quantmleap

One of the scheduling tools at the project manager’s disposal is the Critical Path Method, the outcome of which would be:

1. A list of all activities required to complete the project
2. The time (duration) that each activity will take
3. The dependencies between the activities.

With the above, the longest path of planned activities can be identified, and the “critical” activities (i.e those activities whose combined duration dictate how long the duration is planned to be) are identified.

There are a number of methodological issues with the Critical Path Method, one of which is that the view used to identified the critical path and the tasks it includes is a static view, correct at a point in time, and does not take into account the likelihood of any task on the project schedule taking longer (or shorter) than initially planned.

Let’s look at the following example:

Simply viewing at this schedule, without taking into account other supporting information could be misleading. One issue that could substantially affect the accuracy of this view is the availability (or lack) of resources (see elaboration on  this issue in my earlier post “The Critical Path Does not Tell You Everything You Need to Know About Your Project Constraints“). Another factor that needs to be examined is the level of comfort, or the likelihood of achieving the planned duration.

Having examined the above schedule, would you change your view of this project given the following additional information?

The table above introduces further information regarding the Optimistic, Pessimistic and Most Likely duration for each of these tasks. It clearly demonstrates that although tasks 2 – 5 share a Most Likely Duration, the level of risk associated with each is gradually increasing, from 5 days in task1 to 9 days in task 5.

Utilizing the above added information to better understand the risk dimension associated with the schedule requires the execution of a sensitivity analysis.

Sensitivity Analysis is defined as a “Simulation analysis in which key quantitative assumptions and computations (underlying a decision, estimate, or project) are changed systematically to assess their effect on the final outcome. Employed commonly in evaluation of the overall risk or in identification of critical factors, it attempts to predict alternative outcomes of the same course of action. In comparison, contingency analysis uses qualitative assumptions to paint different scenarios. Also called what-if analysis“.

In other words, a greater insight into the risks hidden behind the project schedule can be derived by adjusting the various tasks’ durations (within their PERT parameters) and confirming, for each such variation, whether a task is included or excluded from the critical path. Performing such adjustments a large number of times would result in an indication of how many times, or in what percentage of times, did any particular task appear on the critical path. The larger the frequency, the greater the need to examine the task and put in place the mechanism to ensure that the task does not negatively deviate from its scheduled duration.

Just to wrap this up, let’s look at the schedule from two additional, extreme perspectives:

The following is a Critical Path view of the project schedule should all tasks durations happen to match the best case duration estimates:

Next is the view of the project schedule should all tasks durations happen to match the worst case duration estimates:

Performing Sensitivity Analysis on the above project would result in a result similar to the one outlined below:

What the above diagram suggests is that when running a simulation with a large number of samples (lets say 1,000 times), then Task1 will appear on the Critical Path 100%, Task4 and Task5 – 39% of the times, etc.

Wouldn’t this be useful to know?

Related posts:

1. The Critical Path does not tell you everything you need to know about your Project’s constraints
2. Monte Carlo Simulation – Project Risk Analysis Report
3. Article review – Exploring Monte Carlo Simulation Applications for Project Management
4. Monte Carlo Simulation for Dummies
5. Project Risk Management and the application of Monte Carlo Simulation