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

• Published in: Computers & operations research Vol. 41; pp. 185 - 195
• Main Authors: Fernández, José, Salhi, Said, -Tóth, Boglárka G.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.01.2014; Elsevier; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Branch & bound algorithms; Continuous location; Cost engineering; Delivered pricing; Demand; Elasticity of demand; Exact sciences and technology; Firm modelling; Game theory; Games; Heuristic; Interval branch-and-bound method; Location analysis; Location-price game; Logistics; Manufacturing engineering; Operational research and scientific management; Operational research. Management science; Operations research; Position (location); Social costs; Studies; Transportation problem (Operations research); Weiszfeld algorithm; Delivered pricing; Interval branch-and-bound method; Continuous location; Location-price game; Weiszfeld algorithm; Economic analysis; Competitiveness; Iterative method; Location problem; Convex programming; Interval arithmetic; Facility location; Inelasticity; Pricing; Profit; Branch and bound method; Global optimum; Non differentiable programming; Descent method; Heuristic method; Production cost; Tariffication; Marginal cost; Economic equilibrium; Logistics
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2013.08.004

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.