A DECENTRALIZED SUPPLY CHAIN NETWORK DESIGN PROBLEM WITH EQUILIBRIUM CONSTRAINTS

This paper addresses a facility location issue arisen in the strategic stage of a supply chain network design problem while the free market competition of participants in a supply chain system cannot be ignored. The supply chain network equilibrium conditions describe the competition behaviors of three kinds of decision-makers, manufacturers, retailers and consumers in a supply chain network for a product. This paper thus develops a universal generalized bilevel programming model for the facility location problem with the supply chain network equilibrium constraints. In the proposed generalized bilevel programming model, the upper level problem is an integer nonlinear program that aims to optimize a utility function by identifying facility locations to produce a kind of product. However, the lower problem, that is a variational inequality problem characterizing the supply chain network equilibrium condition, determines the supply prices and shipments from these new facilities to retailers, which are necessary inputs of the upper level problem. To solve the generalized bilevel programming model involving binary location decision variables, a genetic algorithm, that incorporates a modified projection method for solving the variational inequality problem of the lower level problem, is then suggested. Finally, this study employs a hypothetical numerical example to demonstrate the availability of the proposed model and algorithm.