Abstract
A new mathematical model on human resources divided employees into two compartments, namely, fresher and expert employees, has been designed and analyzed. A system of ordinary nonlinear differential equations has three state variables including vacancies. This model describes the dynamics of the number of fresher employees and expert employees as well as vacancies and shows the impacts of training programs and benefits of provided facilities for employees. The equilibria of this proposed model are determined, and its stability at these points is checked. Moreover, characteristics of state variables with respect to parameters have been discussed. Using two optimal control variables, this study finds the maximum number of experts including the minimum cost of provided facilities as well as the training program based on Pontryagin’s maximum principle.
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