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State Re-union Maintainability for Semi-Markov Models in Manpower Planning

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  • Brecht Verbeken

    (Vrije Universiteit Brussel)

  • Marie-Anne Guerry

    (Vrije Universiteit Brussel)

Abstract

In previous research the importance of both Markov and semi-Markov models in manpower planning is highlighted. Maintainability of population structures for different types of personnel strategies (i.e. under control by promotion and control by recruitment) were 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 duration of stay in the states. Less attention is paid to the study of maintainability for semi-Markov models. The current paper focuses on discrete-time homogeneous semi-Markov models, and explores the concept of maintainable population structures under control by recruitment. In particular, a new concept of maintainability is introduced, the so-called State Re-union maintainability (SR-maintainability). Moreover, we show that, under certain conditions, the seniority-based paths associated with the SR-maintainable structures converge. This allows to characterize the convex set of SR-maintainable structures.

Suggested Citation

  • Brecht Verbeken & Marie-Anne Guerry, 2025. "State Re-union Maintainability for Semi-Markov Models in Manpower Planning," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-21, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10174-6
    DOI: 10.1007/s11009-025-10174-6
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    References listed on IDEAS

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    1. G. S. Davies, 1973. "Structural Control in a Graded Manpower System," Management Science, INFORMS, vol. 20(1), pages 76-84, September.
    2. P.-C. G. Vassiliou & T. P. Moysiadis, 2010. "$\boldsymbol{\mathcal{G}-}$ Inhomogeneous Markov Systems of High Order," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 271-292, June.
    3. Pablo Azcue & Esther Frostig & Nora Muler, 2023. "Optimal Strategies in a Production Inventory Control Model," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-43, March.
    4. Brecht Verbeken & Marie-Anne Guerry, 2021. "Discrete Time Hybrid Semi-Markov Models in Manpower Planning," Mathematics, MDPI, vol. 9(14), pages 1-13, July.
    5. Georgiou, A. C., 1992. "Partial maintainability and control in nonhomogeneous Markov manpower systems," European Journal of Operational Research, Elsevier, vol. 62(2), pages 241-251, October.
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