Vol.:(0123456789) Operational Research https://doi.org/10.1007/s12351-018-0431-0 1 3 ORIGINAL PAPER A new continuous time optimal control model for manpower planning with promotion from inside the system Alireza Pooya 1  · Morteza Pakdaman 2 Received: 23 July 2017 / Revised: 18 August 2018 / Accepted: 26 September 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract 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 of, 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. Keywords Optimal control problem · Linear quadratic optimal control · Manpower planning · Human resource planning 1 Introduction Manpower planning is one of important tasks of decision makers to attain the pre- determined goals of organizations. The aim of organizations is to minimize their cost while identifying the necessary level of human resources for current and future state of the organization. The manpower planning should serve the organization to This work was supported in part by: Research Deputy of Ferdowsi University of Mashhad, under Grant No. 42741 (dated February 8, 2017) * Alireza Pooya alirezapooya@um.ac.ir Morteza Pakdaman pakdaman.m@gmail.com 1 Department of Management, Ferdowsi University of Mashhad, Mashhad, Iran 2 Climatological Research Institute, Mashhad, Iran