American Institute of Mathematical Sciences

June  2018, 8(2): 157-168. doi: 10.3934/naco.2018009

A three echelon revenue oriented green supply chain network design

 Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Received  April 2016 Revised  October 2017 Published  May 2018

Fund Project: 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.

Citation: Ashkan Mohsenzadeh Ledari, Alireza Arshadi Khamseh, Mohammad Mohammadi. A three echelon revenue oriented green supply chain network design. Numerical Algebra, Control & Optimization, 2018, 8 (2) : 157-168. doi: 10.3934/naco.2018009
References:

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References:
A three echelon supply chain network
The impact of demands on selling price
The impact of carbon dioxid emissions on selling price
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]
 $f_{j}$ 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]
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 $5.6*10^{11}$
 $X_{ijk}$ $\begin{array}{l} \begin{array}{ccccc} X_{111} {=\, \, \, \, \, 0\, \, \, \, }&{X_{112} =\, \, \, \, \, 0\, \, \, \, \, }&{X_{113} =1515}&{X_{114} =\, \, \, \, 0\, \, \, \, }&{X_{115} =\, \, \, \, 0\, \, \, \, } \\ {X_{121} =\, \, \, \, \, 0\, \, \, \, }&{X_{122} =1203}&{X_{123} =\, \, \, \, 0\, \, \, \, }&{X_{124} =1545}&{X_{125} =1907} \\ {X_{131} =\, 1657}&{X_{132} =\, \, \, \, 0\, \, \, \, }&{X_{133} =\, \, \, \, 0\, \, \, \, }&{X_{134} =\, \, \, \, 0\, \, \, \, }&{X_{135} =\, \, \, \, 0\, \, \, \, } \\ {X_{211} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{212} =\, \, \, \, 0\, \, \, \, }&{X_{213} =1069}&{X_{214} =\, \, \, \, 0\, \, \, \, }&{X_{215} =\, \, \, \, 0\, \, \, \, } \\ {X_{221} =1804}&{X_{222} =1983}&{X_{223} =\, \, \, \, 0\, \, \, \, }&{X_{224} =1196}&{X_{225} =1695} \\ {X_{311} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{312} =\, \, \, \, 0\, \, \, \, }&{X_{313} =1217}&{X_{314} =\, \, \, \, 0\, \, \, \, }&{X_{315} =\, \, \, \, 0\, \, \, \, } \\ {X_{321} =1639}&{X_{322} =1333}&{X_{323} =\, \, \, \, 0\, \, \, \, }&{X_{324} =1632}&{X_{325} =1012} \\ {X_{411} =1122}&{X_{412} =\, \, \, \, 0\, \, \, \, }&{X_{413} =1946}&{X_{414} =\, \, \, \, 0\, \, \, \, }&{X_{415} =\, \, \, \, 0\, \, \, \, } \\ {X_{421} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{422} =1687}&{X_{423} =\, \, \, \, 0\, \, \, \, }&{X_{424} =1709}&{X_{425} =1075} \\ {X_{511} =1510}&{X_{512} =\, \, \, \, 0\, \, \, \, }&{X_{513} =1196}&{X_{514} =\, \, \, \, 0\, \, \, \, }&{X_{515} =\, \, \, \, 0\, \, \, \, } \\ {X_{521} =\, \, \, \, 0\, \, \, \, \, \, \, }&{X_{522} =1510}&{X_{523} =\, \, \, \, 0\, \, \, \, }&{X_{524} =1273}&{X_{525} =1086}\end{array}\end{array}$ $\begin{array}{l}\\ \\ U_{mjk} \\ \\ \\ \\ \\ y_{j}\end{array}$ $\begin{array}{l} {U_{111} =9575} \\ {U_{121} =25289} \\ {U_{131} =1657} \\ \\{y_{1} =1} \\ {y_{2} =1} \\ {y_{3} =1}\end{array}$ Objective function $5.6*10^{11}$
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 $y_{j} =[1111011111001111101101011]$ $1.4*10^{13}$
 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 $y_{j} =[1111011111001111101101011]$ $1.4*10^{13}$
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 $5.6*10^{11}$
 $S_{mk}$ $\begin{array}{ccccc} {S_{11} =9999999}&{S_{12} =1481632}&{S_{13} =1433065}&{S_{14} =1498182}&{S_{15} =1306987} \\ {S_{21} =6419183}&{S_{22} =1481632}&{S_{23} =1433066}&{S_{24} =1498182}&{S_{25} =1306987} \\ {S_{31} =6438095}&{S_{32} =1481632}&{S_{33} =1433065}&{S_{34} =1498182}&{S_{35} =1306987} \\ {S_{41} =6426776}&{S_{42} =1481633}&{S_{43} =1433065}&{S_{44} =1498182}&{S_{45} =1306988} \\ {S_{51} =6432022}&{S_{52} =1481632}&{S_{53} =1433065}&{S_{54} =1498182}&{S_{55} =1306987} \end{array}$ $U_{mjk}$ $\begin{array}{l} {U_{111} =9575} \\ {U_{121} =25289} \\ {U_{131} =1657} \end{array}$ $S_{jk}^{'}$ $\begin{array}{ccccc} {S'_{11} =9999999}&{S'_{12} =1825318}&{S'_{13} =9999999}&{S'_{14} =1904827}&{S'_{15} =1419765} \\ {S'_{21} =9999999}&{S'_{22} =9999999}&{S'_{23} =1444720}&{S'_{24} =9999999}&{S'_{25} =9999999} \\ {S'_{31} =9999999}&{S'_{32} =1493339}&{S'_{33} =1780413}&{S'_{34} =1509851}&{S'_{35} =1318645} \\ {S'_{41} =9999999}&{S'_{42} =1493334}&{S'_{43} =1444775}&{S'_{44} =1509885}&{S'_{45} =1318716} \\ {S'_{51} =9999999}&{S'_{52} =1493334}&{S'_{53} =1444775}&{S'_{54} =1509885}&{S'_{55} =1318716} \end{array}$ $y_{j}$ $\begin{array}{l} {y_{1} =1} \\ {y_{2} =1} \\ {y_{3} =1} \end{array}$ $X_{ijk}$ $\begin{array}{ccccc} {X_{111} =\, \, \, \, \, 0\, \, \, \, }&{X_{112} =\, \, \, \, \, 0\, \, \, \, \, }&{X_{113} =1515}&{X_{114} =\, \, \, \, 0\, \, \, \, }&{X_{115} =\, \, \, \, 0\, \, \, \, } \\ {X_{121} =\, \, \, \, \, 0\, \, \, \, }&{X_{122} =1203}&{X_{123} =\, \, \, \, 0\, \, \, \, }&{X_{124} =1545}&{X_{125} =1907} \\ {X_{131} =\, 1657}&{X_{132} =\, \, \, \, 0\, \, \, \, }&{X_{133} =\, \, \, \, 0\, \, \, \, }&{X_{134} =\, \, \, \, 0\, \, \, \, }&{X_{135} =\, \, \, \, 0\, \, \, \, } \\ {X_{211} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{212} =\, \, \, \, 0\, \, \, \, }&{X_{213} =1069}&{X_{214} =\, \, \, \, 0\, \, \, \, }&{X_{215} =\, \, \, \, 0\, \, \, \, } \\ {X_{221} =1804}&{X_{222} =1983}&{X_{223} =\, \, \, \, 0\, \, \, \, }&{X_{224} =1196}&{X_{225} =1695} \\ {X_{311} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{312} =\, \, \, \, 0\, \, \, \, }&{X_{313} =1217}&{X_{314} =\, \, \, \, 0\, \, \, \, }&{X_{315} =\, \, \, \, 0\, \, \, \, } \\ {X_{321} =1639}&{X_{322} =1333}&{X_{323} =\, \, \, \, 0\, \, \, \, }&{X_{324} =1632}&{X_{325} =1012} \\ {X_{411} =1122}&{X_{412} =\, \, \, \, 0\, \, \, \, }&{X_{413} =1946}&{X_{414} =\, \, \, \, 0\, \, \, \, }&{X_{415} =\, \, \, \, 0\, \, \, \, } \\ {X_{421} =\, \, \, \, \, 0\, \, \, \, \, \, }&{X_{422} =1687}&{X_{423} =\, \, \, \, 0\, \, \, \, }&{X_{424} =1709}&{X_{425} =1075} \\ {X_{511} =1510}&{X_{512} =\, \, \, \, 0\, \, \, \, }&{X_{513} =1196}&{X_{514} =\, \, \, \, 0\, \, \, \, }&{X_{515} =\, \, \, \, 0\, \, \, \, } \\ {X_{521} =\, \, \, \, 0\, \, \, \, \, \, \, }&{X_{522} =1510}&{X_{523} =\, \, \, \, 0\, \, \, \, }&{X_{524} =1273}&{X_{525} =1086} \end{array}$ $g_{mjk}^{'}$ $\begin{array}{l} {g'_{111} ={\rm 95749990434}} \\ {g'_{121} ={\rm 95749990434}} \\ {g'_{131} ={\rm 16569998344}} \end{array}$ $g_{ijk}$ $\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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