Closed-loop supply chain network equilibrium model with retailer-collection under legislation

Wenbin Wang; Peng Zhang; Junfei Ding; Jian Li; Hao Sun; Lingyun He

doi:10.3934/jimo.2018039

Article Contents

2019, Volume 15, Issue 1: 199-219. Doi: 10.3934/jimo.2018039

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Closed-loop supply chain network equilibrium model with retailer-collection under legislation

1.
School of Management, China University of Mining and Technology, Xuzhou 221116, China
2.
College of Engineering, Nanjing Agricultural University, Nanjing 210031, China
3.
School of Business, Qingdao University, Qingdao 266071, China

^* Corresponding author: lijianzh@njau.edu.cn(Jian Li); rivaldoking@126.com(Hao Sun).
^* Corresponding author: lijianzh@njau.edu.cn(Jian Li); rivaldoking@126.com(Hao Sun).

Received: April 30, 2017

Revised: July 31, 2017

Early access: April 2018

Published: December 2018

The first author is supported by the Fundamental Research Funds for the Central Universities of China (Project No. 2017XKQY034)

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Abstract

This paper examines the waste of electrical and electronic equipments (WEEE) and draws on variational inequalities to model the closed-loop supply chain network. The network consists of manufacturers, retailers and consumer markets engaging in a Cournot-Nash game. Retailers are responsible for collecting WEEE in the network. It is assumed that the price of the remanufactured goods is different from that of the newly manufactured ones. The network equilibrium occurs when all players agree on volumes and prices. Several properties of the model are examined and the modified projection method is utilized to obtain the optimal solutions. Numerical examples are provided to illustrate the impact of CLSC parameters on the profits of channel members and consumer benefits, and to provide policy support for governments. We find that it is necessary to regulate a medium collection rate and a certain minimum recovery rate. This is also advantageous to manufacturers in producing new manufactured products. The impact of collection rate and recovery rate on manufacturers are greater than that on retailers. Consumers can benefit from the increase of the recovery rate as well as the collection rate.

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Mathematics Subject Classification: Primary: 90B10; Secondary: 91A50, 91A10.

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Figure 1. Closed-loop supply chain network with WEEE collected by retailers

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Figure 2. The volume changes of three kinds of products with the changes of collection rate while $\beta = 0.5$ are fixed

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Figure 3. The volume changes of three kinds of products with the changes of recovery rate while $\alpha = 1$ are fixed

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Table 1. The prices under different collection rate ($\alpha$), given $\beta = 0.5$

	$\alpha=0$	$\alpha=0.2$	$\alpha=0.4$	$\alpha=0.6$	$\alpha=0.8$	$\alpha=1$
$w_i^{f^*}$	352.8712	352.8712	358.2704	383.6992	414.7223	435.5493
$w_j^{r^*}$	59.8369	59.8369	71.6460	98.1422	108.6234	106.8103
$w_i^{r^*}$	384.0070	384.0070	376.6145	362.1067	359.6196	375.6179
$P_j^{f^*}$	402.8527	402.8527	406.0255	421.8723	441.8835	456.1049
$P_k^{r^*}$	39.8914	39.8914	47.7639	65.4282	72.4157	71.2072
$P_j^{r^*}$	393.9832	393.9832	388.5579	378.4611	377.7207	390.6693

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Table 2. The prices under different recovery rate ($\beta$), given $\alpha = 1$

	$\beta=0.1$	$\beta=0.2$	$\beta=0.3$	$\beta=0.4$	$\beta=0.5$
$w_i^{f^*}$	422.8170	424.1308	427.8478	433.8971	435.5493
$w_j^{r^*}$	91.0883	97.7935	103.2339	106.4136	106.8103
$w_i^{r^*}$	424.1402	409.5847	394.2371	378.9959	375.6179
$P_j^{f^*}$	450.0756	450.2139	451.9405	455.1846	456.1049
$P_k^{r^*}$	60.7962	65.1957	68.8227	70.9424	71.2072
$P_j^{r^*}$	427.1726	416.1012	404.5575	393.1814	390.6693

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Table 3. The profits of manufacturers and retailers with different collection rate ($\alpha$), given $\beta = 0.5$

Total profits	$\alpha \le 0.2$	$\alpha=0.4$	$\alpha=0.6$	$\alpha=0.8$	$\alpha=1$
Manufactures	13642.876	17247.346	15531.509	12759.803	10108.842
Retailers	2995.498	2993.549	2794.858	2376.378	1916.658

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Table 4. The profits of manufacturers and retailers with different recovery rate ($\beta$), given $\alpha = 1$

Total profits	$\beta=0.1$	$\beta=0.2$	$\beta=0.3$	$\beta=0.4$	$\beta\ge0.5$
Manufactures	9082.426	9616.632	9981.219	10112.544	10108.842
Retailers	1669.838	1785.409	1944.052	2113.821	1916.658

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