Responding to casualties in a disaster relief operation: Initial ambulance allocation and reallocation, and switching of casualty priorities
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This research is concerned with models for response to casualties in a disaster relief operation. Three problems are analyzed. The first is that of initial ambulance allocation to casualty clusters. The second is that of ambulance reallocation between casualty clusters. The third is that of switching casualty priorities. We briefly describe each contribution. The first problem analyzes a deterministic ambulance allocation model for a post-disaster relief operation. Casualties in a natural disaster, e.g., earthquake, tend to be numerous and distributed in space, typically forming clusters. Due to the geographic separation of the clusters it is not practical to switch ambulances between clusters frequently after the rescue starts. Thus it is critical to allocate the correct number of ambulances to each cluster at the beginning of the rescue process. We formulate a deterministic model which depicts how a cluster grows after a disaster strikes. Based on the model and given a number of ambulances, we develop methods to calculate critical time measures, e.g. completion time for each cluster. Then we present two iterative procedures to optimize the makespan and the weighted total flow time, respectively. Our methods are illustrated via a case study, which is based on an earthquake in Northridge, California. The main conclusion is that the optimal ambulance allocation can be significantly dependent upon the desired performance measure. The second problem analyzes the ambulance reallocation problem on the basis of a discrete time policy. The benefits of redistribution include providing service to new clusters and fully utilizing ambulances. We consider the objective of minimizing makespan. The complication is that the distance between clusters needs to be factored in when making an ambulance reallocation decision. Our model permits consideration of travel distance between clusters. The third problem is concerned with servicing casualties with different priorities. We formulate a two-priority, preemptive, single-server queueing model. Each customer is classified into either a high priority class or a low priority class. The arrivals of the two priority classes follow independent Poisson processes and service time is assumed to be exponentially distributed. A queue-length-cutoff method is considered. Under this discipline the server responds only to high priority customers until the queue length of the other class exceeds a threshold L . After that the server switches to handle only the low priority queue. Steady-state balance equations are established for this system. Then we introduce two-dimensional generating functions to obtain the average number of customers for each priority class. We then focus on the preemptive resume case. We develop methodologies to obtain the optimal cutoffs for the situation when the weights of both queues are constant (i.e., not a function of queue length) and the situation when the weights change linearly with the queue lengths.