An extended and tractable approach on the convergence problem of the mixed push–pull manpower model

In this paper, the asymptotic behavior of the time-homogeneous mixed push–pull manpower model is studied under the assumption that the desired stock vector and the recruitment policy are fixed over time. In the mixed push–pull manpower model, the internal mobility of a personnel system can be regulated by both pull and push transitions. Based on those characteristics, we express and examine the dynamics of the personnel system by formulating the mixed push–pull manpower model by means of particular transition matrices, which we demonstrate to have interesting properties. We show that under certain conditions the stock vector converges. An explicit analytical form for this limiting personnel stock vector is found.