Steady State Conditions in Tractable Markov Manpower Model for an Extended Manpower System

In this work, a formulation of manpower structure in discrete-time homogeneous Markov model is done for a multilevel manpower system. The structure of the manpower system is first extended in a departmentalized framework and the features of the extended structure utilized to create a scenario of personnel membership in three classes: the active, non-active and external classes. This allows for the inclusion of different units of the system in the model. Specifically, a pool of members in absorbing states with respect to intra-class transitions is included, which forms a second channel of recruitment. The first channel of recruitment is from the external class and all recruits go to the active class. All states of the active class are non-absorbing and give rise to various intra-class and inter-class transitions. Different probability matrices that form the main components of the Markov manpower model are constructed from probabilities of these transitions. One-step steady state condition on the manpower structure is considered, based on the formulated model, and established to be invariant with respect to varying proportion of recruits into the system.