[en] In this study, the problem of a firm is considered where the firm tries to open new facilities in a market where there are already existing facilities belonging to a competitor. The new entrant firm wishes to find the optimal location and attractiveness levels of its facilities to maximize its profit. On the other hand, the competitor can react to the new entrant by changing the attractiveness levels of its existing facilities, closing them and/or opening new facilities. The gravity-based rule is employed in order to model the customer behavior. According to this rule, the probability that a customer patronizes a facility is proportional to the attractiveness level of the facility and inversely proportional to the distance between the customer and the facility. To this end, a bilevel mixed-integer nonlinear programming problem in discrete space is formulated. The new entrant firm is the leader of the game and the competitor is the follower. In order to find feasible solutions to the model, two tabu search heuristic methods are proposed. Two exact methods are utilized as subroutines of the proposed methods: a gradient ascent algorithm and a branch-and-bound algorithm that uses nonlinear programming relaxation.
Disciplines :
Production, distribution & supply chain management
