The probabilistic multiple-travelling-salesmen facility-location problem: Space-filling curves and asymptotic Euclidean analysis

All of us need to make decision in uncertainty, particularly regarding the demands that are placed upon our day-to-day operations. The operations have to be executed in real time, and long-term plans have to be made. In the defense community, we face such issues as base closures and fleet requirements to sustain a required mission. When locating the base for a fleet of flight-inspection aircraft, Yupo Chan and David Merrill show how some analysts in the US Air Force went through these decisions. While flight-inspection requirements vary from day to day, the authors offer a robust analysis procedure that can respond to these stochastic demands. Furthermore, the same analysis procedure, when carried out over a sufficient lengthy period of time (such as a year), can suggest basing and fleet size alternatives. Best of all, the procedure can be executed in the field with minimal computational requirements. It offers a fast solution to a highly taxing technical problem in Operations Research, while guaranteeing an error bound to the ‘quick solution’ (a ‘75 percent solution’). The model reflects a current trend in combinatorial optimization, wherein the best of heuristics with analytical formulation are combined in a single model.