On the complexity of the Unit Commitment Problem
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.
KeywordsUnit Commitment Problem Complexity Dynamic programming Subproblem of decomposition scheme
The authors would like to thank Christoph Dürr for fruitful discussions.
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