Two-sided vertical competition considering product quality in a manufacturing-remanufacturing system

Kai Li; Yan Li; Jing Liu; Nenggui Zhao

doi:10.3934/jimo.2021187

Article Contents

2023, Volume 19, Issue 1: 338-358. Doi: 10.3934/jimo.2021187

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Two-sided vertical competition considering product quality in a manufacturing-remanufacturing system

School of Management, Hefei University of Technology, Hefei, China
Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, China

^* Corresponding author: Yan Li
^* Corresponding author: Yan Li

Received: March 31, 2021

Revised: July 31, 2021

Early access: November 2021

Published: January 2023

Abstract Full Text(HTML) Figure(7) / Table(4) Related Papers Cited by

Abstract

We study two-sided vertical competition between a manufacturer and a supplier. The problem is formulated as a dynamic game where the supplier has more pricing power than the manufacturer. Based on the one-sided vertical competition modes with different recyclers as benchmarks, we derive optimal pricing and production decisions of manufacturer and supplier and further study the impacts of product quality on those decisions under the two-sided vertical competition mode. A key finding is that manufacturer/supplier prefers to be a follower rather than the first one to engage in recycling activities. Specifically, when the manufacturer/supplier has engaged in recycling activities, the supplier/manufacturer has an incentive to participate in recycling activities as well. We also find that high-quality remanufactured components/products can benefit manufacturer, supplier and consumers at the same time.

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Mathematics Subject Classification: Primary: 91B16, 91A65; Secondary: 91B24.

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Figure 1. Closed-loop supply chain structures

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Figure 2. The profits of manufacturer and supplier vs. $ \delta $

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Figure 3. The profits of manufacturer and supplier vs. $ q_{n} $

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Figure 4. The profits of manufacturer and supplier vs. $ q_{r} $

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Figure 5. The profits of manufacturer and supplier under different competition modes vs. $ \delta $

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Figure 6. The profits of manufacturer and supplier under different competition modes vs. $ q_{n} $

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Figure 7. The profits of manufacturer and supplier under different competition modes vs. $ q_{r} $

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Table 1. Basic symbols in models

Symbol	Definition
$ v $	The consumer's willingness to pay for the new products
$ \delta $	The consumer value discount for remanufactured products
$ \phi $	The percentage of used products that manufacturer recycles
$ c_{n}/c_{r} $	The unit cost when using the new/remanufactured component
$ p_{n}/p_{r} $	The unit price of new/remanufactured product
$ q_{n}/q_{r} $	The quality of new/remanufactured component
$ d_{n}/d_{r} $	The quantity of new/remanufactured products
$ w/f $	The price of new/ remanufactured component
$ U_{n}/U_{r} $	The net utility obtained by consumers when they purchase new/remanufactured product

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Table 2. The effect of $ q_{n} $ and $ q_{r} $ on optimal decisions under vertical competition Ⅰ mode

Symbol	$ p_{n}^{{\rm{NC}}} $	$ p_{r}^{{\rm{NC}}} $	$ {w^{{\rm{NC}}}} $	$ {f^{{\rm{NC}}}} $
$ q_{n} $	$ + $	$ / $	$ + $	$ / $
$ q_{r} $	$ / $	$ + $	$ / $	$ + $

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Table 3. The effect of $ q_{n} $ and $ q_{r} $ on optimal decisions under vertical competition Ⅱ mode

Symbol	$ p_{n}^{{\rm{VC}}} $	$ p_{r}^{{\rm{VC}}} $	$ {w^{{\rm{VC}}}} $
$ q_{n} $	$ + $	$ / $	$ + $
$ q_{r} $	$ \mp $	$ + $	$ \mp $

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Table 4. The effect of $ q_{n} $, $ q_{r} $ and $ \phi $ on optimal decisions under two-sided vertical competition mode

Symbol	$ p_{n}^{{\rm{NC}}} $	$ p_{r}^{{\rm{NC}}} $	$ {w^{{\rm{NC}}}} $	$ {f^{{\rm{NC}}}} $
$ q_{n} $	$ + $	$ / $	$ + $	$ / $
$ q_{r} $	$ / $	$ + $	$ / $	$ +\left(0 <\phi<\frac{1}{2}\right),-\left(\frac{1}{2}<\phi<1\right)$
$ \phi $	$ / $	$ / $	$ / $	Shown in proposition 7

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