Sequential versus simultaneous approach in the location and design of two new facilities using planar Huff-like models

A company frequently decides on location and design for new facilities in a sequential way. However, for a fixed number of new facilities (in this study we restrict ourselves to the case of two new facilities), the company might improve its profit by taking its decisions for all the facilities simultaneously. In this paper a profit maximization problem is considered, where the market share captured by each facility depends on both the distance to the customers (location) and its quality (design), and it is determined by a Huff-like model. Recent research on this type of models was aimed at finding global optima for a single new facility, holding quality fixed or variable, but no exact algorithm has been proposed to find optimal solutions for more than one facility. The existing algorithms coping with the simultaneous problem do a cycle search in which only one location is optimized independently, holding all other locations fixed; therefore it cannot guarantee that an optimal solution has been found. In this paper we propose an exact interval branch-and-bound algorithm to solve the simultaneous location and design 2-facilities problem. We present some computational results to compare the locations and qualities of the optimal solutions obtained by a sequential and two simultaneous approaches.