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

Benrong Zheng; Xianpei Hong

doi:10.3934/jimo.2021035

Article Contents

2022, Volume 18, Issue 3: 1603-1627. Doi: 10.3934/jimo.2021035

This issue Previous Article Linear-quadratic optimal control for discrete-time stochastic descriptor systems Next Article Inventory replenishment policies for two successive generations price-sensitive technology products

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

Benrong Zheng and
Xianpei Hong^,

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

^* Corresponding author: Xianpei Hong
^* Corresponding author: Xianpei Hong

Received: March 31, 2020

Revised: October 31, 2020

Published: May 2022

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)

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Abstract

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.

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Mathematics Subject Classification: Primary: 90B05, 68W27; Secondary: 68W40.

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Figure 1. Effects of $ \tau_g $ on equilibrium prices $ w^{*} $ and $ p^{*} $

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Figure 2. Effect of $ \tau_g $ on equilibrium profits

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Figure 3. Effects of $ \kappa $ and $ \chi $ on equilibrium collection target $ \tau_g^{*} $

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Figure 4. Effects of $ \Delta $ on contract parameters $ \phi^{*} $ and $ F^{*} $

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Table 1. 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 $

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Table 2. Basic parameter set

Parameter	$ a $	$ b $	$ c_m $	$ \Delta $	$ f $	$ C_L $
Initial value	$ 200 $	$ 10 $	$ 10 $	$ 8 $	$ 10 $	$ 900 $

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Table 3. 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 $

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Table 4. 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 $

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