The basics of Monte Carlo simulation

a tutorial

S. Kandaswamy, Ph.D., PMP, AT&T Labs

Almost, every project manager has experience with not meeting the project deadline. They fail to recognize that the estimates (cost or task duration) are probabilistic and not deterministic. Because things rarely happen according to plan, deviations from original estimates cause projects not to meet their delivery dates or budgeted cost exceeding the actual cost. The conventional method of using single-point estimates, in the Critical Path Method, gives a false notion that future can be predicted precisely.

Many project planners erroneously think just because their estimates are based on most likely estimates (in between optimistic and pessimistic), they are safe, and by law of averages things will even out. For instance, they could think in the context of scheduling, some activities take longer than anticipated, some other activities take shorter time than planned, and on the average, these cancel each other with most of the activities centering on the most likely values. The PMBOK® Guide states “Schedule simulation should be used on any large or complex project since traditional mathematical analysis technique such as the Critical Path Method (CPM) and the Program Evaluation and Review Technique (PERT) do not account for path convergence and thus tend to underestimate project duration.”

It is easier to demonstrate, with a simulation, how task(s) not on the critical path (identified by the CPM) may end up on the critical path due to deviations from the plan and derail a project. Also, with simulation one can illustrate the negative impact of parallel paths converging at critical points.

Many project managers are not open to the idea of simulation, because they think the methodology is hard to use and many don't even realize its value. For other reasons, even well known commercially available products such as Microsoft Project do not offer the capability to run simulation.

The objective of this presentation is to:

• Introduce the concept of Monte Carlo simulation with simple examples (applied to schedule as well as cost problems)

• Demonstrate the value of simulation in risk identification, quantification, and mitigation

• Encourage the use of Monte Carlo simulation among practicing project managers.

What is Monte Carlo Simulation?

• It is a technique to emulate project activities (examples: scheduling of activities, estimating project cost).

• It is a technique that is carried out numerous times (hundreds or thousands of iterations) to understand the variability of a process and quantify it.

• It is a method where outcomes of events are determined with the use of random number subject to allocated probabilities.

The Tutorial

The Project Schedule Simulation

The presentation will start a diagram of a small project with three tasks and the audience will be asked to identify the critical path, the earliest completion time for the project, and to estimate the project cost.

The tutorial would start with a schedule example first. With computer-generated random numbers, the task duration estimate, for each task, will be derived 20 times (i.e., the number of iterations is equal to 20). For each run, the critical path will be identified, the duration of the project calculated, and the tasks on the critical path identified. Also, based on the 20 runs, the criticality index for each task will be calculated. With this demonstration/exercise, the audience will be able to appreciate that:

• Each task duration estimate is best guess, which is subject to uncertainty and hence the project duration itself is uncertain

• The critical path itself can vary (a given task may or may not be in the critical path) and understand the concept of “criticality index”

• It is more meaningful to associate a probability statement with project completion date. (Instead of telling management that a project will be completed by November 15th, it makes a lot more sense to state there is an 85% chance that the project will be completed by November 15th.)

The Project Cost Simulation

The second part of the simulation will illustrate the value of simulation in cost estimation. A single activity with two scenarios is given. Scenario #1: Only a single vendor is needed to complete an activity (70% of the times, a single vendor is sufficient). Scenario #2: A second vendor is also needed (30% of the times, a second vendor is also needed). For each scenario, the conservative cost estimate (the worst case), the most likely cost estimate, and the best-case cost estimates will be given. The audience will be shown how to derive a combined cost estimate for this task.

The Input Distributions

If time permitting, a quick overview of potential input distributions to simulation will be provided. These distributions include Beta distribution, Normal distribution, PERT distribution, Triangular distribution, and Uniform distribution. An attempt will also be made to tell the audience what simulation packages are available in the market.


Hulett, David, T. 1995. Project Schedule Risk Assessment. Project Management Journal (March).

Hulett, David, T. 2000. Project Schedule Risk Analysis: Monte Carlo Simulation or PERT? Project Management Journal (February).

Levine, Harvey, A. Risk Management for Dummies: Managing Schedule, Cost and Technical Risk and Contingency. PM Network (October).

MacCrimmon, Kenneth R., and Ryavee, Charles A. An Analytical Study of the PERT Assumptions. Operations Research (January-February).

Risk + for Microsoft Project. ProjectGear, Inc. Tacoma, WA 98406.

Vose, David. Risk Analysis: A Quantitative Guide.

Proceedings of the Project Management Institute Annual Seminars & Symposium
November 1–10, 2001 • Nashville,Tenn.,USA



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