Health Service Support Networks Under Antiaircraft Threat - Beeson, Patrick (My University, 2025)
This thesis aims to provide tools and managerial insights to improve the design of military, air evacuation networks in antiaircraft threat environments. Two novel optimization problems are proposed including the 2-Leg Aeromedical Evacuation Problem (2-LAEP) and the Air Evacuation Location Routing (AELR) problem. 2-LAEP is used to find a path from an airfield to a casualty location and onward to a hospital which minimizes a combined metric of flight path length and antiaircraft threat exposure while respecting limitations on turns and wind operating limits. 2-LAEP is deterministic. AELR is used to site airfields and field hospitals. AELR minimizes fixed facility establishment costs as well as the total flight path length and threat exposure of all evacuation missions flown to satisfy demand. AELR prices out siting and assignment decisions via 2-LAEP within a two-stage, stochastic formulation. Three novel solution methods are proposed. First, a variant of the famous A* algorithm is proposed to solve 2-LAEP. We call this variant Course Alteration Tolerant (CAT) A* and prove that it converges on optimal solutions under certain conditions. Subsequently, we propose two metaheuristic hybrids to solve AELR which combine Simulated Annealing (SA) or Tabu Search (TS) with a parallel processing implementation of CAT A*. Numerical experiments are provided. CAT A* is shown to be superior to both CPLEX and classical A*. CPLEX is slow and cannot solve realistic sized 2-LAEP instances while classical A* frequently fails to find optimal paths. Our SA and TS based metaheuristic hybrids are shown to be superior to CPLEX inasmuch as CPLEX is unable to solve realistic sized AELR instances. These two solution methods seem to be comparable to each other in terms of solution quality and execution speed. Managerial insights are also identified. Techniques for the discretization of real-world battlefield situations into 2-LAEP and AELR instances are provided in an appendix.
A thesis submitted to the DeGroote School of Business and School of Graduate Studies at McMaster University.
Keywords: operations research; management science; military medicine; Shortest Path Problem (SPP); Location-Routing Problem (LRP); dynamic programming; metaheuristics; Health Service Support (HSS); optimization; mathematical modelling