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doi: 10.3934/jimo.2020116

## Channel leadership and recycling channel in closed-loop supply chain: The case of recycling price by the recycling party

 1 College of Information Science and Engineering, Northeastern University, Fundamental Teaching Department of Computer and Mathematics, Shenyang Normal University, Shenyang, Liaoning, 110034, China 2 Research Institute of Business Analytics and Supply Chain Management, College of Management, Shenzhen University, Shenzhen, 518060, China 3 College of Information Science and Engineering, State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning, 110819, China 4 Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong, China 5 College of Computer Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, China

* Corresponding author: Min Huang

Received  June 2019 Revised  March 2020 Published  June 2020

Due to the fast growing of the waste electrical and electronic equipment (WEEE), the business values of closed-loop supply chains (CLSCs) have been well recognized. In this paper, we investigate the performance of the CLSCs under different combinations of the recycling channel and the channel leadership when the recycling price is determined by the recycling party. Specially, we consider a CLSC consisting of two channel members, i.e., a manufacturer and a retailer. Each member acting as the channel leader has three different channels to collect the used products, and they are (ⅰ) the manufacturer (M-channel), (ⅱ) the retailer (R-channel) and (ⅲ) the third-party (T-channel). Given the recycling party determines the recycling price, mathematical models are developed to investigate the performance of the CLSC under different combinations of the channel leadership and the recycling channel. Through a comparison analysis, we find that M-channel is the most effective recycling channel. Moreover, once the M-channel be adopted, the retailer-led structure is as good as manufacture-led structure. We find that the recycling channel structure could be more important than the channel leadership in the CLSC. Finally, we illustrate that the CLSC can be coordinated by a two-part tariff contract.

Citation: Zhidan Wu, Xiaohu Qian, Min Huang, Wai-Ki Ching, Hanbin Kuang, Xingwei Wang. Channel leadership and recycling channel in closed-loop supply chain: The case of recycling price by the recycling party. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020116
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Notations
 Symbol Description Parameters $c_{m}$ Unit producing cost from original materials $c_{0}$ Unit producing cost from returns $\delta$ Unit saving cost by recovery, $\delta=c_{m}-c_{0}$ $A$ The size of the market $\alpha$ Sensitivity of the consumers for the retail price, $\alpha>0$ $k$ The basic recovery quantity, which represents the level of environmental awareness of consumers $h$ Sensitivity of the customers for the recycling price, $h>0$ Decision variables $p$ The unit retail price $w$ The unit wholesale price $b$ The unit recycling price in centralized decision system $b_{j}$ The unit recycling price of the recycling party $j$, subscript $j=t, r, m$ denotes the recycling by the third-party, the retailer and the manufacturer, respectively $b_{mj}$ The unit transfer price, $j=r, t$, denotes R-channel and T-channel, respectively Derived function $D(p)$ The demand of the products $R(b_{j})$ The amount of the recycling products $\pi_{m}$ The profits of the manufacturer $\pi_{r}$ The profits of the retailer $\pi_{t}$ The profits of the third-party $\Pi$ The profits of the system
 Symbol Description Parameters $c_{m}$ Unit producing cost from original materials $c_{0}$ Unit producing cost from returns $\delta$ Unit saving cost by recovery, $\delta=c_{m}-c_{0}$ $A$ The size of the market $\alpha$ Sensitivity of the consumers for the retail price, $\alpha>0$ $k$ The basic recovery quantity, which represents the level of environmental awareness of consumers $h$ Sensitivity of the customers for the recycling price, $h>0$ Decision variables $p$ The unit retail price $w$ The unit wholesale price $b$ The unit recycling price in centralized decision system $b_{j}$ The unit recycling price of the recycling party $j$, subscript $j=t, r, m$ denotes the recycling by the third-party, the retailer and the manufacturer, respectively $b_{mj}$ The unit transfer price, $j=r, t$, denotes R-channel and T-channel, respectively Derived function $D(p)$ The demand of the products $R(b_{j})$ The amount of the recycling products $\pi_{m}$ The profits of the manufacturer $\pi_{r}$ The profits of the retailer $\pi_{t}$ The profits of the third-party $\Pi$ The profits of the system
Main results of the M-led models
 Model MM Model MR Model MT $p^*$ $p^{MM*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{MR*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{MT*}=\frac{3A+\alpha c_m}{4\alpha}$ $b^*_i$ $b^{MM*}_m=\frac{h\delta -k}{2h}$ $b^{MR*}_r=\frac{h\delta -3k}{4h}$ $b^{MT*}_t=\frac{h\delta -3k}{4h}$ $w^*$ $w^{MM*}=\frac{A+\alpha c_m}{2\alpha}$ $w^{MR*}=\frac{A+\alpha c_m}{2\alpha}$ $w^{MT*}=\frac{A+\alpha c_m}{2\alpha}$ $b^*_{mj}$ N/A $b^{MR*}_{mr}=\frac{h\delta -k}{2h}$ $b^{MT*}_{mt}=\frac{h\delta -k}{2h}$ $\pi^*_m$ $\pi^{MM*}_m=\frac{P_f}{2}+P_r$ $\pi^{MR*}_m=\frac{P_f+P_r}{2}$ $\pi^{MT*}_m=\frac{P_f}{2}+\frac{P_r}{2}$ $\pi^*_r$ $\pi^{MM*}_r=\frac{P_f}{4}$ $\pi^{MR*}_r=\frac{P_f+P_r}{4}$ $\pi^{MT*}_r=\frac{P_f}{4}$ $\pi^*_t$ N/A N/A $\pi^{MT*}_t=\frac{P_r}{4}$ $\Pi^*$ $\Pi^{MM*}=\frac{3P_f}{4}+P_r$ $\Pi^{MR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{MT*}=\frac{3(P_f+P_r)}{4}$
 Model MM Model MR Model MT $p^*$ $p^{MM*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{MR*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{MT*}=\frac{3A+\alpha c_m}{4\alpha}$ $b^*_i$ $b^{MM*}_m=\frac{h\delta -k}{2h}$ $b^{MR*}_r=\frac{h\delta -3k}{4h}$ $b^{MT*}_t=\frac{h\delta -3k}{4h}$ $w^*$ $w^{MM*}=\frac{A+\alpha c_m}{2\alpha}$ $w^{MR*}=\frac{A+\alpha c_m}{2\alpha}$ $w^{MT*}=\frac{A+\alpha c_m}{2\alpha}$ $b^*_{mj}$ N/A $b^{MR*}_{mr}=\frac{h\delta -k}{2h}$ $b^{MT*}_{mt}=\frac{h\delta -k}{2h}$ $\pi^*_m$ $\pi^{MM*}_m=\frac{P_f}{2}+P_r$ $\pi^{MR*}_m=\frac{P_f+P_r}{2}$ $\pi^{MT*}_m=\frac{P_f}{2}+\frac{P_r}{2}$ $\pi^*_r$ $\pi^{MM*}_r=\frac{P_f}{4}$ $\pi^{MR*}_r=\frac{P_f+P_r}{4}$ $\pi^{MT*}_r=\frac{P_f}{4}$ $\pi^*_t$ N/A N/A $\pi^{MT*}_t=\frac{P_r}{4}$ $\Pi^*$ $\Pi^{MM*}=\frac{3P_f}{4}+P_r$ $\Pi^{MR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{MT*}=\frac{3(P_f+P_r)}{4}$
Main results of the R-led models
 Model RM Model RR Model RT $p^*$ $p^{RM*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{RR*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{RT*}=\frac{3A+\alpha c_m}{4\alpha}$ $b^*_i$ $b^{RM*}_m=\frac{h\delta -k}{2h}$ $b^{RR*}_r=\frac{h\delta -3k}{4h}$ $b^{RT*}_t=\frac{h\delta -3k}{4h}$ $w^*$ $w^{RM*}=\frac{A+3\alpha c_m}{4\alpha}$ $w^{RR*}=\frac{A+3\alpha c_m}{4\alpha}$ $w^{RT*}=\frac{A+3\alpha c_m}{4\alpha}$ $b^*_{mj}$ N/A $b^{RR*}_{mr}=\frac{3h\delta -k}{4h}$ $b^{RT*}_{mt}=\frac{h\delta -k}{2h}$ $\pi^*_m$ $\pi^{RM*}_m=\frac{P_f}{4}+P_r$ $\pi^{RR*}_m=\frac{P_f+P_r}{4}$ $\pi^{RT*}_m=\frac{P_f}{4}+\frac{P_r}{2}$ $\pi^*_r$ $\pi^{RM*}_r=\frac{P_f}{2}$ $\pi^{RR*}_r=\frac{P_f+P_r}{2}$ $\pi^{RT*}_r=\frac{P_f}{2}$ $\pi^*_t$ N/A N/A $\pi^{RT*}_t=\frac{P_r}{4}$ $\Pi^*$ $\Pi^{RM*}=\frac{3P_f}{4}+P_r$ $\Pi^{RR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{RT*}=\frac{3(P_f+P_r)}{4}$
 Model RM Model RR Model RT $p^*$ $p^{RM*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{RR*}=\frac{3A+\alpha c_m}{4\alpha}$ $p^{RT*}=\frac{3A+\alpha c_m}{4\alpha}$ $b^*_i$ $b^{RM*}_m=\frac{h\delta -k}{2h}$ $b^{RR*}_r=\frac{h\delta -3k}{4h}$ $b^{RT*}_t=\frac{h\delta -3k}{4h}$ $w^*$ $w^{RM*}=\frac{A+3\alpha c_m}{4\alpha}$ $w^{RR*}=\frac{A+3\alpha c_m}{4\alpha}$ $w^{RT*}=\frac{A+3\alpha c_m}{4\alpha}$ $b^*_{mj}$ N/A $b^{RR*}_{mr}=\frac{3h\delta -k}{4h}$ $b^{RT*}_{mt}=\frac{h\delta -k}{2h}$ $\pi^*_m$ $\pi^{RM*}_m=\frac{P_f}{4}+P_r$ $\pi^{RR*}_m=\frac{P_f+P_r}{4}$ $\pi^{RT*}_m=\frac{P_f}{4}+\frac{P_r}{2}$ $\pi^*_r$ $\pi^{RM*}_r=\frac{P_f}{2}$ $\pi^{RR*}_r=\frac{P_f+P_r}{2}$ $\pi^{RT*}_r=\frac{P_f}{2}$ $\pi^*_t$ N/A N/A $\pi^{RT*}_t=\frac{P_r}{4}$ $\Pi^*$ $\Pi^{RM*}=\frac{3P_f}{4}+P_r$ $\Pi^{RR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{RT*}=\frac{3(P_f+P_r)}{4}$
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