Introduction, analysis and asymptotic behavior of a multi-level manpower planning model in a continuous time setting under potential department contraction

A mathematical model in a multi-level manpower planning setting is developed and analyzed incorporating the divisions of an organization’s personnel into several homogeneous groups. The proposed framework builds upon recent research to develop, via the continuous time scale, a departmental model encompassing employees flows within departments (intra-departmental transitions), as well as transfers among departments (inter-departmental transitions). Management-wise, this is a common practice under certain conditions as in restructuring and rightsizing ventures both in private industries and in the public sector. After establishing the baseline differential equations of the system, an investigation follows regarding the system’s limiting behavior integrating the concept of department contraction which can be seen as an indirect and mild control that can be exercised on the manpower system. It is proved that under a set of conditions, the system’s limiting structure exists and is specified. The aforementioned asymptotic analysis can be utilized to predict, in the long run, future stock structures of departments and thus, in the case where these structures diverge from the desired ones, identify departments that could be considered as candidates for probable rightsizing or mergers. The paper concludes with a numerical illustration and some concluding remarks.