Simulating and Optimizing: Military Manpower Modeling and Mountain Range Options

Abstract

In this dissertation we employ two different optimization methodologies, dynamic programming and linear programming, and stochastic simulation. The first two essays are drawn from military manpower modeling and the last is an application in finance. First, we investigate two different models to explore the military manpower system. The first model describes the optimal retirement behavior for an Army officer from any point in their career. We address the optimal retirement policies for Army officers, incorporating the current retirement system, pay tables, and Army promotion opportunities. We find that the optimal policy for taste-neutral Lieutenant Colonels is to retire at 20 years. We demonstrate the value and importance of promotion signals regarding the promotion distribution to Colonel. Signaling an increased promotion opportunity from 50% to 75% for the most competitive officers switches their optimal policy at twenty years to continuing to serve and competing for promotion to Colonel. The second essay explores the attainability and sustainability of Army force profiles. We propose a new network structure that incorporates both rank and years in grade to combine cohort, rank, and specialty modeling without falling into the common pitfalls of small cell size and uncontrollable end effects. This is the first implementation of specialty modeling in a manpower model for U.S. Army officers. Previous specialty models of the U.S. Army manpower system have isolated accession planning for Second Lieutenants and the Career Field Designation process for Majors, but this is the first integration of rank and specialty modeling over the entire officer's career and development of an optimal force profile. The last application is drawn from financial engineering and explores several exotic derivatives that are collectively known Mountain Range options, employing Monte Carlo simulation to price these options and developing gradient estimates to study the sensitivities to underlying parameters, known as "the Greeks". We find that IPA and LR/SF methods are efficient methods of gradient estimation for Mountain Range products at a considerably reduced computation cost compared with the commonly used finite difference methods.