Annals of Operations Research

, Volume 119, Issue 1–4, pp 165–181 | Cite as

Integer Programming Applied to Intensity-Modulated Radiation Therapy Treatment Planning

  • Eva K. LeeEmail author
  • Tim Fox
  • Ian Crocker


In intensity-modulated radiation therapy (IMRT) not only is the shape of the beam controlled, but combinations of open and closed multileaf collimators modulate the intensity as well. In this paper, we offer a mixed integer programming approach which allows optimization over beamlet fluence weights as well as beam and couch angles. Computational strategies, including a constraint and column generator, a specialized set-based branching scheme, a geometric heuristic procedure, and the use of disjunctive cuts, are described. Our algorithmic design thus far has been motivated by clinical cases. Numerical tests on real patient cases reveal that good treatment plans are returned within 30 minutes. The MIP plans consistently provide superior tumor coverage and conformity, as well as dose homogeneity within the tumor region while maintaining a low irradiation to important critical and normal tissues.

intensity-modulated radiation therapy external beam radiotherapy optimization mixed integer programming treatment planning 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  1. 1.Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Radiation OncologyEmory University School of MedicineAtlantaUSA
  3. 3.Radiation OncologyEmory University School of MedicineAtlantaUSA

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