a bi-level competitive facility location model considering the reaction of competitors in the market, using the concept of compromise

a facility location is said to be competitive when other facilities are present in the market and new facilities have to compete with these existing facilities for a market share. in other words, in a competitive facility location problem we do not see monopoly that exists in classic location models. in such a situation, existing facilities react to locate new facilities by adjusting their attractiveness level with the objective of maximizing their own profits. in this study, we have used huff's gravity-based rule to model the behavior of the customers where the probability that a customer visit a certain facility is proportional to the facility attractiveness and inversely is related to the distance between customer and that certain facility. then, the problem is formulated as a bi-level programming model. to solve the model, a solution approach that for the first time provides a compromise between the competitors is proposed. in the solution method, in addition to the competitors, a minimum utility level is considered for customers. finally, a case from the literature is demonstrated to show the feasibility of the model and solution approach.