Mass-casualty events such as terrorist attacks and natural disasters can affect hundreds to thousands of people and place significant burdens on emergency response systems for unpredicted periods of time. During these events, the emergency response management faces several complex operational decisions under time pressure and sometimes security and safety concerns. One fundamental decision is how to distribute casualties from the affected areas to multiple medical facilities that differ in capacity, specialty, and distance. Currently, this decision is left to the emergency transport officer in civilian settings and to battlefield commanders during military operations. Using mathematical modeling and analysis in conjunction with medical expertise, this project will build knowledge and decision tools to make casualty distribution more efficiently and objective. This multi-disciplinary project bringing together operations researchers and emergency physicians, will benefit society directly by facilitating effective casualty distribution during disasters. It will also significantly contribute to the education of a diverse group of students from the operations research, public health, and medical fields.

In its most general form, casualty-distribution problem is a stochastic sequential decision making problem that includes various parameters and variables such as number of casualties at each location; number of emergency vehicles; capacity, capability, and congestion levels of each hospital; travel time between locations and hospitals; and condition of travel routes. The first phase of the project involves identifying the most fundamental tradeoffs underlying this complex decision-making problem and formulating separate models for each. These models will then be analyzed by means of exact methods such as sample-path analysis and Markov decision processes to obtain insights about the characteristics of optimal decision rules. In the second phase of the project, approximate approaches such as fluid models and Lagrangian relaxations will be used to develop heuristic policies. In the final phase, an extensive simulation study will be conducted to test the proposed principles and decision rules in more realistic settings using data from literature and the 2010 National Hospital Ambulatory Medical Care Survey.  The mathematical models developed for this project can equivalently be seen as queueing models with dynamic routing. Hence, this project also contributes to the operations research literature by introducing and studying a new class of queue-routing problems, where the travel to queues takes time and possibly requires a scarce resource.

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