Project crashing in the presence of general non‐linear activity time reduction costs

In this paper, we are concerned with the project crashing problem. The functional form we consider for the crashing costs is a negative‐exponential form of the amount of capital invested that captures most of the more realistic forms that have been proposed in the literature. We formulate a non‐linear optimisation model of the resulting generalised crashing problem, and develop a convex geometric programming approximation of this model. The model can be readily extended to handle situations where it is desired to determine the minimum capital investment needed to crash activities so that the total project duration does not exceed a given time length. Numerical illustrations of the approach are provided.