This paper aims to address an inventory competitive facility location problem with the order quantity in a stochastic environment. In this problem, the facility location, customer design, and inventory control decisions have been integrated for two decision makers, i.e. the leader and the follower. To this end, a bi-level nonlinear nonconvex mixed integer mathematical model was proposed. Next, an alternative bi-level mixed-integer linear model was obtained. The enumeration branch-and-cut method in the field of bi-level linear programming was developed to come up with optimal or near-optimal solutions. To determine the branching choice and specialized cuts, a preference function was used. Computational results of some data tests were reported, and the results were compared with those of previous famous methods to show the efficiency of the algorithm. According to the computational results, the proposed algorithm could find effective solutions for solving such problems, which could compete with other well-known published algorithms.
