent points (the most likely, the most pessimistic and the most optimistic values), respectively. Eqs. (  {\ref 13}) And (  {\ref 14}) define the expected interval (EI) and the expected value (EV) of triangular fuzzy number ?. 			 			  				\begin{bibitemlist}{1}
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\bibitem[Jayaraman et al. ()]{b14}\label{b14} 	 		‘A closed-loop logistics model for manufacturing’.  		 			V Jayaraman 		,  		 			V D R GuigeJr 		,  		 			R Srivastava 		.  	 	 		\textit{J. Oper. Res. Soc}  		1999. 50 p. .  	 
\bibitem[Ko and Evans ()]{b20}\label{b20} 	 		‘A genetic-based heuristic for the dynamic integrated forward/reverse logistics network for 3PLs’.  		 			H J Ko 		,  		 			G W Evans 		.  	 	 		\textit{Comput. Oper. Res}  		2007. 34 p. .  	 
\bibitem[Pishvaee et al. ()]{b19}\label{b19} 	 		‘A memetic algorithm for bi-objective integrated forward/reverse logistics network design’.  		 			M S Pishvaee 		,  		 			R Z Farahani 		,  		 			W Dullaert 		.  	 	 		\textit{Comput. Oper. Res}  		2010. 37 p. .  	 
\bibitem[Pirkul and Jayaraman ()]{b0}\label{b0} 	 		‘A multi-commodity, multiplant, capacitated facility location problem: formulation and efficient heuristic solution’.  		 			H Pirkul 		,  		 			V Jayaraman 		.  	 	 		\textit{Computers \& Operations Research}  		1998. 25  (10)  p. .  	 
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\end{bibitemlist}
 			 		 	 
\end{document}
