IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i14p1681-d596018.html
   My bibliography  Save this article

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

Author

Listed:
  • Brecht Verbeken

    (Department of Business Technology and Operations, Vrije Universiteit Brussel, Pleinlaan, 2, 1050 Brussels, Belgium)

  • Marie-Anne Guerry

    (Department of Business Technology and Operations, Vrije Universiteit Brussel, Pleinlaan, 2, 1050 Brussels, Belgium)

Abstract

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of stay effects. An overview of differences and possible obstacles regarding the use of Markov and semi-Markov models in manpower planning was first given by Valliant and Milkovich (1977). We further elaborate on their insights and introduce hybrid semi-Markov models for open systems with transition-dependent sojourn time distributions. Hybrid semi-Markov models aim to reduce model complexity in terms of the number of parameters to be estimated by only taking into account duration of stay effects for those transitions for which it is useful. Prediction equations for the stock vector are derived and discussed. Furthermore, the insights are illustrated and discussed based on a real world personnel dataset. The hybrid semi-Markov model is compared with the Markov and the semi-Markov models by diverse model selection criteria.

Suggested Citation

  • Brecht Verbeken & Marie-Anne Guerry, 2021. "Discrete Time Hybrid Semi-Markov Models in Manpower Planning," Mathematics, MDPI, vol. 9(14), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1681-:d:596018
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/14/1681/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/14/1681/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. S. I. McClean & J. O. Gribbin, 1987. "Estimation for incomplete manpower data," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 3(1), pages 13-25.
    2. Akaninyene Udo Udom & Ukobong Gregory Ebedoro, 2021. "On multinomial hidden Markov model for hierarchical manpower systems," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(6), pages 1370-1386, March.
    3. Sally McClean & Owen Gribbin, 1991. "A non‐parametric competing risks model for manpower planning," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 7(4), pages 327-341, December.
    4. Chiara Corini & Guglielmo D'Amico & Filippo Petroni & Flavio Prattico & Raimondo Manca, 2015. "Tornadoes and related damage costs: statistical modeling with a semi-Markov approach," Papers 1503.05127, arXiv.org.
    5. Sally McClean & Erin Montgomery & Fidelis Ugwuowo, 1997. "Non‐homogeneous continuous‐time Markov and semi‐Markov manpower models," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(3‐4), pages 191-198, September.
    6. Bickenbach, Frank & Bode, Eckhardt, 2001. "Markov or not Markov - this should be a question," Kiel Working Papers 1086, Kiel Institute for the World Economy (IfW Kiel).
    7. G. D'Amico & F. Petroni & F. Prattico, 2013. "Semi-Markov Models in High Frequency Finance: A Review," Papers 1312.3894, arXiv.org.
    8. Dimitriou, V.A. & Georgiou, A.C. & Tsantas, N., 2013. "The multivariate non-homogeneous Markov manpower system in a departmental mobility framework," European Journal of Operational Research, Elsevier, vol. 228(1), pages 112-121.
    9. Guglielmo D'Amico & Filippo Petroni & Flavio Prattico, 2013. "Wind speed modeled as an indexed semi‐Markov process," Environmetrics, John Wiley & Sons, Ltd., vol. 24(6), pages 367-376, September.
    10. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2010. "Initial and Final Backward and Forward Discrete Time Non-homogeneous Semi-Markov Credit Risk Models," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 215-225, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mark Kiermayer & Christian Wei{ss}, 2022. "Neural calibration of hidden inhomogeneous Markov chains -- Information decompression in life insurance," Papers 2201.02397, arXiv.org.
    2. E. O. Ossai & M. S. Madukaife & A. U. Udom & U. C. Nduka & T. E. Ugah, 2023. "Effects of Prioritized Input on Human Resource Control in Departmentalized Markov Manpower Framework," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-19, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. P.-C.G. Vassiliou, 2020. "Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk," Mathematics, MDPI, vol. 9(1), pages 1-27, December.
    2. Hunt, Julien & Devolder, Pierre, 2011. "Semi Markov regime switching interest rate models and minimal entropy measure," LIDAM Discussion Papers ISBA 2011010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Vlad Stefan Barbu & Guglielmo D’Amico & Thomas Gkelsinis, 2021. "Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    4. Nilsson, Isabelle & Delmelle, Elizabeth, 2018. "Transit investments and neighborhood change: On the likelihood of change," Journal of Transport Geography, Elsevier, vol. 66(C), pages 167-179.
    5. Ambach, Daniel & Schmid, Wolfgang, 2015. "Periodic and long range dependent models for high frequency wind speed data," Energy, Elsevier, vol. 82(C), pages 277-293.
    6. Hunt, Julien & Devolder, Pierre, 2011. "Semi-Markov regime switching interest rate models and minimal entropy measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3767-3781.
    7. Andreas C. Georgiou & Alexandra Papadopoulou & Pavlos Kolias & Haris Palikrousis & Evanthia Farmakioti, 2021. "On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains," Mathematics, MDPI, vol. 9(15), pages 1-17, July.
    8. Santiago Rodriguez Feijoo & Alejandro Rodriguez Caro & Carlos Gonzalez Correa, 2004. "An Empirical Study of the Purchasing Power Parity in the European Union," ERSA conference papers ersa04p369, European Regional Science Association.
    9. Eckey, Hans-Friedrich & Türck, Matthias, 2005. "Convergence of EU-regions: A literature report," Volkswirtschaftliche Diskussionsbeiträge 80, University of Kassel, Faculty of Economics and Management.
    10. D׳Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2015. "Reliability measures for indexed semi-Markov chains applied to wind energy production," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 170-177.
    11. Sabino da Silva Porto Junior & Eduardo Pontual Ribeiro, 2003. "Dinâmica Espacial da Renda Per capita e Crescimento Entre os Municípios da Região Nordeste do Brasil - uma Análise Markoviana," Anais do XXXI Encontro Nacional de Economia [Proceedings of the 31st Brazilian Economics Meeting] e54, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    12. Yousif Alyousifi & Kamarulzaman Ibrahim & Mahmod Othamn & Wan Zawiah Wan Zin & Nicolas Vergne & Abdullah Al-Yaari, 2022. "Bayesian Information Criterion for Fitting the Optimum Order of Markov Chain Models: Methodology and Application to Air Pollution Data," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    13. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2011. "Discrete Time Non-Homogeneous Semi-Markov Reliability Transition Credit Risk Models and the Default Distribution Functions," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 465-481, November.
    14. Puneet Pasricha & Dharmaraja Selvamuthu & Guglielmo D’Amico & Raimondo Manca, 2020. "Portfolio optimization of credit risky bonds: a semi-Markov process approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-14, December.
    15. Zier, Patrick, 2013. "Econometric impact assessment of the Common Agricultural Policy in East German agriculture," Studies on the Agricultural and Food Sector in Transition Economies, Leibniz Institute of Agricultural Development in Transition Economies (IAMO), volume 71, number 71.
    16. Maria Symeonaki, 2015. "Theory of fuzzy non homogeneous Markov systems with fuzzy states," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(6), pages 2369-2385, November.
    17. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2019. "Risk Management of Pension Fund: A Model for Salary Evolution," IJFS, MDPI, vol. 7(3), pages 1-17, August.
    18. Nikolaos Stavropoulos & Alexandra Papadopoulou & Pavlos Kolias, 2021. "Evaluating the Efficiency of Off-Ball Screens in Elite Basketball Teams via Second-Order Markov Modelling," Mathematics, MDPI, vol. 9(16), pages 1-13, August.
    19. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2017. "Insuring wind energy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 542-553.
    20. Guglielmo D'Amico & Raimondo Manca & Giovanni Salvi, 2011. "Bivariate Semi-Markov Process for Counterparty Credit Risk," Papers 1112.0226, arXiv.org, revised Oct 2012.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1681-:d:596018. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.