Optimal interdiction of a supply network

Abstract

Under certain conditions, the re‐supply capability of a combatant force may be limited by the characteristics of the transportation network over which supplies must flow. Interdiction by an opposing force may be used to reduce the capacity of that network. The effects of such efforts vary for differing missions and targets. With only a limited total budget available, the interdictor must decide which targets to hit, and with how much effort. An algorithm is presented for determining the optimum interdiction plan for minimizing network flow capacity when the minimum capacity on an arc is positive and the cost of interdiction is a linear function of arc capacity reduction.

Development of an Algorithm for all type of Network Flow Problems

“…The objective is to determine the flow in each arc and the maximum flow that can be routed through the network. Network flow problems model the essential issues in many real-world resource allocation problems, including coordinating tactical air strikes [13], combating drug trafficking [19], controlling infections in a hospital [2], chemically treating raw sewage [14], and controlling floods [15] The study of network flow problem is basic to many advanced problems such as Maximum Flow Network Interdiction Problem( MFNIP) in particular originates from the Cold War, when analysts at the RAND Corporation studied how to interdict the Soviet Union's railroad traffic into Eastern Europe using the fewest resources [9], They accomplished this by solving a Minimum Capacity s-t Cut Problem; this is the earliest known formulation of this fundamental problem [17]. From the 1960s to the turn of the 21st century, there has been an extensive amount of academic literature on various network problems.…”

“…All the models aimed at finding the solution by considering the arc capacities and less attention has been given to the simplification of the network, most of which is listed in [6]. The basic framework for maximum flow network interdiction with explicit budget constraints was first studied in [13].In the early 1990s, Wood [19], resurrected interest in network interdiction by introducing MFNIP. A similar problem to MFNIP, called the Network Inhibition Problem (NIP), was independently introduced by Phillips in [14].…”

The Maximum Flow Network Interdiction Problem: Valid inequalities, integrality gaps, and approximability

“…Interdiction problems model the essential issues in many real-world resource allocation problems, including coordinating tactical air strikes [13], combatting drug trafficking [19], controlling infections in a hospital [2], chemically treating raw sewage [14], and controlling floods [15]. The study of MFNIP in particular originates from the Cold War, when analysts at the RAND Corporation studied how to interdict the Soviet Union's railroad traffic into Eastern Europe using the fewest resources [9].…”

“…From the 1960s to the turn of the 21st century, there has been an extensive amount of academic literature on various interdiction problems, most of which is listed in [6]. The basic framework for maximum flow network interdiction with explicit budget constraints was first studied in [13]. In the early 1990s, Wood [19] resurrected interest in network interdiction by introducing MFNIP.…”

A Branch-and-cut Algorithm for Integer Bilevel Linear Programs

“…Most research on these models has focused on the network interdiction problem [Wollmer, 1964, McMasters and Mustin, 1970, Ghare et al, 1971, Wood, 1993, Cormican et al, 1998, Israeli and Wood, 2002, Held and Woodruff, 2005, Janjarassuk and Linderoth, 2008, Royset and Wood, 2007, Lim and Smith, 2007, Morton et al, 2007, in which the lower-level DM represents an entity operating a network of some sort. The upper-level DM (or interdictor) attempts to reduce the network performance as much as possible via the removal (complete or otherwise) of portions (subsets of arcs or nodes) of the network.…”