Maintainability and attainability for discrete-time homogeneous semi-Markov models

In previous research the importance of both Markov and semi-Markov models in manpower planning is highlighted. Maintainability and attainability of personnel structures for different types of personnel strategies (i.e. under control by promotion and control by recruitment) is extensively investigated for various types of Markov models (homogeneous as well as non-homogeneous).
Semi-Markov models are extensions of Markov models that account for length of stay in the states. Less attention is paid to the study of maintainability and attainability for semi-Markov models. Although, some interesting maintainability results were obtained for non-homogeneous semi-Markov models. The current paper focuses on discrete-time homogeneous semi-Markov models, and explores concepts of maintainable and attainable personnel structures in this setting. Various types of personnel strategies are presented for which the set of maintainable and attainable structures is examined. The obtained insights can easily be converted to various application domains.