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.

Minimizing the total cost is absolutely the goal of each supply chain, which is most of the time pursued. In this regards, quality related costs that have significant roles are sometimes neglected. Selecting suppliers, which supply relatively high quality raw materials in a lower cost is considered as a strategic decision. Make or Buy decision can be also noticed in supplier selection process. In this paper, the supply strategy: Make or Buy decision (SS: MOB) is studied in order to find which strategy (Make or Buy) should be chosen to minimize the total costs of supply chain. Therefore, two separate models are generated for each strategy and several examples are solved for the respective models. Computational experiments show the efficiency of the proposed models for making decision about selecting the best strategy.

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.