# Sustainability Analysis of Supply Chains with Fashion Products under Alternative Power Structures and Loss-Averse Supplier

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. The Model

**Theorem**

**1.**

- 1.
- $L(q)$ is an increasing function of q;
- 2.
- $R(q)$ is a decreasing function of q, $\forall q\ge 1$;
- 3.
- $SLR(q)$ is a decreasing function of q, $\forall q\ge 1$.

## 4. Sustainability Analysis

#### 4.1. Loss-Neutral Supplier

**Proposition**

**1.**

**Corollary**

**1.**

**Proposition**

**2.**

- 1.
- ${q}^{SN}>{q}^{H}$, for any ${b}_{s}\in (0,p)$;
- 2.
- ${q}^{RN}>{q}^{H}$, for any ${b}_{r}\in (0,p)$.

#### 4.2. Loss-Averse Supplier

**Proposition**

**3.**

**Proposition**

**4.**

- 1.
- ${q}^{SA}$ is increasing in ${b}_{s}$ when $\lambda \in (1,2]$; and
- 2.
- ${q}^{SA}$ is decreasing in ${b}_{s}$ when $\lambda \in [2,+\infty )$.

**Proposition**

**5.**

**Corollary**

**2.**

- 1.
- ${q}^{SA}\le {q}^{RA}$, when $b\in \left(0,\frac{p}{1+\lambda}\right]$;
- 2.
- ${q}^{SA}>{q}^{RA}$, when $b\in \left(\frac{p}{1+\lambda},+\infty \right)$.

**Proposition**

**6.**

- 1.
- in Scenario SA,
- (a)
- ${q}^{SA}>{q}^{H}$, when $\lambda \in (1,2)$;
- (b)
- ${q}^{SA}\le {q}^{H}$, when $\lambda \in [2,+\infty )$;

- 2.
- in Scenario RA,
- (a)
- ${q}^{RA}>{q}^{H}$, when $\lambda \in \left(1,\frac{p+{b}_{r}}{2{b}_{r}}\right)$;
- (b)
- ${q}^{RA}\le {q}^{H}$, when $\lambda \in \left[\frac{p+{b}_{r}}{2{b}_{r}},+\infty \right)$.

## 5. Conclusions

- Supply chain sustainability is increasing (decreasing) in the buy-back price in the supplier-as-the-leader (retailer-as-the-leader) scenario.
- With loss neutral supplier, the buy-back contract results in a lower sustainability than the wholesale price contract.
- Supplier’s loss-averseness helps to improve supply chain sustainability.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Proof.**

**Proof.**

**Proof.**

**Proof.**

**Proof.**

**Proof.**

**Proof.**

**Proof.**

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Author(s) | Sustainability | Supply Chain Management | Structure Power | Attitude to Loss (Risk) |
---|---|---|---|---|

Cachon [13] | √ | |||

Choi [19] | √ | |||

Choi and Chiu [9] | √ | √ | ||

Choi [11] | √ | √ | ||

Chiu et al. [27] | √ | |||

Dong et al. [14] | √ | √ | ||

Donohue [25] | √ | |||

Ferguson [20] | √ | |||

Ferguson et al. [21] | √ | |||

Li et al. [10] | √ | √ | ||

Sarkar et al. [1] | √ | √ | ||

Sarkar et al. [2] | √ | √ | ||

Sarkar et al. [3] | √ | √ | ||

Sarkar [6] | √ | |||

Shen [16] | √ | |||

Shen and Li [17] | √ | √ | ||

Shen et al. [5] | √ | |||

Wang et al. [18] | √ | √ | ||

Wang et al. [23] | √ | |||

Wang et al. [15] | √ | |||

Wang and Zipkin [22] | √ | √ | ||

Wang et al. [24] | √ | |||

Xue et al. [8] | √ | |||

Yang et al. [26] | √ | |||

Zhao et al. [28] | √ | |||

Zhang et al. [12] | √ | √ |

**Table 2.**Four scenarios with the combination of the channel power structures and the supplier’s attitude to loss.

Supplier-as-a-Leader | Retailer-as-a-Leader | |
---|---|---|

entry Loss-Neutral Supplier | Scenario SN | Scenario RN |

entry Loss-Averse Supplier | Scenario SA | Scenario RA |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Niu, B.; Chen, L.; Zhang, J.
Sustainability Analysis of Supply Chains with Fashion Products under Alternative Power Structures and Loss-Averse Supplier. *Sustainability* **2017**, *9*, 995.
https://doi.org/10.3390/su9060995

**AMA Style**

Niu B, Chen L, Zhang J.
Sustainability Analysis of Supply Chains with Fashion Products under Alternative Power Structures and Loss-Averse Supplier. *Sustainability*. 2017; 9(6):995.
https://doi.org/10.3390/su9060995

**Chicago/Turabian Style**

Niu, Baozhuang, Lei Chen, and Jie Zhang.
2017. "Sustainability Analysis of Supply Chains with Fashion Products under Alternative Power Structures and Loss-Averse Supplier" *Sustainability* 9, no. 6: 995.
https://doi.org/10.3390/su9060995