The summed start-up costs in a unit commitment problem

  • René Brandenberg
  • Matthias Huber
  • Matthias Silbernagl
Original Paper


We consider the sum of the incurred start-up costs of a single unit in a Unit Commitment problem. Our major result is a correspondence between the facets of its epigraph and some binary trees for concave start-up cost functions CU, which is bijective if CU is strictly concave. We derive an exponential \({\mathcal{H}}\)-representation of this epigraph, and provide an exact linear separation algorithm. These results significantly reduce the integrality gap of the Mixed Integer formulation of a Unit Commitment Problem compared to current literature.

Mathematics Subject Classification

90C57 90C11 90B99 52B12 


Unit commitment Mixed integer programming Summed Start-up costs Start-up cost epigraph Valid inequalities Integrality gap 


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Copyright information

© EURO - The Association of European Operational Research Societies 2016

Authors and Affiliations

  • René Brandenberg
    • 1
  • Matthias Huber
    • 2
  • Matthias Silbernagl
    • 1
  1. 1.Department of MathematicsTechnische Universität MünchenGarchingGermany
  2. 2.Department of Electrical and Computer EngineeringTechnische Universität MünchenMunichGermany

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