Simulation-Optimization, Markov Chain and Graph Coloring Approaches to Military Manpower Modeling and Deployment Sourcing

Zais, Mark M.

Graduate Thesis Or Dissertation

Simulation-Optimization, Markov Chain and Graph Coloring Approaches to Military Manpower Modeling and Deployment Sourcing Public Deposited

Analytics

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Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/x059c769z

Abstract

The Army manpower system is a integration of numerous elements that can be independently modeled. Identifying and closing gaps in modeling research can reduce workforce inefficiencies and costs. Military manpower models are predominantly focused on forecasting behavior and inventory within given demand requirements. Moreover, research directed towards predicting behavior is almost entirely disaggregated by pecuniary and non-pecuniary goals with disproportionate effort devoted to modeling the external factors that effect such behavior. This thesis proposes modeling approaches to improve the management capabilities of the Army's manpower system. First, we consider a simulation-optimization approach to estimating workforce requirements examines the capabilities and limitations of Monte Carlo simulation and optimization methods within the context of workforce demand forecasting, modeling and planning. Specifically, we focus on these methods as a viable improvement for aligning strategic goals with workforce requirements. A general model is presented for estimating workforce requirements given uncertain demand. Using a real-world data example, we assess the benefits of this methodology to determine an optimal mix of workforce skills while providing the flexibility and robustness to incorporate uncertainty, assess risk and improve effectiveness of the workforce planning process. Second, we address the critical stay-or-leave decision associated with military retention. Personnel retention is one of the most significant challenges faced by the U.S. Army. Central to the problem is understanding the incentives of the stay-or-leave decision for military personnel. Using three years of data from the U.S. Department of Defense, we construct and estimate a Markov chain model of military personnel. Unlike traditional classification approaches, such as logistical regression models, the Markov chain model allows us to describe military personnel dynamics over time and answer a number of managerially relevant questions. Building on the Markov chain model, we construct a finite horizon stochastic dynamic programming model to study the monetary incentives of stay-or-leave decisions. The dynamic programming model computes the expected payoff of staying versus leaving at different stages of the career of military personnel, depending on employment opportunities in the civilian sector. We show that the stay-or-leave decisions from the dynamic programming model possess surprisingly strong predictive power, without requiring personal characteristics that are typically employed in classification approaches. Furthermore, the results of the dynamic programming model can be used as input in classification methods and lead to more accurate predictions. Overall, our work presents an interesting alternative to classification methods and paves the way for further investigations on personnel retention incentives. Finally, a graph coloring approach to deployment sourcing addresses one of the external factors of personnel inventory behavior, deployments. The configuration of persistent unit deployments has the ability to affect everything from individual perceptions of service palatability to operational effectiveness. There is little evidence to suggest any analytical underpinnings to U.S. Army deployment scheduling and unit assignment patterns. This paper shows that the deployment scheduling and unit assignment (DSUA) problem can be formulated as an interval graph such that modifications to traditional graph coloring algorithms provide an efficient mechanism for dealing with multiple objectives.

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