The trade-off between the net present cost of a project and the probability to complete it on schedule

The paper considers the probability of not completing a project on schedule (or the risk of delays) and its effect on the net present cost of the project. It proposes an efficient frontier that points out to management the trade-off between low risk, early start schedules and high risk, late start schedules. Early start schedules minimize the risk of delays at the cost of early investment in project activities and material. Late start schedules delay capital outlays while increasing the risk of not competing the project on its due date. The number of feasible schedules in a real project is typically large and exact analysis of all possible schedules is difficult to perform, if not impossible. This article presents a heuristic procedure that generates an efficient frontier representing the risk of delays versus the net present cost of the project. The efficient frontier is a decision aid for the manager who has to chose the appropriate schedule for the project. Most computer packages for project management are based on CPM (especially packages for personal computers). The present heuristic procedure is designed to be used as an extension of CPM analysis. The procedure starts with the early start schedule developed by CPM and, using the computed slacks, tries to delay activities with high value-added one at a time. At each iteration a Monte-Carlo-type simulation is used to approximate the probability of not completing the project on time. This probability is stored along with the net present cost of the project. The result of the analysis is a set of points on the plane representing the probability of not completing the project on time versus the net present cost of the project. Each point corresponds to a specific schedule. Management can choose the most appropriate schedule for implementation based on its attitude towards risk and its financial policy. The heuristic procedure can be implemented easily on advanced ‘Fourth Generation’ packages for project management such as IBM’s Application System (AS) or Metier’s Artemis system. The heuristic procedure can also be implemented on personal computers by processing the output of any CPM package by the special subroutine that is developed in this study.