The Bi-level Mathematical Model for Competitive Facility Location Problem with Elastic Demand

Facility location whit taking account the competition is a critical component of strategic planning. The location affects the competitiveness and market share of a new entry firms, in long term life. In order to develop a model with more realistic characters, demand is supposed elastic. In this research, demand is defaulted with the help of an exponential function. In this paper a competitive facility location model whit two competitors which produce a commodity with elastic demand is developed The problem is modeled in the form of a location-price game. A bi-level model is developed to investigate the location and price, in location-pricing models, the location decision should come before the pricing game. From the second level and the use of Nash equilibrium, equilibrium will be obtained. In this paper, probabilistic costumer behavior whit the help of exponential function is modeled. A metaheuristic based on tabu search and Simulated annealing algorithm are proposed to search the optimal location-price solution of the model. The analysis shows that price game is more intense when incomes of consumers are lower or there are more substitution products.