Pricing and coordination of competitive recycling and remanufacturing supply chain considering the quality of recycled products

Yanhua Feng; Xuhui Xia; Lei Wang; Zelin Zhang

doi:10.3934/jimo.2021089

Article Contents

2022, Volume 18, Issue 4: 2721-2748. Doi: 10.3934/jimo.2021089

This issue Previous Article Generalized Clarke epiderivatives of the extremum multifunction to a multi-objective parametric discrete optimal control problem Next Article The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain

Pricing and coordination of competitive recycling and remanufacturing supply chain considering the quality of recycled products

1.
Key Laboratory of Metallurgical Equipment and Control of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China
2.
Hubei Provincial Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China

^* Corresponding author: Xuhui Xia
^* Corresponding author: Xuhui Xia

Received: October 31, 2020

Revised: January 31, 2021

Published: July 2022

This research was supported by the National Natural Science Foundation of China (No. 51805385) and Natural Science Foundation of Hubei Province (No. 2018CFB265)

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Abstract

Considering the quality of recycled products, we develop a game model of a multi-level competitive recycling and remanufacturing supply chain with two manufacturers and multiple recyclers. Being focus on two mainstream game models, namely the manufacturer-recycler cooperation game model and the manufacturer-led Stackelberg game model, we explore the connection between optimal pricing decisions and performance levels of the supply chain members. Although researches indicate that the quality of recycled products will not affect the pricing decisions in the forward supply chain, it is positively related to the recycling price, the repurchase price, and the overall profit in the reverse supply chain, and the intensity of competition among manufacturers or recycled products will affect the pricing decisions and the performance levels of the two models. In the manufacturer-led Stackelberg game model, the supply chain does not reach the Pareto optimum, which uses the recycling cost sharing contract to achieve the coordination. Afterwards, the profits of the two manufacturers and multiple recyclers in the supply chain are increased, and the overall profit of the supply chain system is higher than that of the manufacturer-led Stackelberg game model. Finally, numerical analysis is conducted to verify the proposed coordination mechanism and its effectiveness.

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Mathematics Subject Classification: Primary: 90B06.

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Figure 1. System architecture of the recycling and remanufacturing supply chain

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Figure 2. The impact of $ \lambda $ on manufacturer's sale price

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Figure 3. The impact of $ \lambda $ on market demand

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Figure 4. The impact of $ \lambda $ on profits

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Figure 5. The impact of $ \kappa $ on $ b_{m}^{MRC} $ and $ b_{m}^{MS} $

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Figure 6. The impact of $ \kappa $ on $ \eta_{m}^{MS} $

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Figure 7. The impact of $ \kappa $ on $ f_{R}^{MS} $

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Figure 8. The impact of $ \kappa $ on $ f^{MRC} $

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Figure 9. The impact of $ \kappa $ on $ f^{ MS} $

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Figure 10. The impact of Îº on f₁^MS

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Figure 11. The impact of Îº on f₂^MS

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Figure 12. The impact of $ \lambda $ and $ \kappa $ on $ f^{ MRC} $

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Figure 13. The impact of $ \lambda $ and $ \kappa $ on $ f^{ MS} $

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Figure 14. The impact of $ \sigma $ on $ b_{m}^{MRC} $ and $ b_{m}^{MS} $

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Figure 15. The impact of $ \sigma $ on $ \eta_{m}^{MS} $

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Figure 16. The impact of $ \sigma $ on profits

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Figure 17. The impact of Î¸ on f₁^MST

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Figure 18. The impact of Î¸ on f₂^MST

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Figure 19. The impact of $ \theta $ on $ f_{R}^{MST} $

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Table 1. Indices

m	Manufacturer (m=1, 2)
r	Recycler (r=1, 2, 3, ...R)

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Table 2. Decision variables

$ p_{m} $	The unit sale price for new and remanufactured products of manufacturer m
$ b_{m} $	The unit recycling price specified by the recycler for the used products needed by the manufacturer m
$ \eta_{m} $	The unit price at which manufacturer m repurchases used products from recyclers

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Table 3. Definition of Parameters

$\textit{R}$	Number of recyclers
$ c_{mn} $	The unit cost required by the manufacturer m to manufacture a new product
$ c_{mz} $	The unit cost required for manufacturer m to remanufacture the product
$ \omega_{m} $	Manufacturer m uses the used products for remanufacturing cost savings
$ \sigma $	Remanufacturing ratio of recycled used products. It reflects the quality of recycled used products, 0$ \leq $$ \sigma $$ \leq $1
$\textit{s}$	The government subsidies for recycler to recycle every unit of used products
$ c_{d} $	The unit cost for recyclers to dispose of used products
$ c_{q} $	The unit cost for recyclers to dispose of other used products that cannot be used for remanufacturing
$ \delta_{r} $	Economies of market scale for recyclers r, 0 < $ \delta_{r} < $1
$ \lambda $	The intensity of competition between two manufacturers that can replace new products, 0 < $ \lambda < $1, competition, the more intense the competition among manufacturers.
$ \mu $	Market capacity, $ \mu > $0
$ \psi $	When the recycling price is zero, the number of used products voluntarily returned by the consumer market which reflect consumers' environmental awareness, $ \psi > $0
$ \kappa $	The intensity of recycling competition between two used products, 0 < $ \kappa < $1

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Table 4. The main parameter values

$ R $	$ S $	$ c_{d} $	$ c_{q} $	$ \delta_{1} $	$ \delta_{2} $	$ \delta_{3} $	$ \mu $
3	2	2	3	0.1	0.2	0.3	150
$ c_{1n} $	$ c_{1z} $	$ \omega_{1} $	$ c_{2n} $	$ c_{2z} $	$ \omega_{2} $	$ \psi $
40	15	25	30	15	20	3

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Table 5. The optimal solutions in the MRC model and the MS model before the coordination mechanism is adopted

Decision variables	$ p_{1} $	$ p_{2} $	$ b_{1} $	$ b_{2} $	$ \eta_{1} $	$ \eta_{2} $	$ f_{1} $	$ f_{2} $	$ f_{R} $	$ f $
MRC	145	140	9.35	6.87	-	-	-	-	-	14371
MS	118	114	2.79	1.71	11.71	9.52	6207	7072	157	13436

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Table 6. The optimal solution under the coordination mechanism

Decision variables	$ p_{1} $	$ p_{2} $	$ b_{1} $	$ b_{2} $	$ \eta_{1} $	$ \eta_{2} $	$ f_{1} $	$ f_{2} $	$ f_{R} $	$ f $
MS model	117.7	114	2.8	1.7	11.7	9.5	6207	7072	157	13436
Coordination1 mechanism1	117.7	114	9.35	6.87	10.45	8.45	6241	7099	206	13546
Coordination2 1mechanism2	117.7	114	9.35	6.87	9.24	7.49	6257	7109	180	13546

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