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Information casualties can be obtained from satellite images, sensor systems embedded in the infrastructure (e.g., cameras), police reports, property owners, civilians and other individuals. A large number of casualties can easily overwhelm the ambulance system because the number of ambulances is usually determined by reference to a major but not disasterous event. Management of resources in such an environment becomes critical. In this paper we provide efficient methods to improve the performance of rescue work, specifically the allocation of ambulances in an appropriate manner to the casualty clusters and then to reallocate ambulances between clusters as the disaster evolves.

The rest of this paper is organized as follows. Section 2 contains a literature review of related modeling areas from which we have drawn ideas for our model development/analysis. Section 3 provides a brief description of the general setting of our problem. Section 4 focuses on initial ambulance allocation. We first calculate time measures associated with a casualty cluster once a given number of ambulances have been assigned to it at the initial time point. Then these time measures are used to develop algorithms for the minimization of makespan and the minimization of weighted total flow time. Section 5 addresses the ambulance reallocation problem. We consider a discrete time policy which allows redistribution to occur at predetermined instants. Section 6 applies the algorithms of Section 4 to a case study based on an earthquake simulation in the Northridge, CA area. Finally, Section 7 contains a discussion along with future work directions.

2. Literature review

There are several modeling areas that relate to resource allocation in a disaster relief setting. One such area is forest-fire management. Another is the management of enforcement efforts in illicit drug markets. A third is the interplay between data fusion and dispatch/routing of ambulances. We briefly review relevant papers in each of these areas. We also point out which modeling aspects we have utilized in the development of our ambulance allocation model.

Our study of relevant research begins with an interesting problem which relates to forest-fire management. Parks (1964) presented a deterministic model to study the initial attack on wildland fires. His model is also focused on the economic aspect of the problem and the objective is to determine manpower requirements such that the total cost is minimized. The optimal resource allocation balances all the costs including the operating cost of the organization, transportation and logistic cost, emergency cost, damage cost, and cost associated with the length of time for suppression and the size of suppressing force. Islam (1998) considered a daily airtanker deployment problem for forest-fire management, which describes how many airtankers are required per day and where they should be deployed dynamically throughout the day. The growth pattern of a forest fire is used in our problem to describe how a cluster of casualties grows. A cluster is composed of a sufficient number of casualties whose locations are close to one another.

Another related problem can be found in the management of illicit drug markets. To aid the understanding of how drug market management is closely related to our problem, we first identify the similarity between these two problems. The drug dealers and the police enforcement resources can be regarded as casualties and relief resources, respectively. The operation of cracking down on the drug dealers may be thought of as the operation of rescuing casualties. Becker (1976) was one the pioneers who pointed out that utility maximization models are useful in the context of drug dealing. Caulkins (1990) presented an economic model to quantify the rate of growth or decay of a drug market under crackdown enforcement. In his model, the rate of change in the number of dealers is proportional to the difference between the profit available to dealers active in the market and the discouraging utility (including the risk from crackdown enforcement and the reservation wage). Based on the framework of Caulkins' model, Baveja (1993) studied the problem of finding the best rate to crack down on a drug market. He considered both discrete and continuous-time policies. The solutions to both cases gave the same conclusion that the best way is to allocate the maximum possible effort from the earliest possible time. Naik et al. (1996) provided an analytical approach to schedule crackdown enforcement for a series of drug markets. They also extended the problem to incorporate the dealer displacement effect (dealers might respond to a crackdown by relocating from one market to another). Behrens et al. (2000) studied the drug treatment and prevention problem in the framework of dynamic optimal control under different assumptions. Tragler et al. (2001) considered whether to allocate resources to treatment rather than enforcement. They formulated this as an optimal control problem and provided recommendations for a variety of market situations.

Data fusion first appeared in the scientific literature in the late 1960s and found use in multiple disciplines in the 1970s and 1980s (Gros, 1997). Scott and Rogova (2004) gave a general introduction of how to conduct disaster relief management in a data fusion synthetic task environment. Gong et al. (2004) studied the casualty pickup problem and casualty delivery problem based on data fusion methods. Gong and Batta (2004) and Gong (2005) also studied the problem of managing casualties with different priorities. Their work requires the consideration of a methodology to address the problem of identification of casualty clusters. A dynamic method is presented under the assumption that every ambulance can be dispatched to every cluster. In this paper, we study the problem from another aspect: namely the case in which a set of ambulances serve only one cluster until the cluster no longer exists. This requires an efficient method to allocate the available resources to clusters. We later study the problem of reallocating ambulances between clusters as the disaster evolves.

3. Problem description

After a disaster occurs, hundreds or thousands of spatially distributed casualties need to be treated. As we mention in Section 1, information on casualties is assumed to be reported by sensors, which could include calls from injured people, passers by, law enforcement officers, ambulance drivers, etc. The large number and different types of these sources leads to imprecise data, making it difficult to determine the precise situation, i.e., how many distinct casualties there are and where these casualties are located. Instead of exact spatial coordinates for each casualty, we have an estimate of a confidence region, typically using data fusion concepts. Data fusion can be defined as the synergistic use of information from multiple sources in order to assist in the overall understanding of a phenomenon. In our case information flowing from multiple sources has a highly variable character (e.g., human intelligence, signal intelligence, etc.). It is necessary to align the data and develop a comprehensive picture rapidly and accurately in order to take full advantage of it in our emergency relief services. The typical output of a data fusion algorithm is that a casualty is located in a specific region with a probability no smaller than a given value p (0 < p [less than or equal to] 1). If the number of casualties that are likely to be in a small area exceeds a threshold, say N, then these casualties are regarded as a cluster; otherwise, these casualties are treated as individuals. The choice of N should be made so that the total number of clusters does not dilute the available resources for assignment to clusters to an extent that makes the relief operation ineffective.

We assume that the emergency services only respond to casualties in a cluster. An ambulance dispatched to an isolated casualty may take a considerable time to find the patient. Also, in a disaster situation it is more likely that three to four casualties are loaded on to the ambulance prior to a trip back to the hospital. To minimize casualty search time and to simultaneously maximize ambulance utilization, it is more efficient, in general, only to respond to casualties in a cluster.

For the purpose of our mathematical model, we assume that there are m clusters that need to be...

NOTE: All illustrations and photos have been removed from this article.



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