3.9

## Darden School of Business, University of Virginia

Skip to 0 minutes and 1 secondSo when we looked at the variability and tasks durations, we considered how much each task's variability affects the overall project duration when holding the others fixed, or constant at their most likely duration. But in reality, everything is going to be uncertain, and task's durations are going to move all over the place. And we're not going to have one source of variability with everything else staying constant. So our next step is to move beyond changing each task separately. But we're going to throw all of our variability, and we're going to use very cool tools to visualize and to conceptualize what the overall impact is going to be on our project duration.

Skip to 0 minutes and 41 secondsWhen we account for the interactions and the dependencies and the inter, and the links and the vari, different sources of variabilities that we have in our project. So let's go back and see how we can do this, given the same information that we've elicited on our specific example of our start up project. We're going to walk through the example and see what we might, what steps we might take in order to come up with a complete probability distributions for our overall project duration.

Skip to 1 minute and 12 secondsSo we have our list of tasks. We have our eight tasks, and we have our three points, or our three data points of each task's estimate a duration. We have the minimum duration it could be, the maximum duration it could be, and some estimate of the most likely duration as well. Now we're going to allow our tasks to not only obtain their extreme durations, for instance, three or seven weeks for our Creative. But we're going to allow for Creative to move anywhere between three and seven. And we're also going to articulate something around how likely we believe it is that Creative will take a certain length of time. We're going to do this for all our tasks.

Skip to 1 minute and 54 secondsAnd assign a probability distribution for each one of our task durations. Allowing them all to vary simultaneously and preserving our precedence relationship will tell us something about the distribution of the overall project duration. The first step to do this is to replace our estimates here with an entire probability distribution. There are specialized tools out there, Crystal Ball or @RISK or many other alternatives. And I have a separate video that will allow you to walk through the steps that you might take to implement this in Excel. Right now, let's look at a screen shot of what it looks like and what it's trying to convey.

Skip to 2 minutes and 34 secondsUsing these specialized tools, I can replace my minimum, my maximum durations with an estimated duration that is coming from an entire distribution. In this case, I use something fairly simple and intuitive which is called the triangular distribution. In order to use a triangular distribution, I need to assign a minimum and a maximum, which I know. I've obtained that information. I've collected that information for this specific task. And each one of the values in this range can be realized. It is a possible outcome that I might see. But I am telling my tool that it is more likely to be centered. It is more likely in this case to be somewhere around five.

Skip to 3 minutes and 15 secondsSo there's a higher probability to obtain values somewhere in the middle.

Skip to 3 minutes and 21 secondsI could assign this distribution, a fairly intuitive and straightforward distribution, to each one of my tasks separately. And when I press a button, I will see a different possible outcome for my future project. Doing this 10,000, 100,000, even a million times, will simulate a million possible realities that my project might face, a million instances of my future project. And if I look at the patterns that emerge, I will be able to conclude what my average, or my expected duration would be. And also, I might be able to learn something about the likelihood of different values.

Skip to 4 minutes and 3 secondsAnd so, once I throw it all in, into my tool, and I assign a distribution for each one of my tasks, I run it a million times with a million potential futures. I see the following chart. I see a cumulative distribution. What this tells me, it tells me the likelihood that the overall project duration will be a certain number of weeks. You may not be able to see all the numbers, but I will highlight them and talk about them so you can learn from this chart, even visually. What I see here, for instance, is that the 12 weeks, which we initially calculated using our critical path analysis.

Skip to 4 minutes and 40 secondsWell, I see that that there is somewhere around, say, 25% chance that the project will be completed up to 12 weeks. There is closer to 75% chance that it will take us longer. Somewhere around 16 weeks, for instance, if I go all the way up. I estimate somewhere around 95% chance of completing this project within 16 weeks. And so if I'm looking to set a completion date or to report how long it might take me to complete a project, I can choose a confidence level. I can say, I am 95% certain that I will complete within approximately 16 weeks.

Skip to 5 minutes and 21 secondsAnd I can be more accurate, given the information that I have and given the variability that I know that exists in my project. Another way to view it is looking at the frequency, or looking at the probability. What is the chance that I will find myself within a certain range? Or what is the chance that my project duration, my project will be completed within a certain number of weeks? I can use the tool to come up with confidence ranges. In this case, I am 90% certain to finish between 10.5 to somewhere in the region of just over 16 weeks. I can convey my confidence level.

Skip to 5 minutes and 58 secondsI am 90% confidence that this is the range within which my project will be completed.

Skip to 6 minutes and 5 secondsAnd so we started with individual tasks. We started with calculating the most likely out, out, estimated duration, and we then looked at ranges. Next step was to vary each task at a time and to think about what is its impact on the overall project duration. Then, we allowed them all to vary simultaneously. And we created these wonderful charts that tell us something about the probability and the confidence that we have in completing the project within a certain length. What we also have to remind ourselves is that as we start and begin on a project.

Skip to 6 minutes and 40 secondsAnd we acknowledge the fact that the, and variability will occur and tasks, some of them will take shorter and some of them will take longer than our estimations. We are going to see, or we could find ourselves on a different critical path. We're no longer going to be talking about a specific single critical path. And so we're no longer going to be asking which are the tasks that are on the critical path, because the critical path might vary in reality, and might vary as we move and progress through the project.

Skip to 7 minutes and 12 secondsAnd so now that we have a tool that allows us to model the variability in each task, we can also ask the question, what is the chance, or how likely is it, that each one of our tasks is on the critical path? No longer certainty but a degree of likelihood, or some probabilistic statement. And so when we do this and we simulate it, we can see for instance, and we can obtain the following information. We see here that the Creative task is 93% certain, or we're 93% chance that it will be on the critical path.

Skip to 7 minutes and 46 secondsThere is about a 70% chance that the Sales activity will be on the critical path, and there is virtually no chance that the IT will form part of our critical path. And so again we can use our critical index, or the likely that our task is on the critical path, in order to prioritize our attention. And to tell us where to focus, and which task and which resources might require our attention to make sure that we complete our project within the range that we anticipate to complete it on.

# A More Realistic Timeline Part II

In this video, Professor Yael Grushka-Cockayne continues to discuss schedule risks analysis using the start-up example. She explains how to come up with complete probability distributions for an overall project duration using Excel.

Once you’ve finished watching this video, proceed to the Tutorial for Using Monte Carlo Simulations video where Professor Yael Grushka-Cockayne walks you through an example.