Stochastic casualty response planning with multiple classes of patients

Abstract

In this paper, we study the stochastic casualty response planning problem (CRP) in the context of providing treatments to multiple classes of patients with different types of injuries. In this general setting, both patients’ demands and hospitals’ treatment capacity are considered uncertain. To the best of our knowledge, this is the first time that this problem is solved. We propose a novel two-stage stochastic mixed-integer programming model which, in the first stage, determines the location of the Alternative Care Facilities (ACFs) and allocates different resources, such as rescue vehicles, medical equipment, and physicians, to them. In the second stage, this model helps decide how to allocate patients with multiple injuries to either ACFs or hospitals, considering their care itineraries and available resources. Moreover, it recommends potential patient transfers between ACFs and hospitals when required. Furthermore, we introduce an alternative two-stage stochastic model that is more compact than the first. This formulation significantly reduces solution times. We also provide an equivalency proof between the two formulations. As the solution method, we develop both the L-shaped algorithm, a pure cutting-plane method tailored to our stochastic mathematical model, and the branch-and-Benders-cut (B&BC) algorithm. To further enhance the efficiency of these algorithms, we develop a wide range of acceleration techniques, including Benders dual decomposition, Lagrangian dual decomposition, a multi-cut reformulation, Pareto-optimal cuts, and the inclusion of lower bounding functional valid inequalities. We carry out extensive computational experiments demonstrating that these algorithmic enhancements dramatically improve the performance of the B&BC algorithm, reducing the average optimality gap from 7898% in the standard B&BC algorithm to just 0.92% in the enhanced version. Additionally, we benchmark our approach against the progressive hedging algorithm (PHA), a widely used decomposition method in disaster response operations, to further assess its effectiveness. Finally, we present a case study from the 2011 Van earthquake in Turkey, demonstrating the applicability and efficiency of our optimization methods.