Modeling Diminishing Marginal Returns: An Application to the Aircraft Availability Model.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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The Aircraft Availability Model AAM provides the Air Force with a worldwide peacetime requirement for reparable spare parts. This research models AAM methodology as it relates to the concept of diminishing marginal returns in resource application. Three separate modeling techniques are investigated with the goal of reformulating the AAM as a mathematical programming model that provides a comparable solution and a capable tool for the conduct of sensitivity analysis. The general formulations presented here are continuous non-linear, continuous linear, and piecewise linear discretecontinuous models. Two formulations of the piecewise linear discretecontinuous model are presented. The piecewise linear model based on AAM sort values shows the dominance of an optimization routine relative to the AAM shopping list greedy heuristic. The piecewise linear model based on availability rates provides the capability to maximize the mission design series MDS availability level. It has the potential to obtain the highest possible MDS availability relative to reparable spares inventory levels. This mathematical model is discussed in complete detail as a robust platform for conducting extensive post-optimality analysis.
- Numerical Mathematics