Sizing Schedule Margin using Monte Carlo Simulation

Jack has discussed an approach to sizing the "buffer" needed for a schedule. The Monte Carlo approach is discussed as well. Both are needed for a credible plan in our domain. 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 performance the work that deliver the SAs in support of the PEs. This results in a vertically integrated plan. A plan the 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 - 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" - meets the needs of the project.
5. Add buffer(s) in front of high to moderate risk tasks, collection points or milestones that bring the deterministic schedule to the same date as needed by the customer. This deterministic date then includes the "buffer" or margin Jack mentioned.
6. Set these buffer or margin tasks to zero (0) duration and rerun the Monte Carlo Simulation to confirm the 80% confidence date still matches.

The probabilistic duration Jack mentions need to be discussed a bit more. There are several approaches here.

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 ones.
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 are better because they represent are 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, @Risk can be used with 10/90).

Jack free 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, Jacks tool will likely "not scale." But that is of no concern because the concept is what is important in the early rounds of building a credible schedule.

It is important to remember that the probabilistic completion date and the deterministic completion date are tow very different things. In order for the deterministic date to match the probabilistic date the buffers must be set to zero. When the schedule is being 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 along with any margin erosion. Tracking margin erosion is a critical indicator of project health.

Here's an example of a MSC tool pointed at a task with a symmetric distribution - which almost never happen 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 duration of the task.

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

Last Titan Launch. VBAFB, October 27, 2005

Rocky Flats Environmental Technology Site Closure Project October 2005

Hubble Robotic Servicing Mission

F-22 Raptor

But in the end any project that has something other than a simple linear flow - waterfall - type project process can benefit from capabilities based planning with probabilistic assessment of the completion date.