A three echelon revenue oriented green supply chain network design

Ashkan Mohsenzadeh Ledari; Alireza Arshadi Khamseh; Mohammad Mohammadi

doi:10.3934/naco.2018009

Article Contents

2018, Volume 8, Issue 2: 157-168. Doi: 10.3934/naco.2018009

This issue Previous Article Fuzzy target-environment networks and fuzzy-regression approaches Next Article An integrated inventory model with variable holding cost under two levels of trade-credit policy

A three echelon revenue oriented green supply chain network design

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

* Corresponding author. E-mail: Ar_arshadi@khu.ac.ir
* Corresponding author. E-mail: Ar_arshadi@khu.ac.ir

Received: April 2016

Revised: October 2017

Published: May 2018

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.

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Abstract

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.

Keywords:

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

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Figure 1. A three echelon supply chain network

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Figure 2. The impact of demands on selling price

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

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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]

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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} $

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

*Problem size(IJMK)**	Optimal value of binary decision variable	Objective function
*5555**	$y_{j} =[11100]$	$5.6*10^{11} $
*15151515**	$y_{j} =[110111111001111]$	$5.1*10^{12} $
*20202020**	$y_{j} =[11110110101101101111]$	$9.2*10^{12} $
*25252525**	$y_{j} =[1111011111001111101101011]$	$1.4*10^{13} $

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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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