The competitive facility location based on the spatial interaction model

In this paper, a nonlinear model for locating service facilities is introduced in a competitive ‎ region. In the proposed model the factors of travel time, quality of service facilities and price ‎ are considered that are the most important effective factors in attracting and maintaining the ‎ customers in the competitive environments. For identifying the customers’ probabilistic ‎ behavior in selecting the competitor’s and entering firm’s facilities, the spatial interaction ‎ model and Logit function are used. Since the decision making for locating is not only based on ‎ the sale quantity and market demand captured and ignoring other important organizational ‎ goals such as minimizing the cost may provide problems in long term for firms, therefore in ‎ addition to the capturing demand, the fixed cost of locating is considered in the model that ‎ will provide better results in the real world problems. Due to the computational complexity, a ‎ genetic algorithm is developed for solving the model. The numerical results verify the ‎ performance of the proposed model and effectiveness of ‏ ‏ ‎ the genetic algorithm in solving it ‏ ‏ and show that the study of costumers’ ‎ ‏ ‏ probabilistic demand considering the factors of price, ‎ travel time and quality of service facilities has the major role in the increasing of sale and profit ‎ of the entering firm so that, in spite of selecting the most appropriate locations by the ‎ competitor, the ‏ ‏ sale and profit quantities of entering firm are more than the competitor’s, in the ‎ equal situation of price, quality and number of facilities. ‎