# Research on Coordination in a Dual-Channel Green Supply Chain under Live Streaming Mode

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## Abstract

**:**

## 1. Introduction

## 2. Related Literature

#### 2.1. Research on Green Supply Chain

#### 2.2. Research on Supply Chain Coordination

#### 2.3. Research on Supply Chain Models and Decisions

## 3. Model Descriptions, Notations and the Integrated Benchmark

#### 3.1. Model Descriptions, Notations and Assumptions

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Assumption**

**4.**

**Assumption**

**5.**

- Profit function

#### 3.2. The Integrated Benchmark

**Proposition**

**1.**

**Proof of Proposition**

**1.**

## 4. The Decentralized Model

#### 4.1. Manufacturer-Dominant Decentralized Model (MD Model)

**Proposition**

**2.**

**Proof of Proposition**

**2.**

#### 4.2. Retailer-Dominant Decentralized Model (RD Model)

**Proposition**

**3.**

**Proof of Proposition**

**3.**

## 5. Supply Chain Coordination

#### 5.1. RSC Contract

**Proposition**

**4.**

**Proof of Proposition**

**4.**

#### 5.2. CS-GS Contract

**Proposition**

**5.**

**Proof of Proposition**

**5.**

**Proposition**

**6.**

## 6. Analysis

#### 6.1. The Impact of Coordination Contract on the Supply Chain’s Performance

#### 6.2. The Impacts of $\tau $ and $b$ on the Profits of Supply Chain and Members

#### 6.3. The Impacts of Relevant Parameters on the Decisions

#### 6.3.1. The Impacts of $\tau $ and $\gamma $ on the Green Degree of the Product

#### 6.3.2. The Impacts of $b$ and $k$ on the Sales Effort of the Advertisement

#### 6.3.3. The Impacts of $d$ and $\beta $ on the Price

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Decision variables: | |

p | the unit product’s retail price; |

θ | the green degree of the product; |

e | the sales effort of the advertisement; |

D | consumer’s demand, which is a function of p, $\theta $, e, $d$; |

Parameters: | |

c | the unit manufacturing cost; |

$\tau $ | the coefficient of the green investment; |

b | the scale parameter of the advertisement; |

w | the unit wholesale price; |

α | the market base of this product; |

β | the responsiveness of the consumer demand to retail price; |

k | the responsiveness of the consumer demand to the sales effort; |

r | the responsiveness of the consumer demand to the green degree; |

$\tilde{p}$ | the selling price in live streaming rooms |

$d$ | the discount of the retail price in live streaming rooms |

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Optimal Decisions | Green Degree (θ) | Sales Effort (e) | Retail Price (p) |
---|---|---|---|

Centralized model | $\frac{k\tau \left(2\beta c-\alpha +\alpha d-3\beta cd-\alpha dz+2\beta c{d}^{2}\right)}{-2b\tau \beta {d}^{2}+4b\tau \beta d+\tau {k}^{2}+b{\gamma}^{2}-4b\tau \beta}$ | $\frac{b\gamma \left(2\beta c-\alpha +\alpha d-3\beta cd-\alpha dz+2\beta c{d}^{2}\right)}{-2b\tau \beta {d}^{2}+4b\tau \beta d+\tau {k}^{2}+b{\gamma}^{2}-4b\tau \beta}$ | $\frac{c\tau {k}^{2}+bc{\gamma}^{2}-\alpha b\tau -2bc\tau \beta +\alpha bd\tau -\alpha bd\tau z+bcd\tau \beta}{-2b\tau \beta {d}^{2}+4b\tau \beta d+\tau {k}^{2}+b{\gamma}^{2}-4b\tau \beta}$ |

Decentralized model (MD) | $-\frac{\begin{array}{c}\frac{b\hspace{0.17em}\beta \hspace{0.17em}\gamma \hspace{0.17em}\left(c-w\right)}{{\sigma}_{1}}-\frac{b\hspace{0.17em}\gamma \hspace{0.17em}\left(d-1\right)\hspace{0.17em}\left(\alpha \hspace{0.17em}\left(z-1\right)-\frac{\beta \hspace{0.17em}\left(d-1\right)\hspace{0.17em}{\sigma}_{2}}{{\sigma}_{1}}\right)}{{\sigma}_{1}}\\ +\frac{b\hspace{0.17em}\beta \hspace{0.17em}\gamma \hspace{0.17em}\left(c+\frac{\left(d-1\right)\hspace{0.17em}{\sigma}_{2}}{{\sigma}_{1}}\right)\hspace{0.17em}\left(d-1\right)}{{\sigma}_{1}}\end{array}}{\tau +\frac{2\hspace{0.17em}{b}^{2}\hspace{0.17em}\beta \hspace{0.17em}{\gamma}^{2}\hspace{0.17em}{\left(d-1\right)}^{2}}{{\sigma}_{1}{}^{2}}}$ ${\sigma}_{1}=2\hspace{0.17em}b\hspace{0.17em}\beta -{k}^{2}$ ${\sigma}_{2}=-w\hspace{0.17em}{k}^{2}+b\hspace{0.17em}\beta \hspace{0.17em}w+\alpha \hspace{0.17em}b\hspace{0.17em}z$ | $\frac{k\left(\alpha z-\beta w+{\theta}_{d}^{md\ast}\gamma \right)}{2\beta b-{k}^{2}}$ | $\frac{zb\alpha +b{\theta}_{d}^{md\ast}\gamma +b\beta w-{k}^{2}w}{2\beta b-{k}^{2}}$ |

Decentralized model (RD) | $\frac{\gamma \hspace{0.17em}\left(w-c\right)}{\tau}$ | $\frac{k\hspace{0.17em}\left(-\hspace{0.17em}c{\gamma}^{2}+{\gamma}^{2}\hspace{0.17em}w-\beta \hspace{0.17em}\tau \hspace{0.17em}w+\alpha \hspace{0.17em}\tau \hspace{0.17em}z\right)}{\tau \hspace{0.17em}\left(2\hspace{0.17em}b\hspace{0.17em}\beta -{k}^{2}\right)}$ | $\frac{b\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}w-b\hspace{0.17em}c\hspace{0.17em}{\gamma}^{2}-{k}^{2}\hspace{0.17em}\tau \hspace{0.17em}w+b\hspace{0.17em}\beta \hspace{0.17em}\tau \hspace{0.17em}w+\alpha \hspace{0.17em}b\hspace{0.17em}\tau \hspace{0.17em}z}{\tau \hspace{0.17em}\left(2\hspace{0.17em}b\hspace{0.17em}\beta -{k}^{2}\right)}$ |

Coordination model (RSC) | $\frac{-\gamma \hspace{0.17em}\left(\begin{array}{c}c\hspace{0.17em}{k}^{2}\hspace{0.17em}\tau -{k}^{2}\hspace{0.17em}\tau \hspace{0.17em}w+2\hspace{0.17em}b\hspace{0.17em}\beta \hspace{0.17em}\tau \hspace{0.17em}w+b\hspace{0.17em}c\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}\varphi -b\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}\varphi \hspace{0.17em}w\\ -c\hspace{0.17em}{k}^{2}\hspace{0.17em}\varphi \hspace{0.17em}\tau +{k}^{2}\hspace{0.17em}\varphi \hspace{0.17em}\tau \hspace{0.17em}w-2\hspace{0.17em}b\hspace{0.17em}\beta \hspace{0.17em}c\hspace{0.17em}\tau -b\hspace{0.17em}\beta \hspace{0.17em}\varphi \hspace{0.17em}\tau \hspace{0.17em}w\\ +\alpha \hspace{0.17em}b\hspace{0.17em}\varphi \hspace{0.17em}\tau \hspace{0.17em}z\end{array}\right)}{\tau \hspace{0.17em}\left({k}^{2}\hspace{0.17em}\tau -{k}^{2}\hspace{0.17em}\varphi \hspace{0.17em}\tau -2\hspace{0.17em}b\hspace{0.17em}\beta \hspace{0.17em}\tau +2\hspace{0.17em}b\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}\varphi \right)}$ | $\frac{k\hspace{0.17em}\left(1-\varphi \right)\hspace{0.17em}\left(c\hspace{0.17em}{\gamma}^{2}-{\gamma}^{2}\hspace{0.17em}w+\beta \hspace{0.17em}\tau \hspace{0.17em}w-\alpha \hspace{0.17em}\tau \hspace{0.17em}z\right)}{{k}^{2}\hspace{0.17em}\tau -{k}^{2}\hspace{0.17em}\varphi \hspace{0.17em}\tau -2\hspace{0.17em}b\hspace{0.17em}\beta \hspace{0.17em}\tau +2\hspace{0.17em}b\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}\varphi}$ | $\frac{\begin{array}{c}-b\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}w+b\hspace{0.17em}c\hspace{0.17em}{\gamma}^{2}+{k}^{2}\hspace{0.17em}\tau \hspace{0.17em}w-b\hspace{0.17em}\beta \hspace{0.17em}\tau \hspace{0.17em}w-\alpha \hspace{0.17em}b\hspace{0.17em}\tau \hspace{0.17em}z\\ +2\hspace{0.17em}b\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}\varphi \hspace{0.17em}w-{k}^{2}\hspace{0.17em}\varphi \hspace{0.17em}\tau \hspace{0.17em}w\end{array}}{{k}^{2}\hspace{0.17em}\tau -{k}^{2}\hspace{0.17em}\varphi \hspace{0.17em}\tau -2\hspace{0.17em}b\hspace{0.17em}\beta \hspace{0.17em}\tau +2\hspace{0.17em}b\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}\varphi}$ |

Coordination model (CS-GS) | $\frac{\gamma \hspace{0.17em}\left(w-c\right)}{l\hspace{0.17em}\tau}$ | $\frac{k\hspace{0.17em}\left(c\hspace{0.17em}{\gamma}^{2}-{\gamma}^{2}\hspace{0.17em}w+\beta \hspace{0.17em}l\hspace{0.17em}\tau \hspace{0.17em}w-\alpha \hspace{0.17em}l\hspace{0.17em}\tau \hspace{0.17em}z\right)}{l\hspace{0.17em}\tau \hspace{0.17em}\left({k}^{2}-2\hspace{0.17em}b\hspace{0.17em}\beta +2\hspace{0.17em}b\hspace{0.17em}\beta \hspace{0.17em}f\right)}$ | $\frac{\begin{array}{c}b\hspace{0.17em}c\hspace{0.17em}{\gamma}^{2}-b\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}w-b\hspace{0.17em}c\hspace{0.17em}f\hspace{0.17em}{\gamma}^{2}+b\hspace{0.17em}f\hspace{0.17em}{\gamma}^{2}\hspace{0.17em}w+{k}^{2}\hspace{0.17em}l\hspace{0.17em}\tau \hspace{0.17em}w\\ -b\hspace{0.17em}\beta \hspace{0.17em}l\hspace{0.17em}\tau \hspace{0.17em}w-\alpha \hspace{0.17em}b\hspace{0.17em}l\hspace{0.17em}\tau \hspace{0.17em}z+b\hspace{0.17em}\beta \hspace{0.17em}f\hspace{0.17em}l\hspace{0.17em}\tau \hspace{0.17em}w+\alpha \hspace{0.17em}b\hspace{0.17em}f\hspace{0.17em}l\hspace{0.17em}\tau \hspace{0.17em}z\end{array}}{l\hspace{0.17em}\tau \hspace{0.17em}\left({k}^{2}-2\hspace{0.17em}b\hspace{0.17em}\beta +2\hspace{0.17em}b\hspace{0.17em}\beta \hspace{0.17em}f\right)}$ |

Model | Coordination Parameters | θ | e | p | ${\mathit{\pi}}_{\mathit{m}}$ | ${\mathit{\pi}}_{\mathit{r}}$ | $\mathit{\pi}$ |
---|---|---|---|---|---|---|---|

Centralized model | - | 22.3 | 28.6 | 208.5 | - | - | 26,737.6 |

Decentralized model (MD) | - | 16.2 | 15.5 | 137.1 | 17,125.7 | 5055.4 | 22,181.1 |

Decentralized model (RD) | - | 1.25 | 14.4 | 130.1 | 16,658.8 | 4354.7 | 21,013.5 |

Coordination model (RSC) | (w, $\varphi $) (197.3, 0.6) When ${\xi}_{1}=0.6$ | 0.72 | 21.8 | 208.5 | 18,929.8 | 5868.5 | 24,798.3 |

Coordination model (CS-GS) | $\left(w,l,f\right)$ (160.4, 0.73, 0.73) When ${\xi}_{1}=0.6$ | 22.3 | 28.6 | 208.5 | 20,093.4 | 6644.2 | 26,737.6 |

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## Share and Cite

**MDPI and ACS Style**

Chen, T.; Zhou, R.; Liu, C.; Xu, X.
Research on Coordination in a Dual-Channel Green Supply Chain under Live Streaming Mode. *Sustainability* **2023**, *15*, 878.
https://doi.org/10.3390/su15010878

**AMA Style**

Chen T, Zhou R, Liu C, Xu X.
Research on Coordination in a Dual-Channel Green Supply Chain under Live Streaming Mode. *Sustainability*. 2023; 15(1):878.
https://doi.org/10.3390/su15010878

**Chicago/Turabian Style**

Chen, Tianwen, Ronghu Zhou, Changqing Liu, and Xiang Xu.
2023. "Research on Coordination in a Dual-Channel Green Supply Chain under Live Streaming Mode" *Sustainability* 15, no. 1: 878.
https://doi.org/10.3390/su15010878