Invited Review
Static competitive facility location: An overview of optimisation approaches

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Abstract

We give an overview of the research, models and literature about optimisation approaches to the problem of optimally locating one or more new facilities in an environment where competing facilities are already established.

Introduction

A large part of location theory in operational research has been built around the (mostly implicit) modelling assumption of a spatial monopoly: the facility to be located offers a unique product or service and is the single player in the part of the market that is considered. Most situations in practice do not fit such models and the need arises to incorporate competition with other players. This has long been understood by economists who have studied competition, including its spatial aspects, for some 70 years.

A location model is said to be about competitive facilities when it explicitly incorporates the fact that other facilities are already (or will be) present in the market and that the new facility(ies) will have to compete with them for its (their) market share. The apparent simplicity of this statement hides several implicit and explicit notions which have to be made more precise before a clear and well-defined model arises.

It is the aim of this paper to give an overview of these questions and the many different ways in which they may be filled in, leading to as many different models with corresponding theoretical results and/or techniques. Many survey papers about this research area have already appeared in print, such as [14], [19], [21], [22], [23], [34], [61].

What distinguishes this survey is its emphasis on the part of the field clearly lying within Operational Research and in which several developments have taken place in recent years: we focus our attention towards those competitive location models which are directly phrased as (one stage) optimisation problems.

Section snippets

Ingredients

We start by a discussion of the different ingredients and their flavors that enter into the recipe of competitive location models. The three main questions are related to the competition, to the market, and to the decision space.

Static deterministic competitive facility location

The basic assumptions in this section are summarised as follows:

  • existing competition is known and fixed,

  • customers patronise the most attracting facility with their full demand, i.e., `the winner gets it all' principle.

Static probabilistic competitive facility location

The basic assumptions in this section are summarised as follows:

  • existing competition is known and fixed,

  • customers patronise several facilities and split their demand between them.

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