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On the complexity of the Unit Commitment Problem

Pascale Bendotti (pascale.bendotti***at***edf.fr)
Pierre Fouilhoux (pierre.fouilhoux***at***lip6.fr)
CÚcile Rottner (cecile.rottner***at***edf.fr)

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. The UCP is proved to be strongly NP-hard.When either a unitary cost or amount of power is considered, the UCP is polynomial for T=1 and NP-hard for arbitrary $T$. When the constraints are restricted to minimum up and down times, the UCP is shown to be polynomial for a fixed n. 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; Subproblem of decomposition scheme

Category 1: Combinatorial Optimization

Category 2: Applications -- OR and Management Sciences

Citation: Sorbonne UniversitÚs, UniversitÚ Pierre et Marie Curie, LIP6 CNRS UMR 7606, 4 Place Jussieu, 75005 Paris; EDF R&D, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France. May, 2017.

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Entry Submitted: 05/19/2017
Entry Accepted: 06/06/2017
Entry Last Modified: 10/30/2017

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