A Mathematical Model for Competitive Location Problem with Product Selection

Abstract

In this paper, a new competitive location problem for a chain is considered. The owner of the chain can o er 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 Hu 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-re y 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 o er di erent 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.

Influence of Two Different Producers in a Competitive Location Problem

“…The problem is formulated as a bi-level mathematical programming model with binary variables. A new mathematical model for competitive location problem is proposed by Sadjadi et al [17] to determine the location of the new facilities and also the optimal product type for each of opened facility while the behavior of the customers is based on Huff rule. In addition to the above-mentioned studies, some researchers have studied multi objective models of competitive facility location (Bilir et al [18]; Wang & Chen [19]; Konak et al [20]).…”