In this paper, the problem examined concerns a firm entering a new facility in the market where facilities belonging to the firm and another competitor firm exist. The market’s reverse logistics network that has attracted growing attention with stringent pressures from environmental and social requirements is considered. The firm wants to maximize its profit by finding the best location and the most attractive facility to open. The other firm (the competitor) can counteract this situation and attempt to maximize its own profit by adjusting the attractiveness of its existing facilities. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at pre-determined candidate sites. To do this, Huff’s gravity-based rule in modeling the behavior of the customers is employed where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. A mathematical bi-level mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower is delivered. Furthermore, for finding the optimal solution of this model, it is converted into a one-level mixed-integer nonlinear program so that it can be solved by global optimization methods. The computational results on some examples obtained from random generated problems show that the method is able to solve the Bi-Level Programming Problem (BLPP) efficiently in a reasonable time.
