Hidden Semi-markov Model Formulation for Hierarchical Manpower System Planning

While various models in the Markov family have been applied to manpower system analysis, these models typically overlook the distribution of durations spent in unobservable (hidden) states within the manpower system. This study introduces a hidden semi-Markov model (HSMM) framework tailored for manpower system analysis, with a focus on incorporating the random durations of stay in hidden states. By employing the expectation-maximization (EM) algorithm, key model parameters, including the probabilities of employee transitions between states, emission probabilities, and the duration distributions for each state are estimated. The proposed method is validated using academic manpower data from a Polytechnic system in Nigeria. The results demonstrate the effectiveness of the model in capturing the dynamics of manpower transitions, offering valuable insights for improving workforce planning in hierarchical manpower system.