Discrete Time Hybrid Semi-Markov Models in Manpower Planning

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.

Semi-Markov Models for Process Mining in Smart Homes

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Effects of Prioritized Input on Human Resource Control in Departmentalized Markov Manpower Framework

“…The work of Seal ( 1945 ) is a pioneering one in the application of Markov theory in Manpower planning. Though extensions of the application of Markov chain theory in manpower planning now abound, such as in semi-Markov manpower models (McClean et al 1998 ; Yadavalli and Natarajan 2001 ), hybrid manpower models (De Feyter 2007 ; Guerry and De Feyter 2011 ; Verbeken and Guerry 2021 ), Markov manpower models remain very relevant because of their property of being comparatively simple and tractable. These properties are required in practical implementation of manpower models (Barsnet and Ellison 1998 ), and are platforms for the extensions and other new grounds in mathematical manpower modelling.…”

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