Collaborative Research: Distribution of Patients to Medical Facilities in Mass-Casualty Events

大规模伤亡事件，如恐怖袭击和自然灾害，可能会影响到成百上千的人，并在不可预测的时间内对应急系统造成重大负担。在这些事件中，应急响应管理面临着时间压力下的几个复杂的操作决策，有时还面临着安全和安全方面的担忧。一个根本的决定是如何将受影响地区的伤亡人员分配到多个在容量、专科和距离上不同的医疗机构。目前，这一决定在民事环境中由紧急运输官员作出，在军事行动中则由战场指挥官作出。利用数学建模和分析，结合医学专业知识，该项目将建立知识和决策工具，使伤亡分布更加有效和客观。这一多学科项目汇集了业务研究人员和急诊医生，将通过促进灾害期间有效的伤亡分配而直接造福社会。在最一般的形式下，伤亡分配问题是一个随机序列决策问题，它包括各种参数和变量，如每个地点的伤亡人数；急救车辆的数量；每家医院的容量、能力和拥堵程度；地点和医院之间的旅行时间；以及旅行路线的状况。该项目的第一阶段涉及确定这一复杂决策问题背后的最基本的权衡，并为每一种权衡制定单独的模型。然后，将通过样本路径分析和马尔可夫决策过程等精确方法对这些模型进行分析，以获得对最优决策规则特征的见解。在该项目的第二阶段，将使用流体模型和拉格朗日松弛等近似方法来制定启发式政策。在最后阶段，将进行广泛的模拟研究，以在更现实的环境中使用文献数据和2010年全国医院非卧床医疗保健调查数据来测试原则和决策规则。为该项目开发的数学模型可以等价地视为具有动态路由的排队模型。因此，这个项目还通过引入和研究一类新的排队-路由问题来对运筹学文献做出贡献，其中到达队列的旅行需要时间，并且可能需要稀缺的资源。

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 the number of casualties at each location; the number of emergency vehicles; the capacity, capability, and congestion levels of each hospital; the travel time between locations and hospitals; and the 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 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.