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

Fernandez, Jose and Salhi, Said and Toth, Boglarka G (2014) Location equilibria for a continuous competitive facility location problem under delivered pricing: competitive continuous location. Computers and Operations Research, 41 . pp. 185-195. ISSN 0305-0548. (doi:https://doi.org/10.1016/j.cor.2013.08.004) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1016/j.cor.2013.08.004

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.

Item Type: Article
Uncontrolled keywords: Continuous location; Delivered pricing; Location-price game; Interval branch-and-bound method; Weiszfeld algorithm
Subjects: Q Science > Operations Research - Theory
Divisions: Faculties > Social Sciences > Kent Business School
Faculties > Social Sciences > Kent Business School > Management Science
Faculties > Social Sciences > Kent Business School > Centre for Logistics and Heuristic Organisation (CLHO)
Depositing User: Said Salhi
Date Deposited: 15 May 2014 13:20 UTC
Last Modified: 07 Aug 2018 15:03 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41077 (The current URI for this page, for reference purposes)
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