A Distributed Parameter Cohort Personnel Planning Model That Uses Cross-Sectional Data

The two types of mathematical manpower planning models that appear in the literature involve either longitudinal or cross-sectional formulations. Despite the high degree of realism achieved, the use of longitudinal models is limited because the implementation requires the knowledge of a large amount of historical personnel data that is often unavailable. The value of cross-sectional models requiring a minimal amount of data is diminished due to (1) the difficulty in transferring cross-sectional results into cohort information, and (2) an assumption implicit in the structure of these models stating that the movement of an individual from one grade in the organization to another is independent of that person's organizational age. In this paper, we present a cohort (longitudinal) personnel planning model solved using distributed parameter optimal control theory that requires only cross-sectional data. We derive the optimal hiring, promotion, separation and retirement policies of an organization as functions of time and a person's organizational age and grade. In response to changing goal levels of manpower, we observe changes in the optimal policies and their subsequent effect on the career paths of cohort groups over time.