On the complexity of the Unit Commitment Problem

Pascale Bendotti (), Pierre Fouilhoux () and Cécile Rottner ()
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Pascale Bendotti: Sorbonne Université, LIP6-CNRS (Laboratoire d’Informatique de Paris 6)
Pierre Fouilhoux: Sorbonne Université, LIP6-CNRS (Laboratoire d’Informatique de Paris 6)
Cécile Rottner: Sorbonne Université, LIP6-CNRS (Laboratoire d’Informatique de Paris 6)

Annals of Operations Research, 2019, vol. 274, issue 1, No 6, 119-130

Abstract: Abstract 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 $$T=1$$ 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 $$T=1$$ 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.

Keywords: Unit Commitment Problem; Complexity; Dynamic programming; Subproblem of decomposition scheme (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10479-018-2827-x

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