A model for manpower productivity during organization growth

A mathematical model is developed that enables organization and manpower planners to quantify the inefficiencies involved in rapid buildups of organizations, such as is frequently found in the aerospace industry shortly after the award of a major contract. Consideration is given to the time required to train, indoctrinate, and familiarize new workers with their jobs and the general program aspects. Once trained, workers are assumed to be productive. If the ratio of untrained to trained workers exceeds a critical value, called the buildup threshold, then the performance of the trained workers is degraded to the extent that they are no longer 100 percent efficient until this ratio returns to a value less than the threshold. The model is sufficiently general to consider an arbitrary manpower plan with more than one peak or valley. The model outputs are functions of real time and consist of the fraction of the total labor force which is productive, the fraction of the total labor units expended for nonproductive effort, the cumulative labor costs for productive effort, and the cumulative labor cost for all effort.