Optimization Model for Officer Retirement Extension Policies under Budget Constraints: A Constrained Markov Decision Process (CMDP) Approach

This study proposes an optimal implementation strategy for phased officer retirement extension policies to ensure the stability of military personnel structures under demographic changes. While retirement extension enables the effective utilization of experienced personnel, it also introduces constraints such as increased personnel costs and potential congestion across ranks. To address this issue, a constrained Markov decision process (CMDP) model is developed to optimize retirement policies under budget limitations. The proposed model incorporates rank-based promotion rates, separation probabilities, and personnel cost structures into the state transition dynamics, and determines optimal retirement extension policies that maximize long-term operational efficiency within budget constraints. Numerical experiments demonstrate that the CMDP-based approach outperforms simple sequential retirement extension strategies in terms of budget efficiency and personnel stability. In particular, the model contributes to reducing separation rates and strengthening the mid-career officer structure. Sensitivity analysis further reveals that the effectiveness of the policy depends on the level of budget growth, with efficient outcomes observed within a moderate range of budget expansion. The findings suggest that retirement extension policies, when optimized under budget constraints, can serve as an effective tool for sustaining a skilled and stable military workforce. This study provides a quantitative decision-support framework for future defense manpower planning.