Optimal control of promotion and recruitment in a hierarchically graded manpower system

The paper is concerned with the application of optimal control to manpower systems which are hierarchically well-defined according to grade and length of service, such as public or military organizations. A discrete bilinear model is ' developed for the manpower system with promotion and recruitment being the control variables. The decision criteria are to provide consistent promotion opportunity to the staff, to achieve the desired manpower structure, and to maintain a stationary training capacity during the planning horizon. Necessary conditions are derived by using the discrete maximum principle, and solved numerically for an example. To take into account variations in decision criteria, sensitivity analysis is considered and the new set of necessary conditions of variations which implies the attainability of a desirable manpower system.