Protecting Critical Assets: The R-Interdiction Median Problem with Fortification

By Church, Richard L.; Scaparra, Maria Paola | Geographical Analysis, April 2007 | Go to article overview

Protecting Critical Assets: The R-Interdiction Median Problem with Fortification


Church, Richard L., Scaparra, Maria Paola, Geographical Analysis


Many systems contain bottlenecks, critical linkages, and key facilities. Such components, when lost due to a man-made or natural disaster, may imperil a system in performing its intended function. This article focuses on reducing the impact of an intentional strike against a supply system where supply facilities can be fortified in order to prevent such events. It is assumed that fortification resources are limited and must be used in the most efficient manner. In a recent article, Church, Scaparra, and Middleton (2004) introduced the r-interdiction median problem, which can be used to identify the most important facilities in a supply system. In this article, we extend that model to address the option of fortifying such sites against possible interdiction. We present a new integer-linear programming model that optimally allocates fortification resources in order to minimize the impact of interdiction. Computational results are presented in using this model for several hypothetical problems. We also discuss the general properties of fortification and demonstrate that the presence of fortification can impact which system elements are considered critical.

Introduction

Since September 11, 2001, there has been a heightened concern for terrorism and the losses that a terrorist group may cause. As a part of homeland security planning, there has been an interest in identifying critical infrastructure. Examples of recent work on understanding system function and failure can be found in Murray and Grubesic (2006), and courses for action are discussed in a National Research Council Report (2003) and Cutter, Richardson, and Wilbanks (2003). Critical infrastructure can be defined as those elements that, when lost, result in significant disruption of the system in its ability to perform its function. These elements can include transportation linkages (e.g., bridges, tunnels, rail), facilities (e.g., port terminals, production facilities, warehouses, operations centers, emergency response facilities, hospitals), critical stockpiles (e.g., vaccine, drugs, food), key personnel (e.g., water system operators), and landmarks that may contribute to the loss of well being. It is important to note that many systems have built-in redundancy so that a system continues to operate in the event of a failure, such as backup pumps in a sewage collection system. There is a mature literature on system design with probabilistic failure of components (Colbourn 1987). Unfortunately, such a design does not normally take into account the possibility of intentional strikes, like the attack against the World Trade Center.

The military has had a long-term interest in identifying critical supply line targets, so that when such targets are hit or interdicted it will result in decreased supplies or delays in getting supplies to an area of conflict (see, e.g., Ghare, Montgomery, and Turner 1971; Golden 1978; McMusters and Mustin 1970; Wood 1993; Whiteman 1999). Models have been developed to allocate strike resources along supply routes in order to inflict the greatest harm on an enemy's supply system. The literature on this type of modeling is reviewed in Church, Scaparra, and Middleton (2004). For all practical purposes, the focus in such models is directed toward the interdiction of transportation links, like bridges. Our focus in this article is on the possible loss of one or more facilities in a system providing a good or service.

We can measure the impact of supply or service loss in terms of the degraded level of service, the time for the system to recover fully, the increased cost of operation, the costs of system repair, and so forth. For this article, we will assume that we have a set of operating facilities, where each facility has enough capacity to serve assigned customers. If a facility is lost due to interdiction, then the demand served by that facility must be reassigned to other facilities. Then, one can compare the average service distance for the initial system with the average service distance when one or more facilities are lost due to an intentional strike. …

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