Annals of Operations Research

, Volume 207, Issue 1, pp 137–160

Alternative formulations for the Set Packing Problem and their application to the Winner Determination Problem

  • Mercedes Landete
  • Juan Francisco Monge
  • Antonio M. Rodríguez-Chía
Article

DOI: 10.1007/s10479-011-1039-4

Cite this article as:
Landete, M., Monge, J.F. & Rodríguez-Chía, A.M. Ann Oper Res (2013) 207: 137. doi:10.1007/s10479-011-1039-4
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Abstract

An alternative formulation for the set packing problem in a higher dimension is presented. The addition of a new family of binary variables allows us to find new valid inequalities, some of which are shown to be facets of the polytope in the higher dimension. We also consider the Winner Determination Problem, which is equivalent to the set packing problem and whose special structure allows us to easily implement these valid inequalities in a very easy way. The computational experiments illustrate the performance of the valid inequalities and obtain good results.

Keywords

Set packing Valid inequality Boolean quadric polytope 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Mercedes Landete
    • 1
  • Juan Francisco Monge
    • 1
  • Antonio M. Rodríguez-Chía
    • 2
  1. 1.Centro de Investigación OperativaUniversidad Miguel Hernández of ElcheElcheSpain
  2. 2.Facultad de Ciencias, Dpto. Estadística e Investigación OperativaUniv. CádizCádizSpain