Annals of Operations Research

, Volume 249, Issue 1–2, pp 39–53 | Cite as

A simple greedy heuristic for linear assignment interdiction

  • Vladimir Stozhkov
  • Vladimir Boginski
  • Oleg A. Prokopyev
  • Eduardo L. Pasiliao
S.I.: Pardalos60

Abstract

We consider a bilevel extension of the classical linear assignment problem motivated by network interdiction applications. Specifically, given a bipartite graph with two different (namely, the leader’s and the follower’s) edge costs, the follower solves a linear assignment problem maximizing his/her own profit, whereas the leader is allowed to affect the follower’s decisions by eliminating some of the vertices from the graph. The leader’s objective is to minimize the total cost given by the cost of the interdiction actions plus the cost of the assignments made by the follower. The considered problem is strongly \({ NP}\)-hard. First, we formulate this problem as a linear mixed integer program (MIP), which can be solved by commercial MIP solvers. More importantly, we also describe a greedy-based construction heuristic, which provides (under some mild conditions) an optimal solution for the case, where the leader’s and the follower’s edge costs are equal to one. Finally, we present the results of our computational experiments comparing the proposed heuristic against an MIP solver.

Keywords

Bilevel programming Assignment interdiction Linear assignment 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Vladimir Stozhkov
    • 1
  • Vladimir Boginski
    • 1
    • 4
  • Oleg A. Prokopyev
    • 2
  • Eduardo L. Pasiliao
    • 3
  1. 1.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of Industrial EngineeringUniversity of PittsburghPittburghUSA
  3. 3.Munitions DirectorateAir Force Research LaboratoryEglin AFBUSA
  4. 4.Department of Industrial Engineering and Management SystemsUniversity of Central FloridaOrlandoUSA

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