# Does Remanufacturing Always Benefit the Manufacturer and Hurt the Supplier?

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## Abstract

**:**

## 1. Introduction

- (1)
- In an integrated environment, in which the supplier and manufacturer are integrated, do remanufacturing operations absolutely benefit the integrated system?
- (2)
- In a separated environment, in which the supplier and manufacturer behave independently, do the remanufacturing operations definitely benefit the manufacturer and hurt the supplier?

## 2. Literature Review

## 3. Model Description

## 4. An Integrated Case

#### 4.1. Benchmark Case: No Remanufacturing

#### 4.2. Manufacturer Implements Remanufacturing

**Theorem**

**1.**

**Proof.**

- (1)
- if ${c}_{n}<\frac{\left(1-\theta \right)\left(1-\alpha \right)\left(1-\varphi \right)}{1-\alpha \theta -\left(1-\alpha \right)\varphi}$, then ${p}_{n}=\frac{1+{c}_{n}}{2}$, ${p}_{r}=\frac{\varphi}{2}$ and ${p}_{t}=\frac{\theta}{2}$;
- (2)
- if ${c}_{n}>\frac{\left(1-\theta \right)\left(1-\alpha \right)\left(1-\varphi \right)}{1-\alpha \theta -\left(1-\alpha \right)\varphi}$, then ${p}_{r}=\frac{\alpha \left(1-\theta \right)\theta -\left(1-\alpha \right)\left(1-2\theta \right)\varphi +\left(1-\alpha \right)\left(1-2\theta \right){\varphi}^{2}+\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right)\varphi {c}_{n}}{2\left(1-\varphi \right)\varphi +2\alpha \left(1-\theta -\varphi +{\varphi}^{2}\right)}$, ${p}_{n}=\frac{1+{c}_{n}}{2}$, and ${p}_{t}=\frac{\varphi \left(\alpha \left(2-\theta \left(2-\varphi \right)-\left(2-\varphi \right)\varphi \right)-\left(1-\varphi \right)\left(1-\theta -\varphi \right)+\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right){c}_{n}\right)}{2\left(1-\varphi \right)\varphi +2\alpha \left(1-\theta -\varphi +{\varphi}^{2}\right)}$.

#### 4.3. Value of Remanufacturing

**Proposition**

**1.**

**Proposition**

**2.**

## 5. Remanufacturing in a Distribution Channel

#### 5.1. Benchmark Case Without Remanufacturing

**Theorem**

**2.**

**Proof.**

#### 5.2. Manufacturer Undertakes Remanufacturing

**Theorem**

**3.**

**Proof.**

#### 5.3. Effects of Remanufacturing In a Distribution Channel

**Proposition**

**3.**

## 6. Discussion

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Conditions | ${\mathit{c}}_{\mathit{n}}\ge {\widehat{\overline{\mathit{c}}}}_{\mathit{n}}$$\text{}\mathbf{and}\text{}{\mathit{D}}_{\mathit{n}2}^{\mathit{S}\mathit{M}*}={\mathit{D}}_{\mathit{r}}^{\mathit{S}\mathit{M}*}\text{}$ | ${\mathit{c}}_{\mathit{n}}<{\widehat{\overline{\mathit{c}}}}_{\mathit{n}}$$\text{}\mathbf{and}\text{}{\mathit{D}}_{\mathit{n}2}^{\mathit{S}\mathit{M}*}{\mathit{D}}_{\mathit{r}}^{\mathit{S}\mathit{M}*}\text{}$ |
---|---|---|

${w}^{SM*}$ | $\frac{1-\theta -\left(1-\alpha \right)\left(\varphi -\theta \right)\varphi +c\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right)}{2\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right)}$ | $\frac{1-\theta -\varphi +\theta \varphi +{c}_{n}\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right)}{2\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right)}$ |

${p}_{n}^{SM*}$ | $\frac{\left(2+{c}_{n}\right)\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right)+1-\theta -\left(1-\alpha \right)\left(\varphi -\theta \right)\varphi}{4\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right)}$ | $\frac{\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right){c}_{n}+3-\theta -\alpha \theta -\left(3-2\alpha -\theta \right)\varphi}{2\left(1+\alpha \left(\varphi -\theta \right)-\varphi \right)}$ |

${p}_{t}^{SM*}$ | $\frac{\left(1-\varphi \right)\varphi \left(3\theta +\varphi -1+{c}_{n}\right)-\alpha \left(2{\theta}^{2}+\theta \left(\left(4+{c}_{n}-3\varphi \right)\varphi -2\right)-\varphi \left(2-\varphi \left(2-{c}_{n}-\varphi \right)\right)\right)}{4\left(1-\varphi \right)\varphi +4\alpha \left(1-\theta -\varphi +{\varphi}^{2}\right)}$ | $\frac{\theta}{2}$ |

${p}_{r}^{SM*}$ | $\frac{\varphi \left(\left(1-\alpha \right)\left(4-{c}_{n}-\theta \right)\varphi +{c}_{n}+4\alpha +\theta -1-4\alpha \theta -{c}_{n}\alpha \theta -3\left(1-\alpha \right){\varphi}^{2}\right)}{4\left(1-\varphi \right)\varphi +4\alpha \left(1-\theta -\varphi +{\varphi}^{2}\right)}$ | $\frac{\varphi}{2}$ |

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**MDPI and ACS Style**

Deng, W.
Does Remanufacturing Always Benefit the Manufacturer and Hurt the Supplier? *Sustainability* **2019**, *11*, 1805.
https://doi.org/10.3390/su11061805

**AMA Style**

Deng W.
Does Remanufacturing Always Benefit the Manufacturer and Hurt the Supplier? *Sustainability*. 2019; 11(6):1805.
https://doi.org/10.3390/su11061805

**Chicago/Turabian Style**

Deng, Weisheng.
2019. "Does Remanufacturing Always Benefit the Manufacturer and Hurt the Supplier?" *Sustainability* 11, no. 6: 1805.
https://doi.org/10.3390/su11061805