Acta Mathematicae Applicatae Sinica, English Series
Vol. 33, No. 3 (2017) 633–644
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Acta MathemaƟcae Applicatae Sinica,
The Editorial Office of AMAS &
Springer-Verlag Berlin Heidelberg 2017
Solving Multi-period Interdiction via Generalized
, Alireza GHAFFARI-HADIGHEH
Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
E-mail: soleimani email@example.com)
Abstract This paper considers a novel formulation of the multi-period network interdiction problem. In
this model, delivery of the maximum ﬂow as well as the act of interdiction happens over several periods,
while the budget of resource for interdiction is limit. It is assumed that when an edge is interdicted in a
period, the evader considers a rate of risk of detection at consequent periods. Application of the generalized
Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem.
Computational experiences denote reasonable consistency with expectations.
Keywords Bi-level programming; network interdiction; mixed-integer nonlinear programming; generalized
2000 MR Subject Classiﬁcation 90B10
Interdiction, which can be favorable or damaging depending on the problem under consideration,
is the act of preventing ﬂow in a network. The network interdiction models are classically
deﬁned on the interdictor-evader frame as a Bi-Level Programming Problem (BLPP). In the
lower level problem, the evader desires to improve his objective function (obtaining maximum
ﬂow or achieving minimum cost) whereas in the upper level, the interdictor aims to minimize
the evader’s maximum gain by limiting his feasible actions or by increasing the associated cost
Most of the standard interdiction problems proposed in the literature regard Stackelberg
, wherein the two entities (i.e., an interdictor and an evader) operate in turn with full
or partially knowledge of each others actions. However, the role of leader and follower may be
changed in between according to the model’s requirements.
Study on the Network Interdiction Problem (NIP) initiated by Wollmer’s work
goal of removing n arcs from a network to minimize the maximum ﬂow between the source
and the sink nodes. For the ﬁrst time, McMasters and Mustin
added a budget constraint
to the problem by using a mathematical formulation for NIP to prevent enemy’s arsenal trans-
solved this problem using mathematical methods. He considered an integer
programming formulation of the problem and provided a proof of NP-completeness and showed
that the model could be generalized for other possibilities such as multi-commodity networks,
undirected networks, networks with multiple sources and multiple sinks, etc.
Other studies focused on maximizing the shortest path between two speciﬁed nodes in a
Manuscript received January 8, 2015. Revised October 17, 2015.
Supported by Azarbaijan Shahid Madani University.