Step semi-Markov models and application to manpower management

¹ Universitéde Rouen, Laboratoire de Mathématiques Raphaël Salem, UMR 6085, Avenue de l’Université, BP.12, 76801 Saint-Étienne-du-Rouvray, France.
barbu@univ-rouen.fr
² Dipartimento di Farmacia, Università “G. d’Annunzio” di Chieti-Pescara, via dei Vestini 31, 66100 Chieti, Italy.
g.damico@unich.it
³ Dipartimento MEMOTEF, Università di Roma “La Sapienza”, via del Castro Laurenziano, 9, 00161 Rome, Italy.
raimondo.manca@uniroma1.it
⁴ Dipartimento di Scienze Economiche ed Aziendali, Universitá di Cagliari, via Sant’Ignazio, 17, 09123 Cagliari, Italy.
fpetroni@unica.it

Received: 10 February 2016
Revised: 22 August 2016
Accepted: 20 October 2016

Abstract

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.