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March  2022, 18(2): 1161-1183. doi: 10.3934/jimo.2021014

## 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

Received  May 2020 Revised  November 2020 Published  March 2022 Early access  December 2020

Fund Project: 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

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.

Citation: Xiao-Xu Chen, Peng Xu, Jiao-Jiao Li, Thomas Walker, Guo-Qiang Yang. Decision-making in a retailer-led closed-loop supply chain involving a third-party logistics provider. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1161-1183. doi: 10.3934/jimo.2021014
##### References:
 [1] T. M. Choi, Y. J. Li and L. Xu, Channel leadership performance and coordination in closed-loop supply chains, International Journal of Production Economics, 146 (2013), 371-380. [2] C. H. Chuang, C. X. Wang and Y. B. Zhao, Closed-loop supply chain model for a high-tech product under alternative reverse channel and collection cost structures, International Journal of Production Economics, 156 (2014), 108-123. [3] C. J. Chung and H. M. Wee, Short life-cycle deteriorating product remanufacturing in a green supply chain inventory control system, International Journal of Production Economics, 129 (2011), 195-203. [4] Z. W. Feng, T. J. Xiao and C. C. Chai, Recycling and pricing strategies of closed-loop supply chain by the leader of third-party recycler, Chinese Journal of Management Science, 26 (2018), 119-127. [5] B. K. Finshbein, Carpet-take back: EPR American style, Environmental Quality Management, 10 (2000), 25-36. [6] M. Fleischmann, J. M. Bloemhof and R. Dekker, Quantitative models for reverse logistics: A review, European Journal of Operational Research, 103 (1997), 1-17. [7] P. Gao, Z. Q. Xie and Y. C. Xie, Coordination mechanism of closed-loop supply chain with retailer as leader under asymmetric information, Industrial Engineering Journal, 16 (2013), 79-85. [8] Y. D. Gong and Q. L. Da, Research on combinations of closed-loop supply chain dominant mode and logistics mode, Journal of Management Science in China, 18 (2015), 14-25. [9] Y. D. Gong and B. Y. Li, Analysis of supply chain decision, stability and efficiency based on dominant mode, Journal of Industrial Engineering/Engineering Management, 26 (2012), 42-49. [10] Y. D. Gong, B. Y. Li and T. Liu, Model for closed-loop supply chain based on the loading ratio of logistics cost, Journal of Systems Engineering, 26 (2011), 39-49. [11] V. D. R. Guide, V. Jayaraman and J. D. Linton, Building contingency planning for closed-loop supply chains with product recovery, Journal of Operations Management, 21 (2003), 259-279. [12] X. H. Han, Recycling channels decision analysis for uncertainty closed-loop supply chain, Industrial Technology & Economy, 29 (2010), 95-98. [13] I. H. Hong and J. S. Yeh, Modeling closed-loop supply chains in the electronics industry: A retailer collection application, Transportation Research Part E, 48 (2012), 817-829. [14] Z. Q. Huang, R. H. Yi and Q. L. Da, Study on the efficiency of the closed-loop supply chain with remanufacture based on third-party collecting, Chinese Journal of Management Science, 16 (2008), 73-77. [15] J. Li, Retailer-Driven Closed-Loop Supply Chains with Product Remanufacturing, Ames: Iowa State University, 2006. [16] J. Li, W. H. Du and F. M. Yang et al, Evolutionary game analysis of remanufacturing closed-loop supply chain with asymmetric information, Sustainability, 6 (2014), 6312-6324. [17] J. Li, W. H. Du and F. M. Yang et al, The carbon subsidy analysis for the remanufacturing closed-loop supply chain, Sustainability, 6 (2014), 3861-3877. [18] W.-M. Ma, Z. Zhao and H. Ke, Dual-channel closed-loop supply chain with government consumption-subsidy, European J. Oper. Res., 226 (2013), 221-227.  doi: 10.1016/j.ejor.2012.10.033. [19] N. M. Modak, S. Panda and S. S. Sana, Two-echelon supply chain coordination among manufacturer and duopoly retailers with recycling facility, International Journal of Advanced Manufacturing Technology, 87 (2016), 1531-1546. [20] B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, 4 (1985), 1966-1976. [21] L. Qing, M. Goh and R. D. Souza, Remanufacturing in Asia: Location choice and outsourcing, International Journal of Logistics Management, 25 (2014), 20-34. [22] R. C. Savaskan, S. Bhattacharya and L. N. V. Wassenhove, Closed-loop supply chain models with product remanufacturing, Management Science, 50 (2004), 239-252. [23] R. C. Savaskan and L. N. Van Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14. [24] J. R. Stock, Reverse Logistics: White Paper, Oak-Brook: Council of Logistics Management, 1992. [25] M. W. Toffel, The growing strategic importance of end-of-life product management, California Management Review, 45 (2003), 102-129. [26] J. A. E. E. Van Nunen and R. A. Zuidwijk, E-enabled closed-loop supply chains, California Management Review, 46 (2004), 40-54.  doi: 10.2307/41166209. [27] J. C. Wang, A. H. L. Lau and H. S. Lau, Practical and effective contracts for the dominant retailer of a newsvendor product with price-sensitive demand, International Journal of Production Economics, 138 (2012), 46-54. [28] J. J. Wang and M. L. Xu, Study on decisions of a closed-loop supply chain with risk aversion under different power structures and alliance strategies, Chinese Journal of Management Science, 28 (2020), 1-13. [29] Y. Xiong, Q. W. Zhao and Y. Zhou, Manufacturer-remanufacturing vs supplier-remanufacturing in a closed-loop supply chain, International Journal of Production Economics, 179 (2016), 21-28. [30] D. X. Yang, L. Zhang, Y. Wu et al, A sustainability analysis of retailer's sales effort in a closed-loop supply chain, Sustainability, 11 (2019). [31] D. X. Yang, L. Zhang, Y. Wu et al, A sustainability analysis on retailer's sales effort in a closed-loop supply chain, Sustainability, 11 (2019), 4738. [32] F. M. Yao, S. Liu and X. W. Hu et al, Pricing strategies for closed-loop supply chain with dominant retailer considering fairness concerns, Operations Research and Management Science, 29 (2020), 120-127. [33] W. L. Zhou, X. H. Han and Y. Shen, Price and service level decisions and coordination of closed-loop supply chain considering consumer behavior, Computer Integrated Manufacturing Systems, 23 (2017), 2241-2250. [34] Z. B. Zou, J. J. Wang and G. S. Deng, Third-party remanufacturing mode selection: Outsourcing or authorization?, Transportation Research Part E: Logistics and Transportation Review, 87 (2016), 1-19.

show all references

##### References:
 [1] T. M. Choi, Y. J. Li and L. Xu, Channel leadership performance and coordination in closed-loop supply chains, International Journal of Production Economics, 146 (2013), 371-380. [2] C. H. Chuang, C. X. Wang and Y. B. Zhao, Closed-loop supply chain model for a high-tech product under alternative reverse channel and collection cost structures, International Journal of Production Economics, 156 (2014), 108-123. [3] C. J. Chung and H. M. Wee, Short life-cycle deteriorating product remanufacturing in a green supply chain inventory control system, International Journal of Production Economics, 129 (2011), 195-203. [4] Z. W. Feng, T. J. Xiao and C. C. Chai, Recycling and pricing strategies of closed-loop supply chain by the leader of third-party recycler, Chinese Journal of Management Science, 26 (2018), 119-127. [5] B. K. Finshbein, Carpet-take back: EPR American style, Environmental Quality Management, 10 (2000), 25-36. [6] M. Fleischmann, J. M. Bloemhof and R. Dekker, Quantitative models for reverse logistics: A review, European Journal of Operational Research, 103 (1997), 1-17. [7] P. Gao, Z. Q. Xie and Y. C. Xie, Coordination mechanism of closed-loop supply chain with retailer as leader under asymmetric information, Industrial Engineering Journal, 16 (2013), 79-85. [8] Y. D. Gong and Q. L. Da, Research on combinations of closed-loop supply chain dominant mode and logistics mode, Journal of Management Science in China, 18 (2015), 14-25. [9] Y. D. Gong and B. Y. Li, Analysis of supply chain decision, stability and efficiency based on dominant mode, Journal of Industrial Engineering/Engineering Management, 26 (2012), 42-49. [10] Y. D. Gong, B. Y. Li and T. Liu, Model for closed-loop supply chain based on the loading ratio of logistics cost, Journal of Systems Engineering, 26 (2011), 39-49. [11] V. D. R. Guide, V. Jayaraman and J. D. Linton, Building contingency planning for closed-loop supply chains with product recovery, Journal of Operations Management, 21 (2003), 259-279. [12] X. H. Han, Recycling channels decision analysis for uncertainty closed-loop supply chain, Industrial Technology & Economy, 29 (2010), 95-98. [13] I. H. Hong and J. S. Yeh, Modeling closed-loop supply chains in the electronics industry: A retailer collection application, Transportation Research Part E, 48 (2012), 817-829. [14] Z. Q. Huang, R. H. Yi and Q. L. Da, Study on the efficiency of the closed-loop supply chain with remanufacture based on third-party collecting, Chinese Journal of Management Science, 16 (2008), 73-77. [15] J. Li, Retailer-Driven Closed-Loop Supply Chains with Product Remanufacturing, Ames: Iowa State University, 2006. [16] J. Li, W. H. Du and F. M. Yang et al, Evolutionary game analysis of remanufacturing closed-loop supply chain with asymmetric information, Sustainability, 6 (2014), 6312-6324. [17] J. Li, W. H. Du and F. M. Yang et al, The carbon subsidy analysis for the remanufacturing closed-loop supply chain, Sustainability, 6 (2014), 3861-3877. [18] W.-M. Ma, Z. Zhao and H. Ke, Dual-channel closed-loop supply chain with government consumption-subsidy, European J. Oper. Res., 226 (2013), 221-227.  doi: 10.1016/j.ejor.2012.10.033. [19] N. M. Modak, S. Panda and S. S. Sana, Two-echelon supply chain coordination among manufacturer and duopoly retailers with recycling facility, International Journal of Advanced Manufacturing Technology, 87 (2016), 1531-1546. [20] B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, 4 (1985), 1966-1976. [21] L. Qing, M. Goh and R. D. Souza, Remanufacturing in Asia: Location choice and outsourcing, International Journal of Logistics Management, 25 (2014), 20-34. [22] R. C. Savaskan, S. Bhattacharya and L. N. V. Wassenhove, Closed-loop supply chain models with product remanufacturing, Management Science, 50 (2004), 239-252. [23] R. C. Savaskan and L. N. Van Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14. [24] J. R. Stock, Reverse Logistics: White Paper, Oak-Brook: Council of Logistics Management, 1992. [25] M. W. Toffel, The growing strategic importance of end-of-life product management, California Management Review, 45 (2003), 102-129. [26] J. A. E. E. Van Nunen and R. A. Zuidwijk, E-enabled closed-loop supply chains, California Management Review, 46 (2004), 40-54.  doi: 10.2307/41166209. [27] J. C. Wang, A. H. L. Lau and H. S. Lau, Practical and effective contracts for the dominant retailer of a newsvendor product with price-sensitive demand, International Journal of Production Economics, 138 (2012), 46-54. [28] J. J. Wang and M. L. Xu, Study on decisions of a closed-loop supply chain with risk aversion under different power structures and alliance strategies, Chinese Journal of Management Science, 28 (2020), 1-13. [29] Y. Xiong, Q. W. Zhao and Y. Zhou, Manufacturer-remanufacturing vs supplier-remanufacturing in a closed-loop supply chain, International Journal of Production Economics, 179 (2016), 21-28. [30] D. X. Yang, L. Zhang, Y. Wu et al, A sustainability analysis of retailer's sales effort in a closed-loop supply chain, Sustainability, 11 (2019). [31] D. X. Yang, L. Zhang, Y. Wu et al, A sustainability analysis on retailer's sales effort in a closed-loop supply chain, Sustainability, 11 (2019), 4738. [32] F. M. Yao, S. Liu and X. W. Hu et al, Pricing strategies for closed-loop supply chain with dominant retailer considering fairness concerns, Operations Research and Management Science, 29 (2020), 120-127. [33] W. L. Zhou, X. H. Han and Y. Shen, Price and service level decisions and coordination of closed-loop supply chain considering consumer behavior, Computer Integrated Manufacturing Systems, 23 (2017), 2241-2250. [34] Z. B. Zou, J. J. Wang and G. S. Deng, Third-party remanufacturing mode selection: Outsourcing or authorization?, Transportation Research Part E: Logistics and Transportation Review, 87 (2016), 1-19.
Three-echelon closed-loop supply chain system under logistics outsourcing
The effect of market size on decisions and profits
The effect of consumers' sensitivity to sales prices on decisions and profits
The effect of the proportion of forward logistics cost assumed by manufacturers on decisions and profits
The effect of consumers' environmental awareness on decisions and profits
The effect of consumers' sensitivity to recycling prices on decisions and profits
The effect of reverse logistics costs assumed by manufacturers on decisions and profits
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
 $P_l$ $w$ $P_r$ $Q$ $\bar{p}_l$ $\bar{w}$ $\bar{p}_r$ $\bar{Q}$ 31.00 79.00 185.45 14.50 4.60 11.80 0.70 13.00
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
 $\pi_l^z$ $\pi_r^z$ $\pi_m^z$ $\pi_l^y$ $\pi_r^y$ $\pi_m^y$ 420.50 1261.50 630.75 33.80 101.40 50.70

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