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Valid inequalities and Branch-and-Cut for the Clique Pricing Problem

Géraldine Heilporn (Geraldine.Heilporn***at***hec.ca)
Martine Labbé (mlabbe***at***ulb.ac.be)
Patrice Marcotte (marcotte***at***iro.umontreal.ca)
Gilles Savard (gilles.savard***at***polymtl.ca)

Abstract: Motivated by an application in highway pricing, we consider the problem that consists in setting profit-maximizing tolls on a clique subset of a multicommodity transportation network. Following a proof that clique pricing is NP-hard, we propose strong valid inequalities, some of which define facets of the 2-commodity polyhedron. The numerical efficiency of these inequalities is assessed by embedding them within a branch-and-cut framework.

Keywords: Network pricing, mixed-integer programming, combinatorial optimization / Tarification de réseaux, optimisation combinatoire, programmation mixte entière

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Combinatorial Optimization (Branch and Cut Algorithms )

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Entry Submitted: 06/02/2009
Entry Accepted: 06/02/2009
Entry Last Modified: 05/03/2011

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