On the equilibrium personnel structure in the presence of vertical and horizontal mobility via multivariate Markov chains

The present paper employs the Multivariate Homogeneous Markov System (MHMS) in the context of Markov manpower planning modelling. The system is regulated by an embedded multivariate Markov process that allows us to distinguish employees’ mobility patterns that take place either within or among the existing divisions (departments) of an organization. The motivation behind this step arises from the generalization of univariate Markov manpower planning models in which the organization is considered a single (probably hierarchical) group and from the fact that departmental mobility is actually common in most realistic establishments. The first part of the paper presents the functional relations of the MHMS governing intra/inter‐departmental transitions. Using these functional forms, we proceed by studying the system’s equilibrium behaviour. This asymptotic analysis reveals the inherent tendencies of the system to reach the limiting structures of specific forms and properties under conditions imposed in the long run.