The multiple markets competitive location problem

Abstract

Purpose

The purpose of this paper is to investigate a competitive location problem to determine how to allocate a budget to expand company’s chain by either adding new facilities, expanding existing facilities, or a combination of both actions. Solving large problems may exceed the computational resources currently available. The authors treat a special case when the market can be divided into mutually exclusive sub-markets. These can be markets in cities around the globe or markets far enough from each other so that it can be assumed that customers in one market do not patronize retail facilities in another market, or that cross-patronizing is negligible. The company has a given budget to invest in these markets. Three objectives are considered: maximizing profit, maximizing return on investment (ROI), and maximizing profit subject to a minimum ROI. An illustrative example problem of 20 sub-markets with a total of 400 facilities, 4,800 potential locations for new facilities, and 5,000 demand points is optimally solved in less than two hours of computing time.

Design/methodology/approach

Since the market can be partitioned into disjoint sub-markets, the profit at each market by investing any budget in this sub-market can be calculated. The best allocation of the budget among the sub-markets can be done by either solving an integer linear program or by dynamic programming. This way, intractabole large competitive location problems can be optimally solved.

Findings

An illustrative example problem of 20 sub-markets with a total of 400 facilities, 4,800 potential locations for new facilities, and 5,000 demand points is optimally solved in less than two hours of computing time. Such a problem cannot be optimally solved by existing methods.

Originality/value

This model is new and was not done in previous papers.

Citation

Drezner, T., Drezner, Z. and Kalczynski, P.J. (2016), "The multiple markets competitive location problem", Kybernetes, Vol. 45 No. 6, pp. 854-865. https://doi.org/10.1108/K-09-2014-0191