Optimizing the Distribution of United States Army Officers

Abstract

The U.S. Army distributes its 51,000 competitive category officers among manning targets specified by location, rank and skill that change over time in response to changing requirements. The officer inventory also changes over time and does not exactly match the manning target requirements. The Army responds to imbalances by redistributing officers in order to provide each location with the minimum required officers while minimizing the number of unfilled targets and excess officers at each location. This thesis focuses on branch officers, branch targets and generalist targets with ranks from Branch Qualified Captain to Colonel. Using data provided by the Army, we formulate an integer programming model called DISTRIBUTOR. When DISTRIBUTOR allows all officers in the inventory to move, it finds only 340 unfilled targets but this requires 4,688 or 28% of the inventory to move. We reduce the number of moves by using DISTRIBUTOR in two sequential steps. The first step optimally distributes officers at each location and identifies the excess officers and unfilled targets at each location. The second step takes the excess officers and distributes them to unfilled targets at other locations. The two-step leaves only 346 targets unfilled (6 more) but requires only 1,373 or 8% of the inventory to move. By allowing rank substitution DISTRIBUTOR can reduce the unfilled targets to 70.