Exact algorithms and bounds for the dynamic assignment interdiction problem

We study a multi‐stage dynamic assignment interdiction (DAI) game in which two agents, a user and an attacker, compete in the underlying bipartite assignment graph. The user wishes to assign a set of tasks at the minimum cost, and the attacker seeks to interdict a subset of arcs to maximize the user...

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Vydáno v:Naval research logistics Ročník 64; číslo 5; s. 373 - 387
Hlavní autoři: Sefair, Jorge A., Smith, J. Cole
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Wiley Subscription Services, Inc 01.08.2017
Témata:
Algorithms
assignment problem
Costs
dynamic programming
Games
Logistics
Mathematical models
Minimum cost
network interdiction
Objective function
robust optimization
Upper bounds
ISSN:0894-069X, 1520-6750
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Shrnutí:We study a multi‐stage dynamic assignment interdiction (DAI) game in which two agents, a user and an attacker, compete in the underlying bipartite assignment graph. The user wishes to assign a set of tasks at the minimum cost, and the attacker seeks to interdict a subset of arcs to maximize the user's objective. The user assigns exactly one task per stage, and the assignment costs and interdiction impacts vary across stages. Before any stage commences in the game, the attacker can interdict arcs subject to a cardinality constraint. An interdicted arc can still be used by the user, but at an increased assignment cost. The goal is to find an optimal sequence of assignments, coupled with the attacker's optimal interdiction strategy. We prove that this problem is strongly NP‐hard, even when the attacker can interdict only one arc. We propose an exact exponential‐state dynamic‐programming algorithm for this problem as well as lower and upper bounds on the optimal objective function value. Our bounds are based on classical interdiction and robust optimization models, and on variations of the DAI game. We examine the efficiency of our algorithms and the quality of our bounds on a set of randomly generated instances. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 373–387, 2017
Bibliografie:ObjectType-Article-1
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ISSN:0894-069X
1520-6750
DOI:10.1002/nav.21753