Stochastic Optimization Model with Exogenous and Decision-Dependent Uncertainty for Medical Evacuation

The timely and reliable medical evacuation (MEDEVAC) of injured soldiers on the battlefield is a primary concern for every military force. The objective is to design an evacuation network that maximizes the chance of survival and functional recovery of the wounded. We propose a chance-constrained MEDEVAC model that accounts for endogenous and exogenous uncertainty and show how decisions affect endogenous uncertainties. We develop a Boolean reformulation and expose its advantages over standard scenario-based reformulations. We design an algorithmic framework that includes a new convex integer relaxation, a multiterm convexification method, a tight bounding scheme, and the novel smallest domain branching rule. Results based on real-life data show the efficiency of our approach and provide suggestions for solving mixed-integer nonlinear problems. The study provides healthcare planners guidance about how to implement a reliable evacuation network and allows for a proper implementation of the Golden Hour doctrine. We design the value of endogenous uncertainty framework to assess the life-or-death benefits obtained by accounting for endogenous uncertainty. In congested networks, up to about 19% more soldiers can be evacuated with our model versus one disregarding endogenous uncertainty. We also show the importance to take into account the exogenous uncertainty in medical resources’ availability. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods and Analysis. Funding: M. A. Lejeune acknowledges the partial support of the National Science Foundation through Grants DMS2318519 and CMMI2533372 and the Office of Naval Research through Grant N00014-22-1-2649. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0986 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0986 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .