The Augmented Semi-Markov System in Continuous Time

This article proposes a continuous time semi-Markov hierarchical manpower planning model that incorporates the need of the employees to attend seminars, so as to enhance their prospects, as well as the organizations' intention to avoid situations concerning unavailability in skilled personnel when needed. At large, we study a hierarchical system where the workforce demand at each time period can be met via internal mobility and two streams of recruitment; one from the outside environment and another from a supplementary auxiliary system. For the suggested model, namely the Continuous Time Augmented Semi-Markov System, we examine initially its dynamic behavior by deriving the equations reflecting the expected number of persons in each grade. In the sequel, we probe its limiting population structure and it is found that under a set of conditions this structure exists and is specified. Finally, we present a real case which demonstrates the practical motivation of the subject under study.