Identifying Critical Infrastructure: The Median and Covering Facility Interdiction Problems

Abstract

Facilities and their services can be lost due to natural disasters as well as to intentional strikes, either by terrorism or an army. An intentional strike against a system is called interdiction. The geographical distribution of facilities in a supply or service system may be particularly vulnerable to interdiction, and the resulting impacts of the loss of one or more facilities may be substantial. Critical infrastructure can be defined as those elements of infrastructure that, if lost, could pose a significant threat to needed supplies (e.g., food, energy, medicines), services (e.g., police, fire, and EMS), and communication or a significant loss of service coverage or efficiency. In this article we introduce two new spatial optimization models called the r‐interdiction median problem and the r‐interdiction covering problem. Both models identify for a given service/supply system, that set of facilities that, if lost, would affect service delivery the most, depending upon the type of service protocol. These models can then be used to identify the most critical facility assets in a service/supply system. Results of both models applied to spatial data are also presented. Several solutions derived from these two interdiction models are presented in greater detail and demonstrate the degree to which the loss of one or more facilities disrupts system efficiencies or coverage. Recommendations for further research are also made.

A multi-criteria assessment of the p-median, maximal coverage and p-center location models

“…Constraint (7) restricts the number of sited facilities to p. Constraint (8) ensures that all demand locations are covered by at least Q facilities. Constraint (9) declares the variable types.…”

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

“…We would like to determine which R facilities to remove from the graph (V f , V s , E) so as to maximize the number of satellites not adjacent to any facilities in the graph induced on the remaining facilities and the satellites. RIC was first studied in [6] and has applications in identifying critical infrastructure in supply (e.g., food, energy, medicine), domestic service (e.g., police, fire, EMS) and communication networks [6].…”

“…A similar problem to MFNIP, called the Network Inhibition Problem (NIP), was independently introduced by Phillips in [14]. Numerous variants of network interdiction problems have also been studied, including shortest path network interdiction [10], stochastic network interdiction [7,11], multiple commodity network interdiction [12,19], facility interdiction [6], and a variant of MFNIP where flow is routed before arcs are removed [8]. There is also literature on more-than-two-stage interdiction models where infrastructure may be reinforced against attacks [4].…”

“…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 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].…”

Analysis of Facility Systems’ Reliability Subject to Edge Failures: Based on the p-Median Problem

“…Church et al [13] presented a model called the r-interdiction median problem. This model can be used to identify which r of the existing set of p-facilities, when interdicted or lost impacts delivery efficiency the most.…”