# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021035

## Effects of take-back legislation on pricing and coordination in a closed-loop supply chain

 College of Economics & Management, Huazhong Agricultural University, Wuhan, Hubei 430070, China

* Corresponding author: Xianpei Hong

Received  April 2020 Revised  November 2020 Published  March 2021

Fund Project: The study is supported in part by the Humanities and Social Science project of Ministry of Education of China (Project No. 19YJC630229), Natural Science Foundation of Hubei Province (Project No. 2019CFB120), National Natural Science Foundation of China (Project No. 71672071), and the Fundamental Research Funds for the Central Universities (Project No. 2662020JGPYG14)

This study investigates the effects of take-back legislation and channel structures on pricing, collection, and coordination in a closed-loop supply chain (CLSC). By establishing the centralized, manufacturer-led, and retailer-led CLSC models, we analyze the equilibrium solutions of channel players and the government. We obtain the following results. (1) The manufacturer can accept a higher collection target and exit the market later in the centralized model than in decentralized decision-making models. Moreover, the manufacturer exists the market earlier in the retailer-led model with regulation compared with the manufacturer-led model. (2) The government's optimal collection target is the same under manufacturer-led and retailer-led models when the regulation comes into force. (3) Revenue-sharing and two-part tariff contracts can effectively coordinate manufacturer-led and retailer-led CLSCs under take-back legislation. Finally, we conduct several numerical examples and obtain relevant managerial insights. Our results indicate that the correlation between take-back legislation and channel structure has a significant impact on the pricing and coordination decisions of the CLSC; furthermore, the government should flexibly set the collection target when facing different supply chain and channel power structures in a CLSC.

Citation: Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021035
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##### References:
Effects of $\tau_g$ on equilibrium prices $w^{*}$ and $p^{*}$
Effect of $\tau_g$ on equilibrium profits
Effects of $\kappa$ and $\chi$ on equilibrium collection target $\tau_g^{*}$
Effects of $\Delta$ on contract parameters $\phi^{*}$ and $F^{*}$
Comparison of our study and related literature
 Research paper Take-back legislation CLSC power structure Supply chain coordination Endogenous government's decision Choi et al. [14] $\surd$ $\surd$ Chen et al. [11] $\surd$ $\surd$ He et al. [25] $\surd$ Zheng et al. [54] $\surd$ Bai et al. [6] $\surd$ Zheng et al. [53] $\surd$ $\surd$ Wang et al. [45] $\surd$ Toyasaki et al. [43] $\surd$ $\surd$ Esenduran and Kemahlioglu-Ziya [18] $\surd$ $\surd$ Subramanian et al. [42] $\surd$ $\surd$ $\surd$ Jacobs and Subramanian [32] $\surd$ $\surd$ Chen and Akmalul Ulya [9] $\surd$ Alizamir et al. [1] $\surd$ $\surd$ Our work $\surd$ $\surd$ $\surd$ $\surd$
 Research paper Take-back legislation CLSC power structure Supply chain coordination Endogenous government's decision Choi et al. [14] $\surd$ $\surd$ Chen et al. [11] $\surd$ $\surd$ He et al. [25] $\surd$ Zheng et al. [54] $\surd$ Bai et al. [6] $\surd$ Zheng et al. [53] $\surd$ $\surd$ Wang et al. [45] $\surd$ Toyasaki et al. [43] $\surd$ $\surd$ Esenduran and Kemahlioglu-Ziya [18] $\surd$ $\surd$ Subramanian et al. [42] $\surd$ $\surd$ $\surd$ Jacobs and Subramanian [32] $\surd$ $\surd$ Chen and Akmalul Ulya [9] $\surd$ Alizamir et al. [1] $\surd$ $\surd$ Our work $\surd$ $\surd$ $\surd$ $\surd$
Basic parameter set
 Parameter $a$ $b$ $c_m$ $\Delta$ $f$ $C_L$ Initial value $200$ $10$ $10$ $8$ $10$ $900$
 Parameter $a$ $b$ $c_m$ $\Delta$ $f$ $C_L$ Initial value $200$ $10$ $10$ $8$ $10$ $900$
Comparison of equilibrium decisions in CLSC under RS contract
 recycling is not constrained recycling is constrained Model $DM$ $DR$ $CM$ $CR$ $I$ Model $DM$ $DR$ $CM$ $CR$ $I$ $w^{*}$ $14.51$ $11.96$ $3.14$ $25.68$ $-$ $w^{*}$ $13.80$ $10.70$ $3.04$ $25.20$ $-$ $p^{*}$ $17.26$ $16.96$ $13.92$ $13.92$ $13.92$ $p^{*}$ $16.90$ $16.90$ $13.80$ $13.80$ $13.80$ $\tau^{*}$ $0.12$ $0.14$ $0.27$ $0.27$ $0.27$ $\tau^{*}$ $0.30$ $0.30$ $0.30$ $0.30$ $0.30$ $\pi_M^{*}$ $127.20$ $66.01$ $146.14$ $72.18$ $-$ $\pi_M^{*}$ $101.20$ $5.10$ $139.64$ $62.76$ $-$ $\pi_R^{*}$ $75.29$ $152.00$ $147.92$ $221.88$ $-$ $\pi_R^{*}$ $96.10$ $192.20$ $153.76$ $230.64$ $-$ $\pi_{T}^{*}$ $202.49$ $218.01$ $294.10$ $294.10$ $294.10$ $\pi_{T}^{*}$ $197.30$ $197.30$ $293.40$ $293.40$ $293.40$
 recycling is not constrained recycling is constrained Model $DM$ $DR$ $CM$ $CR$ $I$ Model $DM$ $DR$ $CM$ $CR$ $I$ $w^{*}$ $14.51$ $11.96$ $3.14$ $25.68$ $-$ $w^{*}$ $13.80$ $10.70$ $3.04$ $25.20$ $-$ $p^{*}$ $17.26$ $16.96$ $13.92$ $13.92$ $13.92$ $p^{*}$ $16.90$ $16.90$ $13.80$ $13.80$ $13.80$ $\tau^{*}$ $0.12$ $0.14$ $0.27$ $0.27$ $0.27$ $\tau^{*}$ $0.30$ $0.30$ $0.30$ $0.30$ $0.30$ $\pi_M^{*}$ $127.20$ $66.01$ $146.14$ $72.18$ $-$ $\pi_M^{*}$ $101.20$ $5.10$ $139.64$ $62.76$ $-$ $\pi_R^{*}$ $75.29$ $152.00$ $147.92$ $221.88$ $-$ $\pi_R^{*}$ $96.10$ $192.20$ $153.76$ $230.64$ $-$ $\pi_{T}^{*}$ $202.49$ $218.01$ $294.10$ $294.10$ $294.10$ $\pi_{T}^{*}$ $197.30$ $197.30$ $293.40$ $293.40$ $293.40$
Comparison of equilibrium decisions under TPT contract
 recycling is not constrained recycling is constrained Model $DM$ $DR$ $CM$ $CR$ $I$ Model $DM$ $DR$ $CM$ $CR$ $I$ $w^{*}$ $14.51$ $11.96$ $7.84$ $13.92$ $-$ $w^{*}$ $13.80$ $10.70$ $7.60$ $13.80$ $-$ $p^{*}$ $17.26$ $16.96$ $13.92$ $13.92$ $13.92$ $p^{*}$ $16.90$ $16.90$ $13.80$ $13.80$ $13.80$ $\tau^{*}$ $0.12$ $0.14$ $0.27$ $0.27$ $0.27$ $\tau^{*}$ $0.30$ $0.30$ $0.30$ $0.30$ $0.30$ $\pi_M^{*}$ $127.20$ $66.01$ $139.30$ $79.05$ $-$ $\pi_M^{*}$ $101.20$ $5.10$ $124.00$ $78.40$ $-$ $\pi_R^{*}$ $75.29$ $152.00$ $154.80$ $215.05$ $-$ $\pi_R^{*}$ $96.10$ $192.20$ $169.40$ $215.00$ $-$ $\pi_{T}^{*}$ $202.49$ $218.01$ $294.10$ $294.10$ $294.10$ $\pi_{T}^{*}$ $197.30$ $197.30$ $293.40$ $293.40$ $293.40$
 recycling is not constrained recycling is constrained Model $DM$ $DR$ $CM$ $CR$ $I$ Model $DM$ $DR$ $CM$ $CR$ $I$ $w^{*}$ $14.51$ $11.96$ $7.84$ $13.92$ $-$ $w^{*}$ $13.80$ $10.70$ $7.60$ $13.80$ $-$ $p^{*}$ $17.26$ $16.96$ $13.92$ $13.92$ $13.92$ $p^{*}$ $16.90$ $16.90$ $13.80$ $13.80$ $13.80$ $\tau^{*}$ $0.12$ $0.14$ $0.27$ $0.27$ $0.27$ $\tau^{*}$ $0.30$ $0.30$ $0.30$ $0.30$ $0.30$ $\pi_M^{*}$ $127.20$ $66.01$ $139.30$ $79.05$ $-$ $\pi_M^{*}$ $101.20$ $5.10$ $124.00$ $78.40$ $-$ $\pi_R^{*}$ $75.29$ $152.00$ $154.80$ $215.05$ $-$ $\pi_R^{*}$ $96.10$ $192.20$ $169.40$ $215.00$ $-$ $\pi_{T}^{*}$ $202.49$ $218.01$ $294.10$ $294.10$ $294.10$ $\pi_{T}^{*}$ $197.30$ $197.30$ $293.40$ $293.40$ $293.40$
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