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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, Volume 29, Number 3, Pages 156–167
DOI: https://doi.org/10.21538/0134-4889-2023-29-3-156-167 (Mi timm2024) 		 
Comparison and Polyhedral Properties of Valid Inequalities for a Polytope of Schedules for Servicing Identical Requests

R. Yu. Simanchevab, I. V. Urazovaa

a Omsk State University
b Omsk Scientific Center, Siberian Branch of the Russian Academy of Sciences
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DOI: https://doi.org/10.21538/0134-4889-2023-29-3-156-167
Abstract: The paper considers the convex hull of a set of schedules for servicing identical requests by parallel devices. Precedence conditions are given on the set of requests. All requests enter the service queue simultaneously and have the same service duration. Interruptions in request servicing are prohibited. Time is discrete. The polyhedral properties of some previously constructed classes of valid inequalities are studied. The “depth” cuts are compared, and the strongest subclasses of cuts are found. The relative position of the schedule polytope and hyperplanes generated by inequalities is also studied.
Keywords: schedules, polytope, valid inequality, comparison of inequalities.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 121022000112-2
This research was carried out within the state task of the Omsk Scientific Center SB RAS (project registration no. 121022000112-2).
Received: 11.05.2023
Revised: 13.06.2023
Accepted: 19.06.2023
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2023, Volume 323, Issue 1, Pages S243–S254
DOI: https://doi.org/10.1134/S0081543823060202
Bibliographic databases:
Document Type: Article
UDC: 519.85
MSC: 90C10, 90C57
Language: Russian
Citation: R. Yu. Simanchev, I. V. Urazova, “Comparison and Polyhedral Properties of Valid Inequalities for a Polytope of Schedules for Servicing Identical Requests”, Trudy Inst. Mat. i Mekh. UrO RAN, 29, no. 3, 2023, 156–167; Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S243–S254
Citation in format AMSBIB
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\by R.~Yu.~Simanchev, I.~V.~Urazova
\paper Comparison and Polyhedral Properties of Valid Inequalities for a Polytope of Schedules for Servicing Identical Requests
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2023
\vol 29
\issue 3
\pages 156--167
\mathnet{http://mi.mathnet.ru/timm2024}
\crossref{https://doi.org/10.21538/0134-4889-2023-29-3-156-167}
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\edn{https://elibrary.ru/onzgop}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2023
\vol 323
\issue , suppl. 1
\pages S243--S254
\crossref{https://doi.org/10.1134/S0081543823060202}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85185146804}
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