Now, I will go through a different way on how I want to apply PERT, and the PERT techniques, and the whole idea how it helps you, as a scheduler and even a planner. I will study the area of construction costs, instead of the durations. And show how we can use or utilize the PERT method and technique, and also find the probability in finishing the project, within certain budget. And instead of durations, that we refer to as the Range Estimating. And in this method, the estimator provides to you three cost estimates for each construction activity. And instead of three durations as follows. The three cost estimates here, similar concept as the PERT. One, L, we call it here. Which is the optimistic one. The most optimistic or, in this case if you want to think about it. The lowest cost, or the lowest estimate cost that given to you. The H here, the Pessimistic which is the most Pessimistic or, in other words the highest. The highest cost estimate is given for that specific construction activity. And the third one, the last one is the M, or the Most Likely estimate. Similar, if you noticed, to what we had Optimistic, Pessimistic and the Most Likely from the duration point of view. For each activity, then the expected cost estimate, and it's standard deviation similar to what we did, same concept to follow this equations. The expected value for each Activity would be the Optimistic value plus four times the most likely cost estimate, plus the most Pessimistic or the highest cost value. You sum it all up, divide it by six, that will give you the expected cost value for that activity, and the standard deviation, the same, the highest minus the lowest or the pessimistic minus the optimistic divided by 6 for that individual activity. Now, the total Project Estimate, or E, or, in this case, we refer to it in the Pert as a TE, is the summation of all the expected values of all activities. Not just the critical activities. This is very important in variation estimating and comparing it to PERT calculations with the duration. Because, let's stop here just quickly and explain it further. When it comes to the cost and the budget Of the project. You want to add or sum up all the costs you have for each single activity to find the total cost of the project. Makes sense. You want to find the total budget, so you have to add all the activities you have in your project. As for the time and duration, that we use for the PERT calculations, you do not add all the times or all the durations, the expected values of the activities in your project. To find the duration of the entire project, simply because you are not performing one activity at a time. You are not saying, activity one and then, when you finish that, you start activity two. And then you finish that, three. And all the way until you finish the list of activities in your project. You have a lot of activities, that are working on parallel at the same exact time during the construction of the project. As we covered in the previous modules, from that activity on known, the activity on arrow, even the bar chart, gun chart. And the performing of the forward and the backward past calculations and so on. So you have a lot of activities, that is why you just consider that critical activities at the PERT calculation. And for the range estimating, you consider all the activities of the project. Furthermore, the Variance of Project Estimate then would be the summation of all the variance you have for all the activities. And the variance, will be the power of two of the standard deviation here, the same exact as the pair of calculations. So the Standard deviation, then the square root of the variance of the project. And let's take an example here. If we do have the following example, you do have a list of activities. I just took the name of the activities, and just numbered them for simplicity. And what I like in here, The first only 5 and it goes all the way to a hundred activities, and I am sharing only the 5 activities and the numbers in the 5 activities. The Lowest or L number in the second column. It shows that Activity 1, it needs around $6900 for that activity. And the most likely that you would use around $9700, and the highest it might reach almost to to $17,000. And activity two the same concept, 3, 4, and 5. If you noticed, the lowest of course, which will highlight the lowest number and the most likely, and all the way the highest. And the expected, then value. Before we move forward, I want to highlight also, in this case for all the hundred activities. That lowest expected value, for the entire project will be the addition and the summation of all these column here, which these say for simplicity, it give you around $350,000. The most likely, we can also sum all the column to give you around $530,000 and the highest the same. Now, the expected value and the variance, it's a little different. Using the equations that we just highlighted in the previous slide, I put it in the upper right side here. Which is the expected value from all the five, here you apply the formulas and then you apply the variance. And the standard deviation of the square root of the variance. What I highlighted the formula up here is the standard deviation, so you have the square root, to the power of 2 to find the variance of course. So what I would ask you to do, is to find the expected value of the five activities I just gave here, and find the variance of each of the five activities here. Not the standard deviation for the time being. And the variance, don't forget to put it to the power of two when you calculate it. And then let's share the solution together here. So, let's share the numbers. The expected value for the first activities, let's say around 10,000, the second one around 8,000, third one 3,000 approximately and so on. And week, let's take one example as example number, activity two, the expected value would be the 2.3 or 2,300 plus 4 times the 9,000, plus approximately the 10,000 all divided by 6 which will give you that 8,119. The Variance would be then the 10,000 minus the 2,000 divided by 6 to the power of 2, to give you towards the end there. So that will lead us, if you take the square root, will give you the standard deviation in the column in between here. And the summation of all the Expected Values from activity 1, all the way through activity 100 will give you then the Expected Value for the entire project. The same goes to the Variance. You add up all the Variance to give the variance, of the entire project, which then lead to finding the standard deviation of your project. Which is the square root of the variance there to be approximately 14,000. I want you to remember this process, from the PERT or the Range Estimating. You find the expected value for that, and then you find the variance, and then when you sum it up you find the standard deviation from the total variance. So, with that being said, let's move forward, and take an example based on what you just sold. Based on the Range Estimating, it was found that the Expected Project Cost to be around 520,000 as we can see in the number here. And the standard deviation It was the square root of that 200 million, it was the 14,000. So I will give you two questions to solve here, that will be similar to the process that we did in the PERT. The first one is. What is the probability of completing the project at a cost under 540,000? Then I will flip it. I will ask you, What is the project cost that can be achieved with 84% confidence? So, take a minute. Solve these two and then we'll go through the explanation of the calculations. So for the first question, I asked you to try to find the probability of completing the project, with the cost under 540,000. So if you remember, let's do the normal distribution again here. We have. I remember a mean of 520,000 And we're trying to find, the probability for 540,000. Which as, if I'm I'm asking you here to identify the area underneath the scale here from the 540 to the left side. So the two steps is first to find the z value, and we have the z value Which is the coast C, available for you 540 here, minus the mean value, divided by the standard deviation. Let's write the standard deviation quickly before we move forward, which is 14 142. So that will give us then of, 540,000 minus the 520 the expected value for the project, divided by the standard deviation. To give you 1.41. Finding the z value. The second step, we look at the table. From the table, we can highlight that at 1.41, it goes in the upper right side here. So do a linear interpolation, we found the z value is 92%. So in this case, this area here is equivalent to 92% probability of finishing or completing the project under 540,000. So let's move to the second part of the example. So, the second part of our question, we turned it the other way round. We give you the probability and we're trying to find the cost associated with that probability. So from a PERT point of view or Arrange Estimating point of view, instead of going through 1 and 2 you going to go through 2 and 1. Where you find that Probability from the table trying to find the z value. From the z value then go to find that C or the cost. So, the question here for example asking us to find the project cost that can be achieved with an 84% confidence. That means that say 84%. This area, is 50% so it's going to be a little bit above here. So let's say somewhere here, we have the area underneath this curve. I gave it to you as 84%, and we tried to figure out this value here. So that being said, then the value here can be achieved from the table. The 84%, what's the z value for the 84% from the tables? It will be around 1. And, From the equation we have, from the first step to find z, and now we know z as 1%. And we're trying now to find C which is the cost that's shared with this probability minus the mean $520,000 divided by the standard deviation which will give you a $534,142. So that is the cost of the project. That can be achieved with 84% confidence. So with that, we wrapped up our module by covering that PERT and Range Estimating, and how the Range Estimating we cover it from a correspondent review. The PERT calculations cover it from duration point of the view. The PERT focusing more on the critical activities. The Range Estimating focusing on all the activities in the project because you're dealing with the cost and the budget. And that has to be commutative for all the activities in your project. One also major thing that I want you to remember here, which is something kind of common mistake here. When you do calculations to find the standard deviation for either a PERT calculation Or a Range Estimating calculation. The standard deviation you find it by first,find the variance of the activities. In the PERT example you find the variance of the critical activities, you sum it up. Then find the standard deviation. You don't go ahead and find the standard deviation of each of the critical activities and then sum it up. And that would be the standard deviation of the project. You don't do that. You look at the variance first, the distribution, and after you find the variance Which is to the power of two of that sigma of the standard deviation. You sum it up, and from the critical activities, you find then the standard deviation of the entire project. For the Range Estimating, you find the variance for each single activity in your entire project. You sum it, all the variance. Of all these critical activities. The summation then, you take the square root for to find the standard deviation to put it in your calculations later. So this is a common kind of advice I give for all my students and I would love for you to pay attention to. Thank you!
