# American Institute of Mathematical Sciences

• Previous Article
Optimizing 3-objective portfolio selection with equality constraints and analyzing the effect of varying constraints on the efficient sets
• JIMO Home
• This Issue
• Next Article
A lattice method for option evaluation with regime-switching asset correlation structure
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
##### References:

show all references

##### References:
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 $\pi^{RT*}_t=\frac{P_r}{4}$ $\Pi^*$ $\Pi^{RM*}=\frac{3P_f}{4}+P_r$ $\Pi^{RR*}=\frac{3(P_f+P_r)}{4}$ $\Pi^{RT*}=\frac{3(P_f+P_r)}{4}$
 [1] 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 & Management Optimization, 2020  doi: 10.3934/jimo.2021014 [2] Xi Zhao, Teng Niu. Impacts of horizontal mergers on dual-channel supply chain. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020173 [3] Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020167 [4] Hongxia Sun, Yao Wan, Yu Li, Linlin Zhang, Zhen Zhou. Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours. Journal of Industrial & Management Optimization, 2021, 17 (2) : 601-631. doi: 10.3934/jimo.2019125 [5] Simon Hochgerner. Symmetry actuated closed-loop Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 641-669. doi: 10.3934/jgm.2020030 [6] Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020165 [7] Jingrui Sun, Hanxiao Wang. Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability. Mathematical Control & Related Fields, 2021, 11 (1) : 47-71. doi: 10.3934/mcrf.2020026 [8] Wei Chen, Yongkai Ma, Weihao Hu. Electricity supply chain coordination with carbon abatement technology investment under the benchmarking mechanism. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020175 [9] Linfeng Mei, Feng-Bin Wang. Dynamics of phytoplankton species competition for light and nutrient with recycling in a water column. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020359 [10] Honglin Yang, Jiawu Peng. Coordinating a supply chain with demand information updating. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020181 [11] Wenyan Zhuo, Honglin Yang, Leopoldo Eduardo Cárdenas-Barrón, Hong Wan. Loss-averse supply chain decisions with a capital constrained retailer. Journal of Industrial & Management Optimization, 2021, 17 (2) : 711-732. doi: 10.3934/jimo.2019131 [12] Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020172 [13] Puneet Pasricha, Anubha Goel. Pricing power exchange options with hawkes jump diffusion processes. Journal of Industrial & Management Optimization, 2021, 17 (1) : 133-149. doi: 10.3934/jimo.2019103 [14] Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, Stock price fluctuation prediction method based on time series analysis. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 915-915. doi: 10.3934/dcdss.2019061 [15] Musen Xue, Guowei Zhu. Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items. Journal of Industrial & Management Optimization, 2021, 17 (2) : 633-648. doi: 10.3934/jimo.2019126 [16] Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133 [17] Mahir Demir, Suzanne Lenhart. A spatial food chain model for the Black Sea Anchovy, and its optimal fishery. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 155-171. doi: 10.3934/dcdsb.2020373 [18] Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 969-969. doi: 10.3934/dcdss.2019065 [19] Lei Liu, Li Wu. Multiplicity of closed characteristics on $P$-symmetric compact convex hypersurfaces in $\mathbb{R}^{2n}$. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020378

2019 Impact Factor: 1.366

## Tools

Article outline

Figures and Tables