Decision-making in a retailer-led closed-loop supply chain involving a third-party logistics provider

Xiao-Xu Chen; Peng Xu; Jiao-Jiao Li; Thomas Walker; Guo-Qiang Yang

doi:10.3934/jimo.2021014

Article Contents

2022, Volume 18, Issue 2: 1161-1183. Doi: 10.3934/jimo.2021014

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Decision-making in a retailer-led closed-loop supply chain involving a third-party logistics provider

1.
School of Economics and Management, Shanxi University, Taiyuan 030006, China
2.
China Research Institute of Enterprise Governed by Law, Southwest University of Political Science and Law, Chongqing 401120, China
3.
John Molson School of Business, Concordia University, Montreal, QC H3G 1M8, Canada
4.
Department of Medical Imaging, Shanxi Medical University, Taiyuan 030001, China

^* Corresponding author: Peng Xu
^* Corresponding author: Peng Xu

Received: April 30, 2020

Revised: October 31, 2020

Early access: December 2020

Published: March 2022

The first author is supported by Shanxi Intelligent Logistitics Management Service Industry Innovation Science Group Project. The second author is supported by Southwest Univerisity of Political Science Law grant 2019XZZD-10, National Natural Science Foundation of China grant 71872154 and the Youth Foundation of Humanities and Social Sciences of Ministry of Education of China grant 20YJA790030

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Abstract

This paper investigates decisions in a three-echelon closed-loop supply chain composed of one manufacturer, one retailer, and one third-party logistics provider (3PL), with the retailer being dominant. Inspired by game theory, we develop an equilibrium model for a retailer-led, closed-loop supply chain under logistics outsourcing. We derive the optimal forward and reverse logistics decisions of each supply chain member. This article analyzes the effects of market size, consumers' sensitivity to sales prices, the proportion of logistics costs, consumers' environmental awareness, and consumers' sensitivity to recycling prices on decision-making process. Finally, we provide a numerical example to verify the validity of our conclusions. Our results indicate that the higher the manufacturer's share in the forward logistics cost, the higher the sales price, the wholesale price, and the forward logistics service price, and the lower the order quantity. The higher the manufacturer's share in the reverse logistics costs, the lower the recycling price, the transfer price, and the recycling amount, and the higher the reverse logistics service price. Whether it is forward logistics or not, the higher the manufacturer's share in the logistics costs, the lower the profits of each member.

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Mathematics Subject Classification: Primary: 90B06; Secondary: 91A35.

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Figure 1. Three-echelon closed-loop supply chain system under logistics outsourcing

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Figure 2. The effect of market size on decisions and profits

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Figure 3. The effect of consumers' sensitivity to sales prices on decisions and profits

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Figure 4. The effect of the proportion of forward logistics cost assumed by manufacturers on decisions and profits

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Figure 5. The effect of consumers' environmental awareness on decisions and profits

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Figure 6. The effect of consumers' sensitivity to recycling prices on decisions and profits

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Figure 7. The effect of reverse logistics costs assumed by manufacturers on decisions and profits

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Table 1. The optimal decisions of supply chain members

$ P_l $	$ w $	$ P_r $	$ Q $	$ \bar{p}_l $	$ \bar{w} $	$ \bar{p}_r $	$ \bar{Q} $
31.00	79.00	185.45	14.50	4.60	11.80	0.70	13.00

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Table 2. The profits of supply chain members

$ \pi_l^z $	$ \pi_r^z $	$ \pi_m^z $	$ \pi_l^y $	$ \pi_r^y $	$ \pi_m^y $
420.50	1261.50	630.75	33.80	101.40	50.70

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