Strong valid inequalities for fluence map optimization problem under dose-volume restrictions

Ali T. Tuncel, Felisa Preciado, Ronald L. Rardin, Mark Langer, Jean Philippe P. Richard

Research output: Contribution to journalArticle

12 Scopus citations


Fluence map optimization problems are commonly solved in intensity modulated radiation therapy (IMRT) planning. We show that, when subject to dose-volume restrictions, these problems are NP-hard and that the linear programming relaxation of their natural mixed integer programming formulation can be arbitrarily weak. We then derive strong valid inequalities for fluence map optimization problems under dose-volume restrictions using disjunctive programming theory and show that strengthening mixed integer programming formulations with these valid inequalities has significant computational benefits.

Original languageEnglish (US)
Pages (from-to)819-840
Number of pages22
JournalAnnals of Operations Research
Issue number1
StatePublished - Jul 1 2012


ASJC Scopus subject areas

  • Decision Sciences(all)
  • Management Science and Operations Research

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