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# A three echelon revenue oriented green supply chain network design

The reviewing process of this paper was handled by Editors A. (Nima) Mirzazadeh, Kharazmi University, Tehran, Iran, and Gerhard-Wilhelm Weber, Middle East Technical University, Ankara, Turkey. This paper was for the occasion of the 12th International Conference on Industrial Engineering (ICIE 2016), which was held in Tehran, Iran during 25-26 January, 2016

• Green supply chain network designing has been studied during last decades. As carbon emissions considered as a major index in today's activities around the world, here a three echelon-multi product network including manufacturer, distributor, retailer have been provided and tried to minimize the pollution gathered from manufacturing and distribution of products all over the chains which causes extra costs as penalty to the system.

As we faced with these penalties, the model determines selling prices of products for manufacturer and distribution center simultaneously by locating these centers in order to maximize the profits all around the network. Finally, the proposed model is solved through the numerical examples and the sensitivity analysis and important parameters are reported to find some management insights.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

 Citation:

• Figure 1.  A three echelon supply chain network

Figure 2.  The impact of demands on selling price

Figure 3.  The impact of carbon dioxid emissions on selling price

Table 1.  Data for numerical example

 $f_{j}$ Random between [200000, 300000] $a_{k}$ Random between [10000, 10100] $w_{i}^{k}$ Random between [1000, 2000] $c_{mk}$ Random between [1000, 1100] $\gamma _{mk}$ Random between [10000, 12000] $CO_{2}$ Random between [450000000, 500000000] $T_{mjk}$ Random between [500, 600] $v_{jk}$ Random between [200, 300] $R_{m}^{k}$ Random between [10000, 10100] $d_{ij}$ Random between [50, 60] $T_{jik}$ Random between [500, 600] $\alpha _{ji}$ Random between [400, 450] $d_{mj}$ Random between [50, 60] $b$ Random between [50000000, 60000000] $\alpha _{mj}$ Random between [400, 450] $P$ Random between [6000, 7000] $q_{j}$ Random between [10000000, 10100000] $l_{k}$ Random between [1000, 2000]

Table 2.  The decision variables value

 $X_{ijk}$ $\begin{array}{l} \begin{array}{ccccc} X_{111} {=\, \, \, \, \, 0\, \, \, \, }&{X_{112} =\, \, \, \, \, 0\, \, \, \, \, }&{X_{113} =1515}&{X_{114} =\, \, \, \, 0\, \, \, \, }&{X_{115} =\, \, \, \, 0\, \, \, \, } \\ {X_{121} =\, \, \, \, \, 0\, \, \, \, }&{X_{122} =1203}&{X_{123} =\, \, \, \, 0\, \, \, \, }&{X_{124} =1545}&{X_{125} =1907} \\ {X_{131} =\, 1657}&{X_{132} =\, \, \, \, 0\, \, \, \, }&{X_{133} =\, \, \, \, 0\, \, \, \, }&{X_{134} =\, \, \, \, 0\, \, \, \, }&{X_{135} =\, \, \, \, 0\, \, \, \, } \\ {X_{211} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{212} =\, \, \, \, 0\, \, \, \, }&{X_{213} =1069}&{X_{214} =\, \, \, \, 0\, \, \, \, }&{X_{215} =\, \, \, \, 0\, \, \, \, } \\ {X_{221} =1804}&{X_{222} =1983}&{X_{223} =\, \, \, \, 0\, \, \, \, }&{X_{224} =1196}&{X_{225} =1695} \\ {X_{311} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{312} =\, \, \, \, 0\, \, \, \, }&{X_{313} =1217}&{X_{314} =\, \, \, \, 0\, \, \, \, }&{X_{315} =\, \, \, \, 0\, \, \, \, } \\ {X_{321} =1639}&{X_{322} =1333}&{X_{323} =\, \, \, \, 0\, \, \, \, }&{X_{324} =1632}&{X_{325} =1012} \\ {X_{411} =1122}&{X_{412} =\, \, \, \, 0\, \, \, \, }&{X_{413} =1946}&{X_{414} =\, \, \, \, 0\, \, \, \, }&{X_{415} =\, \, \, \, 0\, \, \, \, } \\ {X_{421} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{422} =1687}&{X_{423} =\, \, \, \, 0\, \, \, \, }&{X_{424} =1709}&{X_{425} =1075} \\ {X_{511} =1510}&{X_{512} =\, \, \, \, 0\, \, \, \, }&{X_{513} =1196}&{X_{514} =\, \, \, \, 0\, \, \, \, }&{X_{515} =\, \, \, \, 0\, \, \, \, } \\ {X_{521} =\, \, \, \, 0\, \, \, \, \, \, \, }&{X_{522} =1510}&{X_{523} =\, \, \, \, 0\, \, \, \, }&{X_{524} =1273}&{X_{525} =1086}\end{array}\end{array}$ $\begin{array}{l}\\ \\ U_{mjk} \\ \\ \\ \\ \\ y_{j}\end{array}$ $\begin{array}{l} {U_{111} =9575} \\ {U_{121} =25289} \\ {U_{131} =1657} \\ \\{y_{1} =1} \\ {y_{2} =1} \\ {y_{3} =1}\end{array}$ Objective function $5.6*10^{11}$

Table 3.  The optimal value of binary decision variable and objective function

 Problem size(I*J*M*K) Optimal value of binary decision variable Objective function 5*5*5*5 $y_{j} =[11100]$ $5.6*10^{11}$ 15*15*15*15 $y_{j} =[110111111001111]$ $5.1*10^{12}$ 20*20*20*20 $y_{j} =[11110110101101101111]$ $9.2*10^{12}$ 25*25*25*25 $y_{j} =[1111011111001111101101011]$ $1.4*10^{13}$

Table 4.  The optimal value of binary decision variable and objective function

 $S_{mk}$ $\begin{array}{ccccc} {S_{11} =9999999}&{S_{12} =1481632}&{S_{13} =1433065}&{S_{14} =1498182}&{S_{15} =1306987} \\ {S_{21} =6419183}&{S_{22} =1481632}&{S_{23} =1433066}&{S_{24} =1498182}&{S_{25} =1306987} \\ {S_{31} =6438095}&{S_{32} =1481632}&{S_{33} =1433065}&{S_{34} =1498182}&{S_{35} =1306987} \\ {S_{41} =6426776}&{S_{42} =1481633}&{S_{43} =1433065}&{S_{44} =1498182}&{S_{45} =1306988} \\ {S_{51} =6432022}&{S_{52} =1481632}&{S_{53} =1433065}&{S_{54} =1498182}&{S_{55} =1306987} \end{array}$ $U_{mjk}$ $\begin{array}{l} {U_{111} =9575} \\ {U_{121} =25289} \\ {U_{131} =1657} \end{array}$ $S_{jk}^{'}$ $\begin{array}{ccccc} {S'_{11} =9999999}&{S'_{12} =1825318}&{S'_{13} =9999999}&{S'_{14} =1904827}&{S'_{15} =1419765} \\ {S'_{21} =9999999}&{S'_{22} =9999999}&{S'_{23} =1444720}&{S'_{24} =9999999}&{S'_{25} =9999999} \\ {S'_{31} =9999999}&{S'_{32} =1493339}&{S'_{33} =1780413}&{S'_{34} =1509851}&{S'_{35} =1318645} \\ {S'_{41} =9999999}&{S'_{42} =1493334}&{S'_{43} =1444775}&{S'_{44} =1509885}&{S'_{45} =1318716} \\ {S'_{51} =9999999}&{S'_{52} =1493334}&{S'_{53} =1444775}&{S'_{54} =1509885}&{S'_{55} =1318716} \end{array}$ $y_{j}$ $\begin{array}{l} {y_{1} =1} \\ {y_{2} =1} \\ {y_{3} =1} \end{array}$ $X_{ijk}$ $\begin{array}{ccccc} {X_{111} =\, \, \, \, \, 0\, \, \, \, }&{X_{112} =\, \, \, \, \, 0\, \, \, \, \, }&{X_{113} =1515}&{X_{114} =\, \, \, \, 0\, \, \, \, }&{X_{115} =\, \, \, \, 0\, \, \, \, } \\ {X_{121} =\, \, \, \, \, 0\, \, \, \, }&{X_{122} =1203}&{X_{123} =\, \, \, \, 0\, \, \, \, }&{X_{124} =1545}&{X_{125} =1907} \\ {X_{131} =\, 1657}&{X_{132} =\, \, \, \, 0\, \, \, \, }&{X_{133} =\, \, \, \, 0\, \, \, \, }&{X_{134} =\, \, \, \, 0\, \, \, \, }&{X_{135} =\, \, \, \, 0\, \, \, \, } \\ {X_{211} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{212} =\, \, \, \, 0\, \, \, \, }&{X_{213} =1069}&{X_{214} =\, \, \, \, 0\, \, \, \, }&{X_{215} =\, \, \, \, 0\, \, \, \, } \\ {X_{221} =1804}&{X_{222} =1983}&{X_{223} =\, \, \, \, 0\, \, \, \, }&{X_{224} =1196}&{X_{225} =1695} \\ {X_{311} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{312} =\, \, \, \, 0\, \, \, \, }&{X_{313} =1217}&{X_{314} =\, \, \, \, 0\, \, \, \, }&{X_{315} =\, \, \, \, 0\, \, \, \, } \\ {X_{321} =1639}&{X_{322} =1333}&{X_{323} =\, \, \, \, 0\, \, \, \, }&{X_{324} =1632}&{X_{325} =1012} \\ {X_{411} =1122}&{X_{412} =\, \, \, \, 0\, \, \, \, }&{X_{413} =1946}&{X_{414} =\, \, \, \, 0\, \, \, \, }&{X_{415} =\, \, \, \, 0\, \, \, \, } \\ {X_{421} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{422} =1687}&{X_{423} =\, \, \, \, 0\, \, \, \, }&{X_{424} =1709}&{X_{425} =1075} \\ {X_{511} =1510}&{X_{512} =\, \, \, \, 0\, \, \, \, }&{X_{513} =1196}&{X_{514} =\, \, \, \, 0\, \, \, \, }&{X_{515} =\, \, \, \, 0\, \, \, \, } \\ {X_{521} =\, \, \, \, 0\, \, \, \, \, \, \, }&{X_{522} =1510}&{X_{523} =\, \, \, \, 0\, \, \, \, }&{X_{524} =1273}&{X_{525} =1086} \end{array}$ $g_{mjk}^{'}$ $\begin{array}{l} {g'_{111} ={\rm 95749990434}} \\ {g'_{121} ={\rm 95749990434}} \\ {g'_{131} ={\rm 16569998344}} \end{array}$ $g_{ijk}$ $\begin{array}{ccccc} {g_{111} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{112} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{113} ={\rm 15149998486}}&{g_{114} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{115} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, } \\ {g_{121} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{122} ={\rm 12029998798}}&{g_{123} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{124} ={\rm 15449998456}}&{g_{125} ={\rm 19069998094}} \\ {g_{131} =\, {\rm 16569998344}}&{g_{132} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{133} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{134} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{135} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, } \\ {g_{211} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{212} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{213} ={\rm 10689998932}}&{g_{214} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{215} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, } \\ {g_{221} ={\rm 18039998197}}&{g_{222} ={\rm 19829998018}}&{g_{223} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{224} ={\rm 11959998805}}&{g_{225} ={\rm 16949998306}} \\ {g_{311} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{312} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{313} ={\rm 12169998784}}&{g_{314} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{315} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, } \\ {g_{321} ={\rm 16389998362}}&{g_{322} ={\rm 13329998668}}&{g_{323} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{324} ={\rm 16319998369}}&{g_{325} ={\rm 10119998989}} \\ {g_{411} ={\rm 11219998879}}&{g_{412} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{413} ={\rm 19459998055}}&{g_{414} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{415} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, } \\ {g_{421} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{422} ={\rm 16869998314}}&{g_{423} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{424} ={\rm 17089998292}}&{g_{425} ={\rm 10749998926}} \\ {g_{511} ={\rm 15099998491}}&{g_{512} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{513} ={\rm 11959998805}}&{g_{514} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{515} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, } \\ {g_{521} =\, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{g_{522} ={\rm 15099998491}}&{\, g_{523} =\, \, \, \, \, \, \, \, \, \, \, \, \, \, 0\, \, \, \, \, \, \, \, \, \, \, \, \, \, }&{\, \, g_{524} ={\rm 12729998728}}&{g_{525} ={\rm 10859998915}} \end{array}$ Objective function $5.6*10^{11}$
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