, Volume 16, Issue 4, pp 379–400 | Cite as

Coordination of a socially responsible two-stage supply chain under price-dependent random demand

  • Xia ZhaoEmail author
  • Runsheng Yin
Research Paper


This paper investigates the coordination problem of a supply chain (SC) composed of a manufacturer exhibiting corporate social responsibility (CSR) and a retailer faced with random demand. The random demand is made up of the multiplication of price-dependent demand and random demand factor (RDF), plus the CSR-dependent demand. The centralized decision problem of the SC is an extension of the existing price setting newsvendor problem (PSNP). It is found that the sufficient condition for the quasi-concavity of expected profit (EP) on PSNP can not ensure the quasi-concavity of EP of the SC. Then, the concavity condition of EP related to the CSR effect factor is presented in the case of uniformly distributed RDF and linear demand in price, and the concavity of EP is proven under centralized decision. For decentralized decision under manufacturer’s Stackelberg game, the manufacturer determines wholesale price and its CSR investment, and then the retailer decides the order quantity and the retail price. The standard revenue-sharing (RS) contract is found not able to coordinate the SC, so a modified RS (MRS) contract is proposed to coordinate the SC. Finally, numerical examples illustrate the validity of the theoretical analysis and the coordination effectiveness of the MRS contract via Matlab.


Supply chain coordination Corporate social responsibility Random demand Pricing Revenue-sharing contract 

Mathematics Subject Classification




The authors gratefully acknowledge the support by the National Science Foundation of China (NSFC) under Grant No. 71403114. This study was also supported by China Special Fund for Grain-scientific Research in the Public Interest under Grant No. 201513004. The author also appreciates the support by Priority Academic Program Development of Jiangsu Higher Education Institutions and the support by Collaborative Innovation Center of Modern Grain Circulation and Safety, Nanjing University of Finance and Economics.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Center for Food Security and Strategic StudiesNanjing University of Finance and EconomicsNanjingChina
  2. 2.College of Agriculture and Natural ResourcesMichigan State UniversityEast LansingUSA

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