# Making Better Estimates of Project Duration Using Monte Carlo Analysis

*by Lion "Ari" Ondiappan Arivazhagan, guest blogger. *

Predicting project completion times is one of the major challenges project managers face. Project schedule overruns are quite common due to the high uncertainty in estimating the amount of time activities require, a lack of historical data about project completion, organizational culture, inadequate skills, the complex and elaborative nature of projects, and many other factors.

PMI’s Pulse of the Profession™ research, which is consistent with other studies, shows that "fewer than two-thirds of projects meet their goals and business intent (success rates have been falling since 2008), and about 17 percent fail outright. Failed projects waste an organization’s money: for every US$1 billion spent on a failed project, US$135 million is lost forever…unrecoverable."

In another report on infrastructure project schedule and cost overruns, released in 2013 by PMI-KPMG, 79 percent of the survey respondents agreed that the infrastructure sector in India faces a shortage of skilled project managers with the prerequisite skill set, which results in time/schedule overruns. One of the reasons for inefficient project delivery is the paucity of skilled project managers in the infrastructure sector.

Yet predicting an achievable project completion time is more important today than ever before, due to the high liquidated damages (LD) or penalty charges for late completion and growing dissatisfaction among clients and the public.

## The Drawbacks of Traditional CPM Technique

Deterministic, single-point estimates of project activities are highly risky as it is impossible to complete all the project activities exactly on the estimated single-point durations. Moreover, most estimators tend to estimate activity durations that are closer to optimistic estimates than to pessimistic ones. The most likely estimates are the modal estimates and the traditional Critical Path Method (CPM), which assumes activities are normally distributed. In a normal distribution, the modal estimates have only a 50% chance of being completed within or below the estimated duration, and hence the critical path duration. In other words, we typically start with estimated project completion time that has a 50% chance of being EXCEEDED from the second the project begins.

## Why Probabilistic Method (PERT)

Models that use three-point estimates, such as the PERT model, reduce uncertainty in project completion estimates by taking into account the Optimistic (To), Most-likely (Tml) and Pessimistic (Tp) to some extent. The width of the range (Tp -To) indicates the degree of the risk in each activity duration. While probabilistic estimates can give us three different project completion times based on either To, Tml, or Tp, we generally calculate the project completion time based on an equivalent single-point expected duration by assigning appropriate weights to each of the 3 durations. For example, the PERT model, which assumes a Beta distribution, uses the following formula to calculate the expected duration,Te.

Expected duration,Te = (To + 4Tml +Tp) / 6

Using the PERT's 3-point estimates of activities whose durations are in weeks, we get the following PERT Network Diagram to calculate the critical path.The expected durations so calculated are then used as single-point durations in the traditional CPM method to arrive at the critical path duration. Please note that the Te values have been used as the fixed length or known activity durations (similar to the CPM) and the critical path is found by the traditional CPM way using forward and backward passes to calculate the total float of each activity.The critical path is shown below in red.

The Critical Path Duration , T = A + E + H + I + J = 6 + 3 + 4 + 2 + 2 = 17 Weeks

Unfortunately, this PERT project duration, found by adding the critical activities, *also *enjoys a mere 50% chance of on-time completion.The project completion time, regardless of the distribution shapes of the critical activities, tends to follow an approximately normal distribution if there are a sufficiently large number of activities ( say, >30) in the critical path, according to the Central Limit Theorem (CLT). Hence, our problem is still not solved, as PERT-based project completion time is nothing but a glorified-CPM-based completion time.

## Going to Monte Carlo

This is where simulation techniques, such as Monte Carlo, come in handy. We can use simulation to estimate various project completion times along with their probability of completion so that we can plan contingency reserves (CR) to ensure at least a 90-95% probability of completion (as opposed to 50% by CPM or PERT methods) during the risk management planning stage itself.

In Monte Carlo simulation, the durations of critical path activities are simulated to take on random values between their Low and High limits, depending on the distributions assumed, using a random number generator until the specified number of simulations—say, 5,000—are exhausted. For each simulation, a set of project completion time and its probability of completion is calculated and stored. When all 5,000 simulations are done, we get 5,000 project completion times and their probability values.

Monte Carlo Simulation outputs (with 5,000 simulations using the software Devize^{® }from Minitab) for various target project completion times are given below. These simulated outputs help determine the Contingency Reserves (CR) needed in terms of the project completion time for better planning and completion assurance to clients.

The 5,000-simulation output above predicts that the single-point Critical Path duration of 17 weeks has only a 25.9% chance of completion, or a 74.1% chance of failure (exceeding the estimated duration).

The simulation shown below estimates the probability of completing the project ahead of schedule by 1 month, possibly by fast-tracking. It shows that the chances of completing the project in 16 weeks (as opposed to the baseline duration of 17 weeks from CPM) are only 13.14%. Such predictions are very helpful to project managers in effective planning and deployment of project resources.

If the client wants to know or predict the project completion duration that has at least an 85% chance of success, we can easily do that using simulations performed in Devize. In the output below, we can see that the target completion duration of 21 weeks ( USL=21 weeks) has an 86.58% chance of being completed on time.

If the project manager wants to submit a completion time that has at least an 85% chance of completion with all the duration combinations of the critical path activities taken into account, it will be wiser to commit to a completion time of 21 weeks, as opposed to the contractual completion time of 16 weeks, which had only a 13.14% chance of success.

**Monte Carlo Simulation for Project Managers**

Monte Carlo simulation is a boon to project managers in general—and to risk managers in particular—for simulating various possible combinations of the predictor variables within their range of values. Project managers can use Monte Carlo simulations to make more informed decisions and, as a result, complete more projects within the agreed time. Software packages such as Devize make the analysis simpler and intuitive, which in turn makes it easier for us to mitigate the overall project schedule risks to an acceptable threshold.

**References **

1. *An Introduction to Management Science: Quantitative Approaches to Decision Making*, by Anderson et al.

2.*The PMBOK® Guide *- 5th edition, Project Management Institute (PMI).

3. Devize^{®}, Simulation and Optimization software from Minitab^{®} Inc.

4. PMI’s Pulse of the Profession™ -The High Cost of Low Performance. 2013.

5. PMI-KPMG Study on Project Schedule and Cost Overruns - Expedite Infrastructure Projects. 2013.

**About the Guest Blogger: **

*The author, Ondiappan Arivazhagan, "Ari", is an Honors graduate in Civil / Structural Engineering from University of Madras.He is a certified PMP, PMI-SP, PMI-RMP from PMI, USA. He is also a Master Black Belt in Lean Six Sigma and has done Business Analytics from IIM,Bangalore. He has 30 years of professional global project management experience in various countries around the World and has almost 14 years of teaching / training experience in Project management, Analytics, Risk Management and Lean Six Sigma .He is the Founder-CEO of International Institute of Project Management (IIPM), Chennai and can be reached at askari@iipmchennai.com.*

*An earlier version of the article appeared on LinkedIn. *