Pricing decisions for closed-loop supply chains with technology licensing and carbon constraint under reward-penalty mechanism

Yanting Huang; Zongjun Wang

doi:10.3934/jimo.2022103

Article Contents

2023, Volume 19, Issue 5: 3671-3693. Doi: 10.3934/jimo.2022103

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Pricing decisions for closed-loop supply chains with technology licensing and carbon constraint under reward-penalty mechanism

Yanting Huang^1, , and
Zongjun Wang²

1.
College of Management, Shenzhen University, Shenzhen 518060, China
2.
School of Management, Huazhong University of Science and Technology, Wuhan 430074, China

^*Corresponding author: Yanting Huang (ythuang4028@163.com)
^*Corresponding author: Yanting Huang (ythuang4028@163.com)

Received: June 2021

Revised: December 2021

Early access: June 2022

Published: May 2023

The first author is supported by the National Natural Science Foundation of China (NSFC) under Grant 72001147

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Abstract

This paper investigates the effect of the reward-penalty mechanism in a closed-loop supply chain with a manufacturer, a distributor and a third party under technology licensing and carbon constraints. There remanufacturing scenarios are developed, namely (1) the manufacturer is engaged in remanufacturing activities, (2) the manufacturer subcontracts the distributor to conduct remanufacturing, and (3) the third party undertakes remanufacturing with the manufacturer's authorization. We apply the Stackelberg game to derive the equilibrium strategies of each scenario with and without reward-penalty mechanism. We find that, the implementation of the reward-penalty mechanism is profitable to remanufacturing activities. If producing remanufactured products doesn't effectively reduce carbon emissions, chain members have no incentive to undertake collecting and remanufacturing activities. The manufacturer prefers to license other chain members to remanufacture because more cost savings from remanufacturing and more rewards from government can achieve in distributor-remanufacturing and third-party remanufacturing scenarios.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Closed-loop Supply Chain Models with Remanufacturing

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Figure 2. The acquisition price versus carbon emission discount factor of remanufactured products ($ \lambda $)

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Figure 3. The distributor's payoff versus carbon emission discount factor of remanufactured products ($ \lambda $)

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Figure 4. The OEM's payoff versus carbon emission discount factor of remanufactured products ($ \lambda $)

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Figure 5. The acquisition price versus the reward-penalty intensity of collection activities ($ m $)

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Figure 6. The distributor's profit versus the reward-penalty intensity of collection activities ($ m $)

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Figure 7. The OEM's payoff versus the reward-penalty intensity of collection activities ($ m $)

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Table 1. A brief literature review

Typical literature	Closed-loop supply chain	Technology licensing	Carbon emission	Government policy
Savaskan et al. (2004)	$ \surd $
Atasu et al. (2008)	$ \surd $
Örsdemir et al. (2014)	$ \surd $
Mitra and Webster (2008)	$ \surd $			$ \surd $
Esenduran et al. (2016)	$ \surd $			$ \surd $
Oraiopoulos et al. (2012)	$ \surd $	$ \surd $
Hong et al. (2017)	$ \surd $	$ \surd $
Huang and Wang (2017)	$ \surd $	$ \surd $
Wang et al. (2017)	$ \surd $			$ \surd $
Zhang et al. (2021)	$ \surd $			$ \surd $
Alegoz et al. (2021)	$ \surd $		$ \surd $	$ \surd $
Chen et al. (2020)	$ \surd $		$ \surd $	$ \surd $
This paper	$ \surd $	$ \surd $	$ \surd $	$ \surd $

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Table 2. Parameters and definitions

Notation	Definition
$ w $	The unit wholesale price
$ p $	The unit retail price
$ c_n,c_r $	The average unit cost of manufacturing new products and returned products by the manufacturer, respectively
$ c_d,c_t $	The average unit cost of manufacturing returned products by the distributor and the third party, respectively
$ S_1,S_2,S_3 $	The average unit cost savings from remanufacturing by the manufacturer, the distributor and the third party, respectively
$ r $	The average acquisition price for a used product from consumers
$ D $	The market demand function
$ a $	The market size
$ b $	Sensitivity of consumers to the retail price
$ G $	The supply function of used products
$ Q $	The target collection quantity set by government
$ m $	The reward-penalty intensity of collection quantity established by government
$ k $	The reward-penalty coefficient of carbon emission set by government
$ e_0 $	The upper limit of total carbon emissions
$ F $	The unit licensing fee given by the distributor/ the third party to the manufacturer
$ \Pi $	Profit

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