Graphical models for manpower planning

Abstract

A work-force planning model is developed for minimizing the costs of standard wages, over-time wages, hiring and firing. The optimal work-force size and hiring/firing plan are found by plotting a labour requirement curve and calculating the change in cost due to infinitesimal changes in work-force size. Simple optimality criteria are derived by determining when the change in cost equals zero. Based on the model's assumptions, the following planning principles are identified: (1) Over-time and under-time should only be used during periods when the work-force size is not changing. (2) If work-force size is kept constant, the proportion of time in which over-time is used should equal 1/P, where P is the ratio of the over-time wage rate to the standard wage rate. (3) Cost changes gradually when the work-force size is either made larger or smaller than the optimum. Therefore, a wide range of work-force sizes yields costs that are close to the optimum.