# American Institute of Mathematical Sciences

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

Received  April 2021 Revised  August 2021 Early access November 2021

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.

Citation: Kai Li, Yan Li, Jing Liu, Nenggui Zhao. Two-sided vertical competition considering product quality in a manufacturing-remanufacturing system. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021187
##### References:

show all references

##### References:
Closed-loop supply chain structures
The profits of manufacturer and supplier vs. $\delta$
The profits of manufacturer and supplier vs. $q_{n}$
The profits of manufacturer and supplier vs. $q_{r}$
The profits of manufacturer and supplier under different competition modes vs. $\delta$
The profits of manufacturer and supplier under different competition modes vs. $q_{n}$
The profits of manufacturer and supplier under different competition modes vs. $q_{r}$
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
 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
The effect of $q_{n}$ and $q_{r}$ on optimal decisions under vertical competition Ⅰ mode
 Symbol $p_{n}^{{\rm{NC}}}$ $p_{r}^{{\rm{NC}}}$ ${w^{{\rm{NC}}}}$ ${f^{{\rm{NC}}}}$ $q_{n}$ $+$ $/$ $+$ $/$ $q_{r}$ $/$ $+$ $/$ $+$
 Symbol $p_{n}^{{\rm{NC}}}$ $p_{r}^{{\rm{NC}}}$ ${w^{{\rm{NC}}}}$ ${f^{{\rm{NC}}}}$ $q_{n}$ $+$ $/$ $+$ $/$ $q_{r}$ $/$ $+$ $/$ $+$
The effect of $q_{n}$ and $q_{r}$ on optimal decisions under vertical competition Ⅱ mode
 Symbol $p_{n}^{{\rm{VC}}}$ $p_{r}^{{\rm{VC}}}$ ${w^{{\rm{VC}}}}$ $q_{n}$ $+$ $/$ $+$ $q_{r}$ $\mp$ $+$ $\mp$
 Symbol $p_{n}^{{\rm{VC}}}$ $p_{r}^{{\rm{VC}}}$ ${w^{{\rm{VC}}}}$ $q_{n}$ $+$ $/$ $+$ $q_{r}$ $\mp$ $+$ $\mp$
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
 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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