A mathematical model for competitive location problem with product selection

In this paper, a new competitive location problem for a chain is considered. The chain’s owner can offer a variety of products. The model’s objective is to determine both the location of the new facilities and the optimal product type for each opened facility. The patronizing behavior of the customers is based on Huff rule and the location of new facilities is selected from a set of potential sites. As a result, the model is a nonlinear integer programming problem and for solving the proposed model, the problem is reformulated as a mixed integer linear programming and therefore a standard optimization solver can be used for obtaining the optimal solutions for small and medium-size problems. To cope with large-size problems, we develop two methods: 1) a heuristic method for a special case and 2) a hybrid heuristic-firefly algorithm for general cases. By using the proposed model, it is shown numerically that in multi-product industries in which owner of the facilities is able to offer different types of products, in addition to the optimal location, it is necessary to determine the best products. In the end, a real-world case study for locating a new bakery is presented.