Sizing Schedule Margin with Monte Carlo Simulation

I encountered a question a few weeks back about the tolerance to schedule risk and how to model the variances in the schedules behaviors to reveal the risk of showing up on time.

Tolerance is usually defined as being an allowed variance from a set standard. Just about every profession has some tolerance or ranges of tolerance. For example, buildings are designed to standards that allow certain deflections of floors (Deflection of l/360 is one common tolerance for beam design). The floor can bend by that amount before it is considered a problem.

Projects also have certain tolerances. How firmly fixed is the end date of your project? Is there any leeway one way or the other? If there isn't, there should be. The real question is how to determine the appropriate tolerance and convey it to someone who needs to be more informed about the project than you are. There are people whom you give a date, and that date becomes the single acceptable value. They implicitly turn your "plus or minus" into "minus" and allow no plus. This means that you have to adjust your target so that even if you reach the limit of your tolerance, you are within the tolerances set by others.

There are a few ways to do this. The theory of Constraints does this with a project buffer. A number of vendors have determined rules of thumb for the sizing of these buffers. The problem with them is that they are just rules of thumb. It takes a few projects to determine the real size of the project and the team.

Another approach is probabilistic scheduling and simulation. In this approach, you build a schedule model, and instead of a fixed duration for each task, you enter a probability distribution. Then the schedule is calculated based on a large number of random samples. The result is a probability distribution for the completion of your project. If you are successful at this, it gives you a tool that you can use to set a tolerance that you have a high probability of meeting or exceeding.

Here's how you do it:

1. Build the plan (Integrated Master Schedule - IMS) from the top down. Starting with the Program Events (PE) - maturity assessment points. The Significant Accomplishments identified as "entry criteria" for the PE. Define the Accomplishment Criteria (AC) for the tasks that perform the work that delivers the SAs in support of the PEs. This results in a vertically integrated plan. A plan that defines all the work needed to have the project arrive at a known point along its maturity path to completion.
2. Make the horizontal connections between ACs and other ACs or ACs and Tasks. These connections define the program "flow" for work completion, while the vertical connections define the "flow" of product maturity.
3. Next, identify the risk buy-down activities. This is work done to reduce risk in the technical or programmatic aspects of the project. These tasks are explicitly identified.
4. Using a Monte Carlo Simulation (MCS) tool - Risky Project, Risk+, @Risk for Project, PERTMaster - construct a probabilistic estimate of the completion of the maturity assessment points. Confirm that the 80% confidence points on the CDF - "there is an 80% chance that the task will complete on or before this date" - meet the project's needs.
5. Add buffer(s) before high to moderate-risk tasks, collection points, or milestones that bring the deterministic schedule to the customer's desired date. This deterministic date then includes the "buffer" or margin.
6. Set these buffer or margin tasks to zero (0) duration and rerun the Monte Carlo Simulation to confirm that the 80% confidence date still matches.

There are several approaches to the probabilistic duration.

1. Get three-point estimates from historical data or subject matter experts.
2. Get variance values from historical data or subject matter experts.
3. In both cases, confirm that the three-point estimates match some probability distribution - Triangle or BetaPERT are useful.
4. Confirm that the three-point estimates are either 0/100 estimates - that is, they are the 0% or the 100% points in the PDF or they are the 10/90 points - the 10% or 90% points. The 10/90 is better because they represent a better narrative of the estimate

• 10% says - when repeated 10 times under the same conditions, this task completes 1 out of 10 times on or before this duration or date
• 90% says - when repeated 10 times under the same conditions, this task completes 9 out of 10 times on or before this date or duration

With this three-point information, the MSC can be run (Risk+ assumes 0/100, and @Risk can be used with 10/90).

Using an MSC simulator is a nice start at the topic, something to get a feel for the approach. For an IMS with 8,000 activities, each with a distribution and some form of branching probability.

It is important to remember that the probabilistic and deterministic completion dates are two very different things. The buffers must be set to zero for the deterministic date to match the probabilistic date. When the schedule is executed, they are set to the forecasted duration needed to "protect" the assigned dates.

Finally, the MSC is usually run weekly, after the status meeting when the Estimates to Complete are in from the project team. This run forecasts any changes in the probabilistic complete dates and any margin erosion. Tracking margin erosion is a critical indicator of project health.

Here's an example of an MSC tool pointed at a task with a symmetric distribution - which almost never happens in real life (the symmetric part).

The 80% confidence value is shown in the table to the right. The Cumulative Distribution Function (CDF) shows the likelihood of each specific date occurring during the simulation. The symmetric form of the distribution is suspect from the start since, in practice, tasks hardly ever finish early in the same number of time. They finish late in the random sampling of all the durations in the distribution describing the task's duration.

Here are some samples of the types of projects that make use of MCS on a weekly basis.