Location equilibria for a continuous competitive facility location problem under delivered pricing

Location equilibria for a continuous competitive facility location problem under delivered pricing

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Article ID: iaor20141065
Volume: 41
Issue: 6
Start Page Number: 185
End Page Number: 195
Publication Date: Jan 2014
Journal: Computers and Operations Research
Authors: , ,
Keywords: game theory, optimization, social, demand, heuristics
Abstract:

The problem of finding location equilibria of a location‐price game where firms first select their locations and then set delivered prices in order to maximise their profits is investigated. Assuming that firms set the equilibrium prices in the second stage, the game can be reduced to a location game for which a global minimiser of the social cost is a location equilibrium, provided that the demand is completely inelastic and the marginal production cost is constant. When the set of feasible locations is a region of the plane the minimisation of the social cost becomes a hard‐to‐solve global optimisation problem. We propose an exact interval branch‐and‐bound algorithm suitable for small and medium size problems and an alternating Weiszfeld‐like heuristic for larger instances. The latter approach is based on a new iterative formula for which the validity of the descent property is proved. The proposed heuristic performs extremely well against the exact method when tested on small to medium size instances while requiring a tiny fraction of its computational time.

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