# Dynamic Collection Strategy and Coordination of a Remanufacturing Closed-Loop Supply Chain under Uncertainty

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## Abstract

**:**

## 1. Introduction

## 2. The Model

## 3. Benchmark Model: The Integrated Channel

**Proposition**

**1.**

- (1)
- The optimal retail price control strategy of the central decision maker is given by:$${p}^{C*}=\frac{\varphi +\beta {c}_{m}-\beta \Delta \tau}{2\beta};$$
- (2)
- The optimal collection effort level control strategy is given by:$${A}^{C*}=\frac{\rho}{k}\left({e}_{1}\tau +{e}_{2}\right);$$
- (3)
- The value function of the integrated channel is calculated by$${V}^{C*}=\frac{1}{2}{e}_{1}{\tau}^{2}+{e}_{2}\tau +{e}_{3}(1),$$

## 4. Model Analysis: The Decentralized Channel

#### 4.1. Feedback Stackelberg Equilibrium

**Proposition**

**2.**

#### 4.2. The Evolutionary Path of the Stochastic Return Rate

**Proposition**

**3.**

**Proposition**

**4.**

#### 4.3. The Probability Distribution of the Stochastic Return Rate

**Proposition**

**5.**

## 5. Channel Coordination

**Proposition**

**6.**

**Proof.**

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**The simulation of the stochastic return rate of decentralized closed-loop supply chain (CLSC).

Equilibrium Strategies | Parameters | ||
---|---|---|---|

Δ | C_{m} | σ | |

w^{D*} | ↓ | ↑ | – |

P^{D*} | ↓ | ↑ | – |

A^{D*} | ↑ | ↓ | ↑ |

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## Share and Cite

**MDPI and ACS Style**

Huang, Z.; Nie, J.; Tsai, S.-B.
Dynamic Collection Strategy and Coordination of a Remanufacturing Closed-Loop Supply Chain under Uncertainty. *Sustainability* **2017**, *9*, 683.
https://doi.org/10.3390/su9050683

**AMA Style**

Huang Z, Nie J, Tsai S-B.
Dynamic Collection Strategy and Coordination of a Remanufacturing Closed-Loop Supply Chain under Uncertainty. *Sustainability*. 2017; 9(5):683.
https://doi.org/10.3390/su9050683

**Chicago/Turabian Style**

Huang, Zongsheng, Jiajia Nie, and Sang-Bing Tsai.
2017. "Dynamic Collection Strategy and Coordination of a Remanufacturing Closed-Loop Supply Chain under Uncertainty" *Sustainability* 9, no. 5: 683.
https://doi.org/10.3390/su9050683