The summed start-up costs in a unit commitment problem

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 exponenti...

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Autores principales:	René Brandenberg, Matthias Huber, Matthias Silbernagl
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2017
Materias:	90C57 90C11 90B99 52B12 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/81334a3e739a41808fcb7a90146d887d
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spelling	oai:doaj.org-article:81334a3e739a41808fcb7a90146d887d2021-12-02T05:01:00ZThe summed start-up costs in a unit commitment problem2192-440610.1007/s13675-016-0062-2https://doaj.org/article/81334a3e739a41808fcb7a90146d887d2017-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000794https://doaj.org/toc/2192-4406We 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 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.René BrandenbergMatthias HuberMatthias SilbernaglElsevierarticle90C5790C1190B9952B12Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 5, Iss 1, Pp 203-238 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C57 90C11 90B99 52B12 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C57 90C11 90B99 52B12 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 René Brandenberg Matthias Huber Matthias Silbernagl The summed start-up costs in a unit commitment problem
description	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 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.
format	article
author	René Brandenberg Matthias Huber Matthias Silbernagl
author_facet	René Brandenberg Matthias Huber Matthias Silbernagl
author_sort	René Brandenberg
title	The summed start-up costs in a unit commitment problem
title_short	The summed start-up costs in a unit commitment problem
title_full	The summed start-up costs in a unit commitment problem
title_fullStr	The summed start-up costs in a unit commitment problem
title_full_unstemmed	The summed start-up costs in a unit commitment problem
title_sort	summed start-up costs in a unit commitment problem
publisher	Elsevier
publishDate	2017
url	https://doaj.org/article/81334a3e739a41808fcb7a90146d887d
work_keys_str_mv	AT renebrandenberg thesummedstartupcostsinaunitcommitmentproblem AT matthiashuber thesummedstartupcostsinaunitcommitmentproblem AT matthiassilbernagl thesummedstartupcostsinaunitcommitmentproblem AT renebrandenberg summedstartupcostsinaunitcommitmentproblem AT matthiashuber summedstartupcostsinaunitcommitmentproblem AT matthiassilbernagl summedstartupcostsinaunitcommitmentproblem
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The summed start-up costs in a unit commitment problem

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