| Summary: | Catastrophic health events are natural or man-made incidents that result in casualty numbers that overwhelm the immediate response capabilities of healthcare systems. These events overpower hospitals even when the latter trigger contingency capacity surges that are usually sufficient to deal with regular disasters. We seek to build effective location-allocation plans for the overwhelming number of casualties expected in these events by using alternative care facilities to address surge capacity issues and incorporating triage and the movement of self-evacuees for effective treatment allocation.
We first tailor and apply our framework in a deterministic location-allocation model for catastrophic radiological incidents, which are events whereby the release of radioactive material leads to significant consequences to people, the environment, and facilities. We formulate a mixed integer linear programming model to locate alternative care facilities, allocate casualties for triage, and allocate triaged casualties for treatment to minimize the total weighted casualty transportation time. The model is applied to the study of two separate radiological dispersal device incidents, both based on Department of Homeland Security's National Planning Scenario 11. We generate the optimal plan for each incident and use sensitivity analyses to draw insights on facility budgeting and triage capacity allocation at hospitals. These insights lead to some response planning rules of thumb.
With the above model as a basis, we incorporate data uncertainties, using probabilistically distributed scenarios, and the time sensitivity of information to create a three-stage stochastic programming location-allocation model for general catastrophic health events. In the first stage, the model locates alternative care facilities prior to any scenario realization. In the second stage, it allocates casualties for triage, given initial damage scenarios involving uncertainties in casualty demands, transportation times, and numbers of self-evacuees. In the third stage, it allocates casualties for treatment, given triage scenarios and initial damage scenarios. Model solution time increases exponentially with the number of binary location variables. Given that large solution times are unacceptable in disaster response, we propose an algorithm based on Benders' decomposition to obtain good solutions fast. The algorithm uses valid inequalities to reduce feasibility cuts, flow cover inequalities to generate stronger cuts, and perturbed dual subproblems to reduce the effect of degeneracy. We implement the model and algorithm in the case study of an earthquake situation in the southernmost part of the San Andreas Fault. We compare the effectiveness of our algorithm to classical Benders' decomposition and perform sensitivity analyses on facility budgets and capacities to obtain interesting insights.
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