Optimizing the Purchases of Military Air-to-Ground Weapons

The US military uses modeling and simulation when determining how many air-to-ground weapons to include in its annual procurement budget. We pose the problem of aircraft weapon budgeting as a nonlinear program, and we use both analytical and numerical methods to investigate the solution's theoretical properties. We determine when heuristics are useful to reduce the dimensionality of the optimization problem. One heuristic pairs aircraft types with weapons having the least cost-to-kill when a budget constraint is binding. Another chooses pairings with the highest expected kills per sortie when sortie constraints are binding instead. Either heuristic, or a hybrid of the two, can greatly accelerate a solution by predetermining a small subset of the many available aircraft-weapon-target combinations to be employed in positive quantities. The military requirements problem is to select the set of weapons that destroy the highest-value set of targets, constrained by the number of aircraft sorties but not a procurement budget. An expected-kills-per-sortie heuristic is useful when solving that problem. However, if the available budget is too small to fully fund the military requirement, then the budget constraint drives the solution, and the least-cost-to-kill heuristic helps identify weapons to be purchased in the optimal solution.