Identifying Critical Infrastructure: The Median and Covering Facility Interdiction Problems Richard L. Church, Maria P. Scaparra, and Richard S. Middleton Department of Geography, University of California, Santa Barbara 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. Key Words: critical infrastructure, facility location, p-median problem, maximal covering, interdiction. S upply systems involve a set of manufacturing, storage, and transportation facilities and assets that accomplish the supply of goods and services. There is a risk of sudden loss of facilities and assets due to natural causes such as floods and fire and due to man- made causes such as terrorism and military action. Our concern in this article deals with the latter type of problem, that is, a loss of capacity due to some type of attack. Intentional disruption of a supply system is called interdiction. The problem of interdiction has received considerable attention due to the interest in interdicting supply lines during warfare (McMasters and Mustin 1970). More recently, interest has focused on what is termed ‘‘critical infrastructure.’’ We define critical in- frastructure 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. These services and sup- plies are often termed ‘‘lifelines.’’ Losing capacity of a lifeline could have a great impact on a population or army. Each lifeline system has certain elements that are more important than others. Those elements of infra- structure that are most important in a lifeline system are often called the ‘‘vital’’ links. For example, one element of a power transmission system may be a key link in providing power to a very large area, and alternate system routes may not have the capacity to provide ad- equate supply. The loss of that key link would be det- rimental to the full operation of the system and is therefore vital to system supply. Cutter, Richardson, and Wilbanks (2003) have identified the need to develop methods for identifying critical infrastructure as one of several national research priorities. In this article we introduce two new 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. In the next section, we give a brief review of the literature on modeling interdiction. Then we define a general problem of facility interdiction that can be used to help identify ‘‘critical facilities,’’ that is, which facilities to interdict or which facilities to protect. In a subsequent section, we define the p-median location model and its interdiction model counterpart. We then define the maximal covering location problem along with its interdiction model counterpart. Both of these interdiction models are new, innovative models that can be used to identify critical facility assets. We follow with some computational experience and present several example solutions to both interdiction models. We Annals of the Association of American Geographers, 94(3), 2004, pp. 491–502 r 2004 by Association of American Geographers Initial submission, April 2003; final acceptance, August 2003 Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, and 9600 Garsington Road, Oxford OX4 2DQ, U.K.