Annals of Operations Research

, Volume 274, Issue 1–2, pp 119–130 | Cite as

On the complexity of the Unit Commitment Problem

  • Pascale Bendotti
  • Pierre FouilhouxEmail author
  • Cécile Rottner
Short Note


This article analyzes how the Unit Commitment Problem (UCP) complexity evolves with respect to the number n of units and T of time periods. A classical reduction from the knapsack problem shows that the UCP is NP-hard in the ordinary sense even for \(T=1\). The main result of this article is that the UCP is strongly NP-hard. When the constraints are restricted to minimum up and down times, the UCP is shown to be polynomial for a fixed n. When either a unitary cost or amount of power is considered, the UCP is polynomial for \(T=1\) and strongly NP-hard for arbitrary T. The pricing subproblem commonly used in a UCP decomposition scheme is also shown to be strongly NP-hard for a subset of units.


Unit Commitment Problem Complexity Dynamic programming Subproblem of decomposition scheme 



The authors would like to thank Christoph Dürr for fruitful discussions.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Sorbonne Université, LIP6-CNRS (Laboratoire d’Informatique de Paris 6)ParisFrance
  2. 2.EDF R&DPalaiseauFrance

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