A mathematical model for competitive location problem with product selection

In this paper, a new competitive location problem for a chain is considered. The owner of the chain can offer a variety of products. The objective of the model is to determine both the location of 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 proposed model is a nonlinear integer programming problem and for solving it, the problem is reformulated as a mixed integer linear programming one. Therefore, a standard optimization solver can be used for obtaining the optimal solutions to 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 numerically shown that in multi-product industries in which the 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. At the end, a real-world case study for locating a new bakery is presented. (C) 2020 Sharif University of Technology. All rights reserved.