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

Abstract

The purpose of this thesis is to develope mathematical tools for optimal control of promotion and recruitment of a manpower system which is well defined according to grade and length of service such as public or military organization. The decision criteria are to achieve the desired structure, to maintain consistent promotion opportunity to staffs, and to keep stationary training capacity during a finite planning horizon. Two models for manpower planning are developed; one is a deterministic optimal control model, and the other is a stochastic optimal control model. In addition to the modelling, sensitivity analysis is studied for the case of not-too-large variations in parameter of the models. The decision process for manpower planning of the manpower system is nonlinear and dynamic. Considering these characteristics of the manpower system, deterministic optimal control model is formulated and solved first. The performance index of the model is a quadratic penalty functional reflecting the importance of the decision criteria. The set of optimality conditions is a two point boundary value problem which has been solved by the steepest descent method. Secondly, the extended model of the deterministic optimal control model is developed by introducing noises (uncertainty) of white Gaussian process caused wastage in the manpower system. The stochastic optimal control model can not be solved directly. Using the property of white Gaussian noise process, the model is converted into deterministic equivalent model. A numerical example is also illustrated for the applicability of the model. Finally, sensitivity analysis is performed to obtain a new optimal solution efficiently for the cases of infinitesimal changes in parameters of the manpower system. The set of the sensivity functions derived through variational approach is another set of two point boundary value problem, which can be solved numerically. The results of the illustrative examples suggest that this meth...