# The summed start-up costs in a unit commitment problem

## Author

Listed:
• René Brandenberg

() (Technische Universität München)

• Matthias Huber

() (Technische Universität München)

• Matthias Silbernagl

() (Technische Universität München)

## Abstract

Abstract We consider the sum of the incurred start-up costs of a single unit in a Unit Commitment problem. Our major result is a correspondence between the facets of its epigraph and some binary trees for concave start-up cost functions CU, which is bijective if CU is strictly concave. We derive an exponential $${\mathcal{H}}$$ H -representation of this epigraph, and provide an exact linear separation algorithm. These results significantly reduce the integrality gap of the Mixed Integer formulation of a Unit Commitment Problem compared to current literature.

## Suggested Citation

• René Brandenberg & Matthias Huber & Matthias Silbernagl, 2017. "The summed start-up costs in a unit commitment problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 203-238, March.
• Handle: RePEc:spr:eurjco:v:5:y:2017:i:1:d:10.1007_s13675-016-0062-2
DOI: 10.1007/s13675-016-0062-2
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## References listed on IDEAS

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1. Matthias Nowak & Werner Römisch, 2000. "Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty," Annals of Operations Research, Springer, vol. 100(1), pages 251-272, December.
2. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
3. Jonas Egerer & Clemens Gerbaulet & Richard Ihlenburg & Friedrich Kunz & Benjamin Reinhard & Christian von Hirschhausen & Alexander Weber & Jens Weibezahn, 2014. "Electricity Sector Data for Policy-Relevant Modeling: Data Documentation and Applications to the German and European Electricity Markets," Data Documentation 72, DIW Berlin, German Institute for Economic Research.
Full references (including those not matched with items on IDEAS)

### Keywords

Unit commitment; Mixed integer programming; Summed Start-up costs; Start-up cost epigraph; Valid inequalities; Integrality gap;

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