On the dynamics of workforce-mix in a manpower system

Abstract

This paper focuses on a manpower system with a xed number of jobs that uses both per-
manent and temporary sta. The dynamics of workforce-mix in such a system is modelled
as an optimal control problem. The objective is to nd the most economical workforce-mix
for the manpower system, subject to the uctuations in workforce caused by wastage and the
hiring of temporary sta. The uctuations in the workforce-mix are modelled using a model similar to the Vidale-Wolfe advertising model. The solution is found by applying Pontrya-gin's principle, and a number of resulting propositions are presented along with their proofs. A real-life manpower setting is used to illustrate the utility of the model.

Key words: Manpower system, optimal control problem, Pontryagin's principle, Vidale-Wolfe model, workforce