A class of competitive facility location and allocation (routing) models on the market in which two competing companies successively open their facilities is considered in this paper. Each client chooses an open facility according to some preference rule and returns interests to one of the two firms. In this paper, a bi-level fractional mixed-integer nonlinear programming model in which the fixed cost and transportation cost are incorporated is formulated. In this model, the firm entering the market is the leader and the competitor is the follower. The problem is to locate the leader firm so as to find out the maximum capture per unit cost subject to the responses of the follower company and the available preferences of clients. The market includes reverse logistics network that has attracted a growing attention with the stringent pressures from environmental and social requirements. In order to convert this problem to a soluble model, it is converted into an equivalent two-level mixed-integer linear program.
