Developing a Mathematical Model for Competitive Facility Location with Multiple Commodities and Multiple Competitors

Abstract

Facility location along with taking account the competition is a critical component of strategic planning. The location affects the competitiveness and market share of new entrants, in long-term. Because of the complications of location problems, most of the location models are faced whit many different limitations. In this paper a competitive facility location model with three competitors which produce two commodities 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 with the help of exponential function is modeled. A metaheuristic based on tabu search is proposed to search the optimal location-price solution of the model. Findings show that changing the equilibrium price affect the profitability of new entry firms.

Keywords

• competitive facility location
• nash equilibrium
• location-price game
• probabilistic costumer behavior
• tabu search algorithm