Optimizing the U.S. Marine Corps' Selective Reenlisted Bonus program for the career force retention

Abstract

The Marine Corps uses its Selective Reenlisted Bonus (SRB) Program to influence Marines to reenlist for a designated term into certain Military Occupational Specialties (MOSs) in order to reach planned manpower goals. The bonus amount is determined by selecting an "SRB multiplier" for each combination of MOS and Zone ("MOSZ"). ("Zone" corresponds to length of service.) A higher multiplier means a larger bonus and leads to a higher percentage of Marines reenlisting. That percentage, predicted by an existing forecasting model, is assumed exact here. The "SRB multiplier model" assigns multipliers to minimize a sum of weighted squared deviations from MOSZ targets subject to a budget constraint. This model is implemented as a generalized assignment problem, and solved approximately on a personal computer using Lagrangian relaxation and a secondary heuristic. (The algorithm is programmed in Visual Basic for Applications and has an Excel interface.) Data for FY04 shows 491 bonus-eligible MOSZs. With up to 11 possible multiplier values, this yields a model with 5,401 0-1 variables and 491 constraints. A solution within 0.0018% of optimality is reached in 1.4 seconds on 1.58 GHz personal computer. Standard integer-programming software verifies the correctness of the solution.