Static competitive facility location: An overview of optimisation approaches

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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 o€ers 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 ®t 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.



Ingredients
We start by a discussion of the di€erent ingredients
and their ¯avors 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.

2.1. Features of competition

2.1.1. Static competition
The simplest competitive models arise when
competition is assumed to be already present in the
market. The whereabouts and characteristics of
this competition are known in advance and assumed
to be ®xed. This kind of static situations are
discussed in more detail in the remainder of this
paper.
Such models correspond to a short term view:
they are based on the assumption that the time
and/or e€ort/cost needed for the competition to
react is suciently long to harvest the main bene
®ts of the new facility. These models also form the
basis on which more complex models may be built.

2.1.2. Competition with foresight
The situation becomes quite di€erent when a
virgin market is entered in the knowledge that
other competing actors will enter it soon afterwards.
It will then be necessary to make decisions
with foresight about this competition, which itself
will enter a market where competition is already
present. The ensuing Stackelberg-type models,
where each evaluation of the main objective involves
the solution of the competitor's nontrivial
optimisation model, quickly become extremely
complex. We enter here the realm of sequential
models, which were recently extensively surveyed
in [21].


Static probabilistic competitive facility location
The basic assumptions in this section are summarised
as follows:
· existing competition is known and ®xed,
· customers patronise several facilities and split
their demand between them.