Estimating the pareto front of a hard Bi-criterion competitive facility location problem

Abstract

We deal with the location problem for a franchise type expanding firm in competition with other firms in a geographical area. The firm aims at maximization of the market share captured by the new facilities and minimization of the lost market share of the old facilities caused by the entering of the new facilities in the market. The market share of each facility is estimated assuming that customers are served by the most attractive facility. A new tie breaking rule is introduced to serve the customers for which there are more than one facility with the maximum attraction, which leads to a hard nonlinear bi-objective optimization problem. A heuristic algorithm is proposed which obtains a good approximation of the Pareto front when the new facilities have to be selected from a finite set of candidates.