Next Article in Journal
New Urban Transitions towards Sustainability: Addressing SDG challenges (Research and Implementation Tasks and Topics from the Perspective of the Scientific Advisory Board (SAB) of the Joint Programming Initiative (JPI) Urban Europe)
Previous Article in Journal
Archaeoastronomy: A Sustainable Way to Grasp the Skylore of Past Societies
Previous Article in Special Issue
On the Environmental and Social Sustainability of Technological Innovations in Urban Bus Transport: The EU Case
Article Menu

Export Article

Open AccessArticle
Sustainability 2019, 11(8), 2241; https://doi.org/10.3390/su11082241

A Stochastic Differential Game in the Closed-Loop Supply Chain with Third-Party Collecting and Fairness Concerns

1
School of Business, Qingdao University, Qingdao 266071, China
2
School of Economics and Management, Shanghai Maritime University, Shanghai 201306, China
3
School of Computer Science, Fudan University, Shanghai 200433, China
*
Author to whom correspondence should be addressed.
Received: 18 March 2019 / Revised: 6 April 2019 / Accepted: 10 April 2019 / Published: 14 April 2019
  |  
PDF [2488 KB, uploaded 14 April 2019]
  |  

Abstract

This paper investigates the optimal return control problem in a closed-loop supply chain consisted of one manufacturer, one retailer, and one third-party collector, in the presence of stochastic return disturbance and fairness concern of followers. We formulate the stochastic differential game-theoretic models and resolve the feedback Stackelberg equilibriums without and with fairness concern. We also derive the evolutionary paths of the stochastic return rate and the value functions of the supply chain members under the optimal control strategies. We find that the feedback equilibrium exists only under a specific condition, and the expectation and variance of the return rate both approach the stable state for a specific closed-loop supply chain system. We further discussed the impact of fairness concerns on the supply chain system. The manufacturer would shift profit to the retailer by lowering the wholesale price, and the stable expected return rate will be lower in the supply chain with fairness concerns, as the third party will have less incentive to collect used products, considering unfairness. The manufacturer should set a higher transfer subsidy to incentivize the third party to collect when the third party is concerned with fairness. View Full-Text
Keywords: closed-loop supply chain; stochastic disturbance; differential game; feedback control strategy; third-party collecting; fairness concern closed-loop supply chain; stochastic disturbance; differential game; feedback control strategy; third-party collecting; fairness concern
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Xiao, J.; Huang, Z. A Stochastic Differential Game in the Closed-Loop Supply Chain with Third-Party Collecting and Fairness Concerns. Sustainability 2019, 11, 2241.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Sustainability EISSN 2071-1050 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top