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Joint Design and Pricing on a Network

LAMIH/ROI, Université de Valenciennes, 59313 Valenciennes Cedex 9, France
SMG and ISRO, Université Libre de Bruxelles, 1050 Brussels, Belgium
CIRRELT and Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Montreal, Quebec, Canada H3C 3J7
GERAD and Département de Mathématiques et de Génie Industriel, Ecole Polytechnique de Montréal, Montreal, Quebec, Canada H3C 3A7
luce.brotcorne{at}univ-valenciennes.fr
mlabbe{at}ulb.ac.be
marcotte{at}iro.umontreal.ca
gilles.savard{at}polymti.ca

To optimize revenue, service firms must integrate within their pricing policies the rational reaction of customers to their price schedules. In the airline or telecommunication industry, this process is all the more complex due to interactions resulting from the structure of the supply network. In this paper, we consider a streamlined version of this situation where a firm's decision variables involve both prices and investments. We model this situation as a joint design and pricing problem that we formulate as a mixed-integer bilevel program, and whose properties are investigated. In particular, we take advantage of a feature of the model that allows the development of an algorithmic framework based on Lagrangean relaxation. This approach is entirely novel, and numerical results show that it is capable of solving problems of significant sizes.

Subject classifications: economics; pricing; games; integer programming; heuristics; transportation; programming; nonlinear; nondifferentiable.
History: Received June 2004; revision received August 2006; accepted September 2006.

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