Application of optimal control in man power planning

Many techniques are met in the literature (see for instance Bartholomew and Forbes (Statistical Techniques for Manpower Planning. wiley, New York 1979); Gunz (Organiz. Stud. 9(4), 529–554, 1988); Becker and Huselid (Human Resour. Manage. 38, 287–301, 1999); Wagner et al. (J. Manage. Med. 14(5/6), 383–405, 2000); Harris and Ogbonna (J. Business Res. 51, 157–166, 2001); Rogg et al. (J. Manage. 27, 431–449, 2001), among others), for planning the manpower resources. However, we haven’t seen in the literature an empirical study regarding the proper application of optimal control, which considered to be the most efficient method for multi-objective programming. With this in mind, we analyse in this paper the way of applying optimal control for manpower planning. For this purpose, and in order to facilitate the presentation, we first adopted a comparatively simple dynamic system (plant), with analytical presentation of stocks and flows. Next we proceed to the formulation of an optimal control problem, aiming to achieve in the most satisfactory way some preassigned targets. These targets mainly refer to a desirable trajectory of the plant stocks over time, in order to fully satisfy the needs for human resources over the planning horizon. Finally we present a method of solution of the formulated control problem which is based on the use of the generalized inverse Lazaridis (Qual. Quan. 120, 297–306, 1986). We believe that it is very important for successful management, that the policy makers have to know the effect of their polices and to determine the optimal path of the state variables (i.e. the ones describing the system) before the realization of the plan, so as to be able to reform their strategies, reallocate the resources and arrange the infrastructure accordingly, if all these are necessary, as it can be depicted from the optimal control solution.