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.

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Recent events have highlighted the need for planners to consider the risk of disruptions when designing supply chain networks. Supply chain disruptions have a number of causes and may take a number of forms. Once a disruption occurs, there is very little recourse regarding supply chain infrastructure because these strategic decisions cannot be changed quickly. Therefore, it is critical to account for disruptions during the design of supply chain networks so that they perform well even after a disruption. Indeed, these systems can often be made substantially more reliable with only small additional investments in infrastructure. Planners have a range of options available to them in designing resilient supply chain networks, and their choice of approaches will depend on the financial resources available, the decision maker's risk preference, the type of network under consideration, and other factors. In this tutorial, we present a broad range of models for designing supply chains resilient to disruptions. We first categorize these models by the status of the existing network: A network may be designed from scratch, or an existing network may be modified to prevent disruptions at some facilities. We next divide each category based on the underlying optimization model (facility location or network design) and the risk measure (expected cost or worst-case cost).

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. IntroductionSince 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 th...

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