Schedule Risk Analysis Simplified
by
David T. Hulett, Ph.D.1
Critical Path Method Scheduling - Some Important Reservations
The critical path method (CPM) is a key tool for managing project schedules. A schedule "network" represents the project strategy or plan. CPM computes the shortest project completion duration and earliest completion date. The longest path through the network is called the "critical path." According to CPM, any delay on the critical path will delay the project.
On the one hand, CPM is traditional and well-accepted. It is essential for developing the logic of the project work and for managing the day-to-day project activities. On the other hand, the accuracy of CPM completion date forecast depends on every task taking just as long as its duration estimate indicates – in short, CPM is accurate only if everything goes according to plan. Experienced project managers realize that real projects do not often go according to plan:
- The estimates of activity durations are at best careful estimates of future work and at worst just guesses or unrealistically short, calculated by how much time you have rather than how long the work takes.
- Even if the activity durations are most likely estimates, the CPM completion date is not the most likely project completion date.
- The path identified as the "critical path" may not be the one that will be most likely to delay the project and which may need management attention.
Is there some method of analysis and planning that can improve the accuracy of our scheduling? Yes, there is, and it is schedule risk analysis.
Three Steps to a Successful Schedule Risk Analysis
The three steps to a successful risk analysis are described. They are: (1) create the CPM schedule for the project, (2) estimate the uncertainty in the activity durations with low and high ranges, and (3) perform a risk analysis of the schedule, using a Monte Carlo simulation method.
Step 1: A CPM Schedule
Assume a simple project with two activities and a finish milestone. Suppose the durations are set at 40 working days for A101 and 70 working days for A102. If this project is scheduled to start on January 2, 2000, CPM shows that this simple project will take 110 working days (40 + 70 = 110) and complete on June 2, 2000 (see Figure 1, below).
Step 2: The Activity Duration Rangers
To do a risk analysis we need to estimate duration ranges for each activity which are based on the low (optimistic) and high (pessimistic) scenarios for the work on the activity. High ranges, for instance, can be determined by examining the various things that could go wrong such as technical problems, site conditions, supplier delays, and permitting issues -- factors which are often called "risk drivers."
These duration ranges are determined by searching interviews of the project manager and the staff who made the estimates, will manage the project and are familiar with the possible problems. The ranges of pessimistic (Max Rdur) and optimistic (Min Rdur) durations for the two-activity schedule are shown in Figure 1.
Figure 1
Step 3: Simulate the Project Schedule
Once the activities' duration ranges and distributions have been determined, the schedule risk analysis can determine how risky the entire project schedule is.
- How likely are we to overrun the completion date of June 2, 2000? Is June 2 even the "most likely" date for this simple project? If not, what completion date is most likely?
- How many days are needed for a contingency to reduce the overrun risk exposure to an acceptable level?
- Which activities are the most likely to delay the project?
The most common method of determining schedule overrun risk is to simulate the project by solving (or iterating) it hundreds or thousands of times on the computer. This is called Monte Carlo simulation, and it combines the distributions of uncertain duration accurately.
Suppose that the risk analyst determines that 2,500 iterations will be sufficient for the accuracy needed. The result of that simulation is a cumulative likelihood distribution that represents the likelihood of the project completing on or before each possible date. This distribution is shown in Figure 2 below:
Figure 2
From the risk analysis we can see:
- The CPM completion date of June 2, 2000 is between 10% and 15% likely to be adequate for this simple project. Placing confidence in completion by June 2 is very likely to get the contractor and customer in trouble.
- The most likely completion date is close to June 19, not June 2 as predicted by CPM. The common sense notion, that adding "most likely" durations along a critical path will result in the most likely project completion date, is simply wrong, in all cases.
- The average completion date is June 23, 2000. If this simple project were done 100 times, its average completion would be about a 3-week overrun of the CPM duration, providing for the holidays.
- The results show that July 11, 2000 has an 80% likelihood of success. This is a level of protection from overruns that might be required for a conservative contractor or owner/customer . Hence, a 6-week contingency is needed to reduce the risk of overrun to an acceptable level for this conservative company.
The CPM project end-date of June 2 is highly optimistic. Any owner, customer or contractor who agrees to that date is in trouble now on this project. Without a risk analysis, the existence or degree of trouble is unknown.
Risk Analysis Topics - the Merge Bias
This is only a 2-activity project. Real life projects are subject to more risk than this.
Most projects have activities planned simultaneously along parallel paths. At the end of the project, and often at important internal milestones, these paths converge. Examples include; (a) piping, duct, framing and electrical work must be completed before an inspection can be conducted, or (b) several components that must be finished before systems integration and testing can be done. Most project overrun risk occurs at path convergence (or merge) points because projects can be delayed because a delay on any one of the paths will delay the work. This is the "merge bias" at work.
To see the merge bias, consider expanding the simple schedule above to a 2-path project where the second path is exactly the same as the one in Figure 1 above. Clearly, CPM analysis shows that this project, too, will finish at the same time as the one-path schedule does, June 2, 2000. When we analyze the risk of this two-path schedule, however, we see that it is riskier because either path can cause an overrun. Compare Figure 3 results to those in Figure 2 above.
Figure 3
- The average completion date is now July 6, 2000, not June 23.
- The CPM date of June 2, 2000 is now less than 5% likely, not 10 or 15%.
- The 80th percentile is now July 20, 2000 rather than July 11.
These results reflect the working of the merge bias when parallel paths converge.
The Highest Risk Path
The highest risk path (sometimes called the risk-critical path) is the path through the network that has the greatest likelihood of delaying the project. In CPM this is confidently identified as the critical path. When activity durations are uncertain, the very concept of critical path is murky. Risk analysis identifies the paths that determine the project duration in each iteration, and computes the relative likelihood of any activity being on that path for the overall simulation. Often, a non-critical path with high risk is the path that has the greatest likelihood of overrun. This is important information for the project manager.
Summary
This paper has shown that a simple project can be in serious trouble of not making the CPM completion date. It follows that real projects, which are infinitely more complex, are even more likely to be infeasible because they have more parallel paths and merge points. A risk analysis identifies and quantifies the difficulties faced by the project manager.
There is risk in every project. Ignoring risk doesn't make it go away. This three-step risk analysis process can and must be conducted for every important project.
- 1© 1999 by David Hulett. The author is Principal, Hulett & Associates, Project Management Consultants of Los Angeles, CA. Hulett & Associates can be reached at (310) 476-7699 or info@projectrisk.com.
- This is a condensation adapted from an article that appeared in the July 1996 Project Management Network of the Project Management Institute, Upper Darby, PA, a worldwide organization advancing the state-of-the art in project management (610) 734-3330
For more information:
David T. Hulett, Ph.D.
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