The trade‐off between the net present cost of a project and the probability to complete it on schedule
Authors: Shtub Avraham 
Published: October 2002

In this article we consider 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. We propose 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 completing the project on its due date.

The methodology developed in this study is aimed at strategic level decision making. At this level, decisions are based on incomplete information that calls for stochastic analysis and the introduction of uncertainty. Uncertainty in project management is introduced through stochastic activity duration and stochastic lead times of resources required for the project. The commonly used CPM analysis ignores those aspects of uncertainty. PERT analysis does consider the stochastic nature of activity durations but computes only the probability to complete the project on a given date for a single schedule.

A crucial decision at the strategic level of project management is when to schedule activities with high value‐added. The decision makers have to trade‐off the advantages of delaying such activities, thus reducing the net present cost of the project, with the disadvantages associated with increasing the probability of not completing the project on time.

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 choose the appropriate schedule for the project.

Most computer packages for project management are based on CPM (especially packages for personal computers). Our heuristic procedure is designed to be used as an extension to 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.

A simple example is used to illustrate the heuristic procedure. In the example, a project with six activities and two types of resources is analyzed. Five schedules are generated with net present cost ranging from $45,000 to $8,191,000 and the probability of not completing the project on time ranging from 0.0001 to 0.75. Our experience with a real project of 400 activities is reported as well.

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.