# Decision Models for a Dual-Recycling Channel Reverse Supply Chain with Consumer Strategic Behavior

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Analytical Models

#### 3.1. Problem Description

#### 3.2. Basic Assumption

## 4. Optimization Problems

#### 4.1. The Benchmark Case

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

#### 4.2. The Model of Reverse Supply Chain with Dual-Channel in Decentralized Case (SG Model)

**Theorem**

**2.**

**Proof**

**of**

**Theorem**

**2.**

#### 4.3. A Numerical Example

**Proposition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

**Proposition**

**4.**

## 5. Coordination

#### 5.1. Coordination via Revenue Cost-Sharing Contracts

#### 5.2. Coordination via a Two-Part Tariff Contract

**Theorem**

**3.**

**Theorem**

**4.**

- (1)
- ${P}_{r}^{*}>{P}_{r}^{\beta}$, ${P}_{o}^{*}>{P}_{o}^{\beta}$;
- (2)
- ${b}_{t}^{*}<{b}_{t}^{\beta}$;
- (3)
- ${\mathsf{\Pi}}_{RD}^{*}<{\mathsf{\Pi}}_{RD}^{**}$, ${\mathsf{\Pi}}_{R}^{*}<{\mathsf{\Pi}}_{R}^{**}$, ${\mathsf{\Pi}}^{*}<{\mathsf{\Pi}}^{**}$.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Model Parameters | Definition |
---|---|

${P}_{r}$ | Recycling price of the offline channel |

${P}_{o}$ | Recycling price of the online channel |

$\theta >1$ | The consumer popularity of online recycling methods |

$v$ | The expected revenue from the disposal of one unit of scrap product |

$s$ | The willingness of the consumer to return one unit of scrap |

$\lambda $ | Reference-price effect degree |

${c}_{t}$ | The cost of recycling one unit of scrap product by a recycler |

$c$ | The disposal cost of one unit of scrap product by the RD |

${b}_{t}$ | The internal transfer price paid by the RD to the recycler |

${Q}_{i}$ | The function of the amount of recycling scrap product in offline and online recycling channel, where $i$ takes $r$ and $O$ |

${\mathsf{\Pi}}_{j}^{k}$ | The profit function of recycling scrap products in offline recycling and online recycling channels in case $k$; subscript $i$ takes $r$ and $O$ |

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**MDPI and ACS Style**

Wang, B.; Wang, N.
Decision Models for a Dual-Recycling Channel Reverse Supply Chain with Consumer Strategic Behavior. *Sustainability* **2022**, *14*, 10870.
https://doi.org/10.3390/su141710870

**AMA Style**

Wang B, Wang N.
Decision Models for a Dual-Recycling Channel Reverse Supply Chain with Consumer Strategic Behavior. *Sustainability*. 2022; 14(17):10870.
https://doi.org/10.3390/su141710870

**Chicago/Turabian Style**

Wang, Bo, and Ning Wang.
2022. "Decision Models for a Dual-Recycling Channel Reverse Supply Chain with Consumer Strategic Behavior" *Sustainability* 14, no. 17: 10870.
https://doi.org/10.3390/su141710870