A tool for managing projects: an analytic parameterization of the S-curve

The solution to a differential equation used frequently in ecology is found to reproduce the well-known S-curve seen in various aspects of project management. The solution is modified in a minor way to fit project management boundary conditions. An excellent fit of this theoretical curve to two samples of project cost data shows the utility of the formula. Numerical approximations valid under typical project conditions are utilized to produce an analytic expression that can easily generate classic project management evolution curves under a variety of conditions. The curves are normalized to two basic parameters: the total of the relevant quantity (e.g., project costs) and the duration of the project. The user can choose the steepness of the climb and the point in time at which half the total has been accumulated.