# Sustainability Analysis and Buy-Back Coordination in a Fashion Supply Chain with Price Competition and Demand Uncertainty

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## Abstract

**:**

## 1. Introduction

- (1)
- How to design a buy-back contract with return cost to achieve supply chain coordination?
- (2)
- What are the effects of price competition and demand uncertainty on supply chain sustainability in each channel?

## 2. Literature Review

## 3. Model Formulation

#### 3.1. Notation and Game Structure

**Parameters: ($\mathit{i}\mathit{\u03f5}\left\{\mathit{D},\mathit{R}\right\}$)**

- $a$: Market potential (maximum attainable without cross-effects).
- $b$: Cross-price sensitivity on demand.
- ${q}_{i}$: Demand in channel $i$.
- ${\u03f5}_{i}$: Random demand in channel $i$.
- $w$: Wholesale price in retail channel.
- ${c}_{M}$: Production cost of fashion brand.
- $v$: Unit salvage value at the end of the selling season.
- ${f}_{i}(\xb7),{F}_{i}(\xb7),{\mu}_{i},{\sigma}_{i}$: Probability density function, cumulative distribution function, mean, and standard deviation of random variable ${\u03f5}_{i}$.
- ${X}_{i},{Y}_{i}$: Lower bound and upper bound of ${\u03f5}_{i}$.
- $m$: Return price from the retailer.
- $n$: Return cost (including logistics cost, repacking cost, etc.).

**Decision variables:**

- ${p}_{i}$: Selling price in channel $i$.
- ${Q}_{i}$: Order quantity in channel $i$.
- ${\tau}_{i}$: Safety stock in channel $i$.

#### 3.2. Optimal Decisions

**Lemma**

**1.**

## 4. Supply Chain Coordination under a Buy-Back Contract

**Proposition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

**Proposition**

**4.**

## 5. Sustainability Analysis

#### 5.1. Effect of Price Competition on Supply Chain Sustainability

**Proposition**

**5.**

#### 5.2. Effect of Demand Uncertainty on Sustainability

**Proposition**

**6.**

**Proposition**

**7.**

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. All Proofs

**Proof**

**of**

**Lemma**

**1.**

**Proof**

**of**

**Proposition**

**1.**

**Proof**

**of**

**Proposition**

**2.**

**Proof**

**of**

**Proposition**

**4.**

**Proof**

**of**

**Proposition**

**5.**

**Proof**

**of**

**Proposition**

**6.**

**Proof**

**of**

**Proposition**

**7.**

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**MDPI and ACS Style**

Wang, F.; Zhuo, X.; Niu, B.
Sustainability Analysis and Buy-Back Coordination in a Fashion Supply Chain with Price Competition and Demand Uncertainty. *Sustainability* **2017**, *9*, 25.
https://doi.org/10.3390/su9010025

**AMA Style**

Wang F, Zhuo X, Niu B.
Sustainability Analysis and Buy-Back Coordination in a Fashion Supply Chain with Price Competition and Demand Uncertainty. *Sustainability*. 2017; 9(1):25.
https://doi.org/10.3390/su9010025

**Chicago/Turabian Style**

Wang, Fan, Xiaopo Zhuo, and Baozhuang Niu.
2017. "Sustainability Analysis and Buy-Back Coordination in a Fashion Supply Chain with Price Competition and Demand Uncertainty" *Sustainability* 9, no. 1: 25.
https://doi.org/10.3390/su9010025