Estimating project S-curves using polynomial function and neural networks

The S-curve is a graphical representation of a construction project's cumulative progress from start to finish. While S-curves for project control during construction should be estimated analytically based on a schedule of activity times, empirical estimation methods using various mathematical S-curve formulas have been developed for initial planning at predesign stages, with the mean for past similar projects often used as the basis of prediction. In an attempt to make an improvement, a succinct cubic polynomial function for generalizing S-curves is proposed and a comparison with existing formulas shows its advantages of accuracy and simplicity. Based on an analysis of the attributes and actual progress of 101 projects, four factors, i.e., contract amount, duration, type of work, and location, are then used as the inputs of a model developed for estimating S-curves as represented by the polynomial parameters. For model development, it is proposed to use neural networks for their ability to perform complex nonlinear mapping. The neural network model is compared with statistical models with respect to modeling and testing accuracy. The results show that the presented methodology can achieve error reduction consistently, thereby being potentially useful for owners and contractors in early financial planning and checking schedule-based estimates.