A new continuous time optimal control model for manpower planning with promotion from inside the system

The aim of this paper is to face the manpower planning problem from a continuous time optimal control perspective. A new continuous-time manpower planning model is proposed in which the promotions occur inside the system. The proposed model contains four main sections: applicants, newcomers, experienced employees and supervisors (or managers). Each of these sections has a target value which we try to attain them by applying appropriate control variables, such as lay off, degradation, promotion and retirement. To attain the targets, we formulated an optimal control problem using a linear system transition equation with a quadratic cost functional. Finally, the proposed model is applied for a real-world organization as a case study.