A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints

Original Paper


This paper provides the convex hull description of the single thermal Unit Commitment (UC) problem with the following basic operating constraints: (1) generation limits, (2) start-up and shut-down capabilities, and (3) minimum up and down times. The proposed constraints can be used as the core of any unit commitment formulation to strengthen the lower bound in enumerative approaches. We provide evidence that dramatic improvements in computational time are obtained by solving the self-UC problem and the network-constrained UC problem with the new inequalities for different case studies.


Unit commitment (UC) Mixed-integer programming (MIP) Facet/convex hull description 

Mathematics Subject Classification

90C11 90C57 90C90 



The authors thank Laurence Wolsey, Santanu Dey, Antonio Frangioni, and Paolo Ventura for useful discussions on the paper.


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Copyright information

© EURO - The Association of European Operational Research Societies 2016

Authors and Affiliations

  1. 1.Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle RicercheRomaItaly
  2. 2.Department of Electrical Sustainable EnergyDelft University of TechnologyDelftThe Netherlands
  3. 3.Institute for Research in Technology (IIT) of the School of Engineering (ICAI)Universidad Pontificia ComillasMadridSpain

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