Practical military applications of timetabling, path planning, and time-varying networks for maximizing mission success and minimizing risk

Abstract

This dissertation consists of three papers in various stages of publication. The first paper, "Optimal Course Scheduling for United States Air Force Academy Cadets" is currently in the final stage of review by the journal Interfaces. The paper presents a mixed integer program that considers faculty preferences along with cadet military, athletic, and academic requirements for on-time commissioning. The model is developed as part of an iterative process between faculty and the registrar to build course timetables and student schedules that honor the limited university resources and manpower. The second paper, "Minimum-Risk Routing Through a Mapped Minefield," has been submitted and is currently under review by Networks. We build a "threat-additive" approach to measuring the risk incurred by a ship navigating a naval minefield. We employ this approach, both as an integer program and as an A* search, to identify minimum-risk paths that may not be found by traditional "edge-additive" models. The last paper, "Navigating Free-Floating Minefields via Time-Evolving Voronoi Graphs," is ready for submission pending journal-specific formatting. We use environmental data to generate Voronoi graphs representing static "snapshots" of a free-floating minefield over time. Using these snapshots, we build a time-varying graph through which parametrically defined minimum-risk journeys can be found.