Optimal time and cost balance in project risk management

Abstract

In almost all real-life projects, activity durations are not known with certainty. Therefore, adopting a schedule that ensures the successful completion of a project on time with a high probability is critical. This often requires, starting the project activities as soon as possible, while abiding by precedence constraints, as advocated by the classical methods of CPM and PERT. However, from a cost control and financing prospective, performing an activity in early stages of a project may not be the best course of action. On the contrary, the present worth criterion advocates starting activities as late as possible, to save on financing costs. The present research is aimed at determining the optimal start time of activities in a project network while accounting for both time value of costs and the risk of scheduling delays. A mathematical program is developed in order to find the optimal starting time of each activity under different structures of the project network topology, while assuming that the activity durations approximately follow independent normal distributions. We find that the optimal delay structure advocates delaying activities at the beginning of the project. In addition, we observe that it might be optimal to delay activities that fall on the path with the longest expected duration, which are deemed “critical” in the classic CPM-PERT approach. A bi-product of our work is a new method to estimate schedule risk, PERT-X, which is found to be more accurate than the classic PERT by comparison with Monte Carlo Simulation results. PERT-X approximates the duration of the maximum of all the project paths by a Normal random variable.