A Non-linear Integer Bi-level Programming Model for Competitive Facility Location of Distribution Centers

The facility location problem is a strategic decision-making for a supply chain, which determines the profitability and sustainability of its components. This paper deals with a scenario where two supply chains, consisting of a producer, a number of distribution centers and several retailers provided with similar products, compete to maintain their market shares by opening new distribution centers because of increase in demand. The competition problem is formulated as a non-linear integer bilevel mathematical model, where the upper level represents the decisions of the leader producer and the lower level administrates the decisions of the follower producer. It has been shown that even small-scale, bilevel mathematical programming problems are strongly NP-hard, so an adapted bilevel ant colony algorithm with inter-level information sharing is developed to solve the problem. To evaluate the performance of the developed ant colony algorithm, the upper bound of the competitive facility location problem is determined by solving the upper-level problem as an integer linear programming model without considering the follower’s decision. Comparing the computational results of the developed ant colony algorithm with those of the determined upper bounds shows the satisfactory capability of the proposed approach of solving even medium- and large-scale problems.