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Diskretnyi Analiz i Issledovanie Operatsii, 2020, Volume 27, Issue 3, Pages 5–27
DOI: https://doi.org/10.33048/daio.2020.27.687
(Mi da954)
 

Planning a defense that minimizes a resource deficit in the worst-case scenario of supply network destruction

V. L. Beresnevab, A. A. Melnikovab

a Sobolev Institute of Mathematics, 4 Koptyug Avenue, 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov Street, 630090 Novosibirsk, Russia
References:
Abstract: We consider same model of planning the defense of edges of a supply network. The vertices of the network represent the consumers and the providers of a resource, while the edges allow us to transmit the resource without delays and capacity constraints. The Defender commits a bounded budget to protect some of the edges, aiming to minimize the damage that is caused by the destruction of the unprotected edges. To measure the damage, we apply the value of the total resource deficit caused by the worst-case scenario of partial network destruction. The Defender's problem falls into the family of “Defender–Attacker” problems that are formalized as the minimax mixed-integer programming problems. To find an optimal Defender's solution, we suggest some two cut generation schemes based on a reformulation of the problem as a mixed-integer problem with exponentially many constraints. Tab. 2, illustr. 4, bibliogr. 13.
Keywords: “defender–attacker” problem, total deficit, cut generation.
Funding agency Grant number
Russian Science Foundation 17-11-01021
This research is supported by the Russian Science Foundation (Project 17–11–01021).
Received: 09.05.2020
Revised: 22.05.2020
Accepted: 25.05.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 3, Pages 416–429
DOI: https://doi.org/10.1134/S1990478920030023
Bibliographic databases:
Document Type: Article
UDC: 519.8+518.25
Language: Russian
Citation: V. L. Beresnev, A. A. Melnikov, “Planning a defense that minimizes a resource deficit in the worst-case scenario of supply network destruction”, Diskretn. Anal. Issled. Oper., 27:3 (2020), 5–27; J. Appl. Industr. Math., 14:3 (2020), 416–429
Citation in format AMSBIB
\Bibitem{BerMel20}
\by V.~L.~Beresnev, A.~A.~Melnikov
\paper Planning a defense that minimizes a~resource~deficit in~the~worst-case scenario of~supply network destruction
\jour Diskretn. Anal. Issled. Oper.
\yr 2020
\vol 27
\issue 3
\pages 5--27
\mathnet{http://mi.mathnet.ru/da954}
\crossref{https://doi.org/10.33048/daio.2020.27.687}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 3
\pages 416--429
\crossref{https://doi.org/10.1134/S1990478920030023}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85094637726}
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    References:17
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