In recent decades, global economy pressures and developments force companies to make new competitiveness advantages to come up them. Not only companies were encouraged by environment regulation to be cautious about new and used product but also they had understood that could be economical and beneficial if they can reuse product in end of life cycle. In this paper, a class of competitive facility location and allocation problems at an integrated forward and reverse logistic network (closed supply chain) was studied, in which two competing companies successively opened their facilities. Then, each customer chooses an open facility according to some preference rules. The problem was formulated as a bi-level fractional mixed-integer nonlinear programming model in which the fixed and variable costs were incorporated. The problem was to realize the maximum capture per unit cost for leader subject to the responses of the follower and the available preferences of customers in a closed logistics network. An equivalent bi-level mixed-integer linear model was obtained and solved by Lagrangean Relaxation method. The computational result showed that the proposed method could solve the converted model efficiently.
