A modified branch and cut algorithm for Bi-level Competitive Location Problem in the Closed Chain

In this paper, firstly a class of competitive facility location problems in an integrated forward and reverse logistics network is presented, in which two competing companies successively opened their facilities. Then, customer preferences for choosing an open facilities are applied based on some rules. The problem is formulated as a bi-level competitive maximum capture location problem. Also, we present a method of solution using a modified optimization algorithm based on the branch and cut method. We use a preference function to determine the choice of branching and specialized cuts in a branch and cut tree.