Kaveh Fahimi - Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran
Seyed Mohammad Hosseini - Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran
Ahmad Makui - Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran

This paper presents a competitive supply chain network design problem in which one, two, or three supply chains are planning to enter theprice-dependent markets simultaneously in uncertain environments and decide to set the prices and shape their networks. The chains produce competitive products either identical or highly substitutable. Fuzzy multi-level mixed integer programming is used to model the competition modes, and then the models are converted into an integrated bi-level one to be solved, in which the inner part sets the prices in dynamic competition and the outer part shapes the network cooperatively.Finally, a real-world problem is investigatedto illustrate how the bi-level model works and discuss how price, market share, total income, and supply chain network behave with respect to key marketing activities such as advertising, promotions, and brand loyalty.

Competitive supply chain network design, Fuzzy multi-level mixed integer programming, Bi-level programming, Nash equilibrium