Geodesic
Planning a defense that minimizes a~resource~deficit in~the~worst-case scenario of~supply network destruction
Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 3, pp. 5-27

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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. 
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     title = {Planning a defense that minimizes a~resource~deficit in~the~worst-case scenario of~supply network destruction},
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     publisher = {mathdoc},
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V. L. Beresnev; A. A. Melnikov. Planning a defense that minimizes a~resource~deficit in~the~worst-case scenario of~supply network destruction. Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 3, pp. 5-27. http://geodesic.mathdoc.fr/item/DA_2020_27_3_a0/