Step semi-Markov models and application to manpower management
Barbu, Vlad Stefan1  ; D’Amico, Guglielmo2 ; Manca, Raimondo3  ; Petroni, Filippo4
1 Universitéde Rouen, Laboratoire de Mathématiques Raphaël Salem, UMR 6085, Avenue de l’Université, BP.12, 76801 Saint-Étienne-du-Rouvray, France.
2 Dipartimento di Farmacia, Università “G. d’Annunzio” di Chieti-Pescara, via dei Vestini 31, 66100 Chieti, Italy.
3 Dipartimento MEMOTEF, Università di Roma “La Sapienza”, via del Castro Laurenziano, 9, 00161 Rome, Italy.
4 Dipartimento di Scienze Economiche ed Aziendali, Universitá di Cagliari, via Sant’Ignazio, 17, 09123 Cagliari, Italy.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 555-571

The purpose of this paper is to introduce a class of stochastic processes that we call step semi-Markov processes and to illustrate the modelling capacity of such processes in practical applications. The name of this process comes from the fact that we have a semi-Markov process and the transition between two states is done through several steps. We first introduce these models and the main quantities that characterize them. Then, we derive the recursive evolution equations for two-step semi-Markov processes. The interest of using this type of model is illustrated by means of an application in manpower planning.

DOI : 10.1051/ps/2016025
Classification : 60K15, 60K20, 90B25, 91B28
Keywords: Semi-Markov processes, manpower management, stochastic modelling

Barbu, Vlad Stefan 1 ; D’Amico, Guglielmo 2 ; Manca, Raimondo 3 ; Petroni, Filippo 4

1 Universitéde Rouen, Laboratoire de Mathématiques Raphaël Salem, UMR 6085, Avenue de l’Université, BP.12, 76801 Saint-Étienne-du-Rouvray, France.
2 Dipartimento di Farmacia, Università “G. d’Annunzio” di Chieti-Pescara, via dei Vestini 31, 66100 Chieti, Italy.
3 Dipartimento MEMOTEF, Università di Roma “La Sapienza”, via del Castro Laurenziano, 9, 00161 Rome, Italy.
4 Dipartimento di Scienze Economiche ed Aziendali, Universitá di Cagliari, via Sant’Ignazio, 17, 09123 Cagliari, Italy. 
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Barbu, Vlad Stefan; D’Amico, Guglielmo; Manca, Raimondo; Petroni, Filippo. Step semi-Markov models and application to manpower management. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 555-571. doi: 10.1051/ps/2016025

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