A branch-and-cut algorithm for the Winner Determination Problem

Authors:
Laureano F. Escudero;Mercedes Landete;Alfredo Marín
Affiliations:
Departamento de Estadística e Investigación Operativa, Universidad Rey Juan Carlos, Spain;Centro de Investigación Operativa, Universidad Miguel Hernández of Elche, Spain;Departamento de Estadística e Investigación Operativa, Universidad de Murcia, Spain
Venue:
Decision Support Systems
Year:
2009

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Abstract

The Winner Determination Problem is the problem of maximizing the benefit when bids can be made on a group of items. In this paper, we consider the set packing formulation of the problem, study its polyhedral structure and then propose a new and tighter formulation. We also present new valid inequalities which are generated by exploiting combinatorial auctions peculiarities. Finally, we implement a branch-and-cut algorithm which shows its efficiency in a big number of instances.