ABSTRACT

This thesis considered the theoretical aspects of a network of personnel flow in a fixed size hierarchically structured manpower systems modelled within the framework of Markov chains. Two major problems arising in the system were studied: the embedding problem and the intra/intergrade mobility problem. In the first instance, conditions for which a stochastic matrix can have a stochastic root within the context of discrete-time Markov chains were the main focus. In the second case, the expected evolution of the system over time where individuals can move within (horizontally) and between (vertically) grades is examined.

Under the condition that recruitment is done to replace outgoing flows, the Markov chain describing the system is constructed. The thesis takes up the embeddability problem in the graded manpower system and examines it in relation to the z-transform of stochastic matrices. The method constructs a stochastic matrix that is made up of a limiting-state probability matrix and a partial sum of transient matrices. To account for intra/intergrade mobility in the system, the grade levels were unbundled into heterogeneous sizes and a first-order difference equation was used to unify the stocks and flows in the system.

 Results showed that the stochastic matrix can have a stochastic root, if it satisfies certain embeddability conditions. The study also revealed that as long as the Markov chain describing the system is stochastic, the system would remain finite and bounded. A case in a university comprising academic staff was studied and the structure of the system was extrapolated. It was found that the fixed size policy would result to a bottom-heavy structure.