This paper considers simultaneously two areas of facility location and assortment planning in a competitive environment. In fact, a chain store that has competitors in the market locates a new facility. As there are different products in the market that can substitute with each other, it is intended to determine the best product assortment as well. An integer nonlinear programming problem is proposed to model the mentioned subject. For solving the model, the problem is reformulated as a mixed integer linear programming one. Therefore, a MIP solver software can be used for solving the small- and medium-size problems. For large-scale problems, a firefly algorithm is designed for obtaining a satisfactory solution. By using the proposed model, it is numerically shown that, in addition to the optimal location, it is also necessary to determine simultaneously the best product assortment for the new store. Actually, comparison results reveal that the location significantly affects the assortment scenarios for the new store. In other words, the selection of new store locations may lead to loss of large profit if the assortment planning is neglected.

This paper provides a review on recent works in the field of competitive facility location models based on the following seven components: 1) Variables, 2) Competition type, 3) Solution space, 4) Customer behavior, 5) Demand type, 6) Number of new facilities and 7) Relocation and redesign possibility. First, the components are introduced and then based on these components; different studies are compared with each other via a proposed taxonomy and finally a review on work of each paper is provided.

Consider a chain as leader that wants to open p new facilities in a linear market, like metro. In this market, there is a competitor, called follower. The leader and the follower have established some facilities in advance. When the leader opens p new facilities, its competitor, follower, reacts the leader’s action and opens r new facilities. The optimal locations for leader and follower are chosen among predefined potential locations. Demand is considered as demand points and is assumed inelastic. Considering huff model, demand points are probabilistically absorbed by all facilities. The leader’s objective is maximization of its market share after opening follower’s new facilities. For solving leader problem, first the follower’s problem is solved for all leader’s potential locations and the best location for leader is obtained and then, a heuristic model is proposed for leader problem when the leader and the follower want to open one new facility. Computational results show that the proposed method is efficient for large scale problems.