# Coordination of Retailer-Led Closed Loop Supply Chain Considering Corporate Social Responsibility

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Decision Analysis and Coordination Mechanism of Supply Chain Considering CSR

#### 3.1. Basic Model

**Hypothesis**

**1.**

**Hypothesis**

**2.**

**Hypothesis**

**3.**

**Hypothesis**

**4.**

**Hypothesis**

**5.**

#### 3.2. Decision Analysis of Closed-Loop Supply Chain without CSR

#### 3.2.1. The Optimal Pricing Strategies without CSR under Decentralized Decisions (Model A)

**Theorem**

**1.**

**Proof.**

#### 3.2.2. The Optimal Pricing Strategies without CSR under Centralized Decision Making (Model B)

**Theorem**

**2.**

**Proof.**

#### 3.3. Decision Analysis of Closed-Loop Supply Chain with CSR

#### 3.3.1. The Optimal Pricing Strategies with CSR under Decentralized Decision Making (Model C)

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Theorem**

**5.**

**Proof.**

**Theorem**

**6.**

**Proof.**

#### 3.3.2. The Optimal Pricing Strategies with CSR under Centralized Decision Making (Model D)

**Theorem**

**7.**

**Proof.**

#### 3.3.3. Comparative Analysis under Different Decision Situations

**Theorem**

**8.**

**Proof.**

**Theorem**

**9.**

**Proof.**

**Theorem**

**10.**

**Proof.**

**Theorem**

**11.**

**Proof.**

**Theorem**

**12.**

**Proof.**

**Theorem**

**13.**

**Proof.**

#### 3.4. A Coordination Mechanism

**Conclusion**

**1.**

**Proof.**

## 4. Numerical Illustration

#### 4.1. The Influence of Enterprise Recovery Scale Parameter on Various Variables

#### 4.2. The Influence of CSR Cost Coefficient on Various Variables

#### 4.3. Coordination Result Analysis

## 5. Conclusions

- (1)
- CSR input can promote the overall development of a closed-loop supply chain. The product recovery rate, product pricing, CSR, consumer product demand and other aspects have been strengthened, and the overall revenue has been improved. However, the investment in CSR must be within a certain range, that is, the investment in CSR should be moderate, in line with the development of the enterprise itself, in order to play a greater effect. Too little or too much CSR investment cannot greatly promote the development of a closed-loop supply chain.
- (2)
- With a slow increase in CSR cost, the equilibrium price, CSR input level, recovery rate and wholesale price of the closed-loop supply chain all decrease. However, with a gradual increase in the equilibrium price of the closed-loop supply chain, the CSR input level, the recovery rate and the wholesale price of products will all stabilize around a value and will not change. In summary, CSR input in a closed-loop supply chain cannot always improve consumer surplus and environmental performance, or social welfare. The optional decisions will be realized when they happen to be within an appropriate range.
- (3)
- The proposed pricing coordination mechanism can improve the profits of the manufacturer, retailer and the whole closed-loop supply chain, and make the decision level reach or approach to the best level under centralized decision making. The above conclusions indicate that in the daily operation of enterprises, it is necessary to strengthen the cooperation between upstream and downstream and share information, and at the same time, appropriately consider the implementation of CSR in the daily operation of the company. Secondly, in the daily operation of the supply chain, considering the retailer as the leader is conducive to obtaining the demand of the market, consumers and customers, and is conducive to timely communication with the manufacturer, so as to promote an increase in enterprise efficiency and income.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The changing of the demand and total profits of closed-loop supply chain with ${C}_{L}$ (

**a**,

**b**).

$\mathit{\xi}$ | $\mathit{\tau}$ | ${\mathit{e}}_{\mathit{m}}$ | $\mathit{p}$ | $\mathit{w}$ | ${\mathit{\pi}}_{\mathit{m}}$ | ${\mathit{\pi}}_{\mathit{r}}$ | ${\mathit{\tau}}^{\mathit{T}\mathit{P}\mathit{T}}$ | ${\mathit{e}}_{\mathit{m}}{}^{\mathit{T}\mathit{P}\mathit{T}}$ | ${\mathit{p}}^{\mathit{T}\mathit{P}\mathit{T}}$ | ${\mathit{w}}^{\mathit{T}\mathit{P}\mathit{T}}$ | ${\mathit{\pi}}_{\mathit{m}}{}^{\mathit{T}\mathit{P}\mathit{T}}$ | ${\mathit{\pi}}_{\mathit{r}}{}^{\mathit{T}\mathit{P}\mathit{T}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

6 | 0.500 | 5.000 | 10.250 | 7.750 | 46.875 | 93.750 | 0.483 | 4.986 | 10.366 | 7.774 | 46.875 | 90.448 |

10 | 0.305 | 1.829 | 9.177 | 6.677 | 28.528 | 57.165 | 0.362 | 1.693 | 8.643 | 6.393 | 28.528 | 65.677 |

20 | 0.236 | 0.708 | 8.797 | 6.297 | 22.111 | 44.222 | 0.337 | 0.490 | 7.864 | 5.552 | 22.111 | 56.416 |

30 | 0.219 | 0.439 | 8.706 | 6.206 | 20.599 | 41.118 | 0.341 | 0.240 | 7.632 | 5.218 | 20.599 | 54.695 |

40 | 0.212 | 0.318 | 8.665 | 6.165 | 19.862 | 39.725 | 0.347 | 0.143 | 7.514 | 5.024 | 19.862 | 54.130 |

50 | 0.208 | 0.249 | 8.642 | 6.142 | 19.466 | 38.933 | 0.351 | 0.096 | 7.441 | 4.895 | 19.466 | 53.901 |

60 | 0.205 | 0.205 | 8.627 | 6.127 | 19.211 | 38.422 | 0.355 | 0.068 | 7.391 | 4.803 | 19.211 | 53.800 |

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**MDPI and ACS Style**

Zhao, H.; Liu, Y.; Liu, Z.
Coordination of Retailer-Led Closed Loop Supply Chain Considering Corporate Social Responsibility. *Sustainability* **2022**, *14*, 10851.
https://doi.org/10.3390/su141710851

**AMA Style**

Zhao H, Liu Y, Liu Z.
Coordination of Retailer-Led Closed Loop Supply Chain Considering Corporate Social Responsibility. *Sustainability*. 2022; 14(17):10851.
https://doi.org/10.3390/su141710851

**Chicago/Turabian Style**

Zhao, Huanhuan, Yong Liu, and Zhiyang Liu.
2022. "Coordination of Retailer-Led Closed Loop Supply Chain Considering Corporate Social Responsibility" *Sustainability* 14, no. 17: 10851.
https://doi.org/10.3390/su141710851