# How Does Retailer-Oriented Remanufacturing Affect the OEM’s Quality Choice?

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## Abstract

**:**

## 1. Introduction

## 2. Literature

#### 2.1. Remanufacturing Supply-Chain Management

#### 2.2. Environmental Impact of Remanufacturing

#### 2.3. Quality Decision in Supply-Chain Operation

## 3. Model and Equilibrium Results

#### 3.1. Model Description

#### 3.1.1. Customer Choice Behavior

#### 3.1.2. Demand Functions

#### 3.1.3. Cost Functions

#### 3.2. Model and Equilibrium Result

#### 3.2.1. Basic Model without Remanufacturing (Model NR)

#### 3.2.2. Retailer Developed Remanufacturing (Model R)

## 4. Equilibrium Result Analysis

#### 4.1. Operation Decision and Profits

**Proposition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

**Proposition**

**4.**

**Proposition**

**5.**

#### 4.2. Customer Surplus and Social Welfare

**Proposition**

**6.**

#### 4.3. Environmental Impact

**Proposition**

**7.**

## 5. Conclusions and Managerial Implications

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Proof**

**of**

**Table**

**2.**

**Proof**

**of**

**Table**

**3.**

**Proof**

**of**

**Proposition**

**1**

**.**The results of Proposition 1 are easy to obtain from Table 3, so we omit the proof process. □

**Proof**

**of**

**Proposition**

**2.**

**Proof**

**of**

**Proposition**

**3.**

**Proof**

**of**

**Proposition**

**4.**

**Proof**

**of**

**Proposition**

**5.**

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Symbol | Definition |
---|---|

$v$ | The consumers willing to pay for the new product |

$\delta $ | The valuation of the remanufactured products relative to the new products |

$s$ | The quality level of the new products |

$\alpha $ | The ratio of unit variable cost of remanufactured product to new product |

$w$ | The wholesale price of the new products |

${Q}_{\mathrm{N}}$ | The quantity of the new products |

${p}_{\mathrm{N}}$ | The price of the new products |

${Q}_{\mathrm{R}}$ | The quantity of the remanufactured products |

${p}_{\mathrm{R}}$ | The price of the remanufactured products |

Variable | Equilibrium Result |
---|---|

${s}_{\mathrm{NR}}^{*}$ | $\frac{1}{3\beta}$ |

${w}_{\mathrm{NR}}^{*}$ | $\frac{2}{9\beta}$ |

${Q}_{\mathrm{N}\text{-}\mathrm{NR}}^{*}$ | $\frac{1}{6}$ |

${p}_{\mathrm{N}\text{-}\mathrm{NR}}^{*}$ | $\frac{5}{18\beta}$ |

${\mathsf{\Pi}}_{\mathrm{R}\text{-}\mathrm{NR}}^{*}$ | $\frac{1}{108\beta}$ |

${\mathsf{\Pi}}_{\mathrm{OEM}\text{-}\mathrm{NR}}^{*}$ | $\frac{1}{54\beta}$ |

Variable | Equilibrium Result | ||
---|---|---|---|

Range | $\alpha /\delta >2$ | $2/\left(1+\delta \right)<\alpha /\delta <2$ | $\alpha /\delta <2/\left(1+\delta \right)$ |

${s}_{\mathrm{R}}^{*}$ | $\frac{1}{3\beta}$ | $\frac{2\delta}{3\alpha \beta}$ | $\frac{1-\delta}{3\left(1-\alpha \right)\beta}$ |

${w}_{\mathrm{R}}^{*}$ | $\frac{2}{9\beta}$ | $\frac{4\delta}{9\alpha \beta}$ | $\frac{\left(2-\alpha \right){\left(1-\delta \right)}^{2}}{9{\left(1-\alpha \right)}^{2}\beta}$ |

${Q}_{\mathrm{N}\text{-}\mathrm{R}}^{*}$ | $\frac{1}{6}$ | $\frac{1}{6}$ | $\frac{1}{6}$ |

${Q}_{\mathrm{R}\text{-}\mathrm{R}}^{*}$ | 0 | 0 | $\frac{2\delta -\delta \alpha -\alpha}{6\delta \left(1-\alpha \right)}$ |

${p}_{\mathrm{N}\text{-}\mathrm{R}}^{*}$ | $\frac{5}{18\beta}$ | $\frac{5\delta}{9\alpha \beta}$ | $\frac{\left(\left(5-2\delta \right)-\left(4-\delta \right)\alpha \right)\left(1-\delta \right)}{18{\left(1-\alpha \right)}^{2}\beta}$ |

${p}_{\mathrm{R}\text{-}\mathrm{R}}^{*}$ | NA | NA | $\frac{\left(3\delta +\left(1-4\delta \right)\alpha \right)\left(1-\delta \right)}{18{\left(1-\alpha \right)}^{2}\beta}$ |

${\mathsf{\Pi}}_{\mathrm{R}\text{-}\mathrm{R}}^{*}$ | $\frac{1}{108\beta}$ | $\frac{\delta}{54\alpha \beta}$ | $\begin{array}{l}\frac{\left(\left(1+2\delta \right)-\left(2+\delta \right)\alpha \right)\left(1-\delta \right)}{108{\left(1-\alpha \right)}^{2}\beta}+\\ \frac{\left(1-\delta \right)\left(2\delta -\delta \alpha -\alpha \right)\left(3\delta -\left(1+2\delta \right)\alpha \right)}{108\delta {\left(1-\alpha \right)}^{3}\beta}\end{array}$ |

${\mathsf{\Pi}}_{\mathrm{OEM}\text{-}\mathrm{R}}^{*}$ | $\frac{1}{54\beta}$ | $\frac{4\delta \left(\alpha -\delta \right)}{54{\alpha}^{2}\beta}$ | $\frac{{\left(1-\delta \right)}^{2}}{54\beta \left(1-\alpha \right)}$ |

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**MDPI and ACS Style**

Zou, Z.; Wang, C.; Zhong, Q.
How Does Retailer-Oriented Remanufacturing Affect the OEM’s Quality Choice? *Sustainability* **2022**, *14*, 8028.
https://doi.org/10.3390/su14138028

**AMA Style**

Zou Z, Wang C, Zhong Q.
How Does Retailer-Oriented Remanufacturing Affect the OEM’s Quality Choice? *Sustainability*. 2022; 14(13):8028.
https://doi.org/10.3390/su14138028

**Chicago/Turabian Style**

Zou, Zongbao, Cong Wang, and Qinjia Zhong.
2022. "How Does Retailer-Oriented Remanufacturing Affect the OEM’s Quality Choice?" *Sustainability* 14, no. 13: 8028.
https://doi.org/10.3390/su14138028