Planning a Defense That Minimizes a Resource Deficit in theWorst-Case Scenario of Supply Network Destruction

• Published in: Journal of applied and industrial mathematics 2020-01, Vol.14 (3), p.416-429
• Main Authors: Beresnev, V L, Melnikov, A A
• Format: Article
• Language: English
• Subjects: Apexes; Damage; Destruction; Graph theory; Integer programming; Minimax technique; Mixed integer
• ISSN: 1990-4789; 1990-4797
• DOI: 10.1134/S1990478920030023

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.