# Ihab Saad – Tegrity Lecture Arrow Diagramming Method

The speakers discuss scheduling techniques for networking methods, including AOA activity, Gantt chart, units of time, units of time, and Gantt bar chart. They emphasize the importance of creating a logical sequence for activities and the use of the Gantt chart to graph the network. They also discuss the process of merging projects into a network, including the use of the forward pass, backward pass, and the criticality of each activity. They also discuss the use of float and the importance of knowing who owns the float. The speakers emphasize the importance of knowing work days and the use of work days for practice.
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Welcome to another class in construction scheduling, and today

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we're going to start talking about one of the scheduling techniques,

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which is the activity on arrow, also known as Arrow Diagramming

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Method. So sometimes it's referred to as AOA activity on arrow, or

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sometimes also referred to as ADM Arrow Diagramming Method. So

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what's the Arrow Diagramming Method? How does it work? What are

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these calculations? This is basically what we're going to be

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discussing in this lecture. We're

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going to have an introduction to what this scheduling technique is

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and what's the advantage of the scheduling technique. We're going

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to talk about the network diagram and some common issues related to

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its use network calculations, which is basically used to

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establish the dates for the network. And then we're going to

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discuss another elaboration or another iteration in improvement

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of scheduling techniques, which is called the time scaled network.

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And then finally, we're going to talk about units of time.

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The activity on aeronnetwork is the first developed networking

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method. We started talking about scheduling techniques. We talked

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about a checklist, basically write down all the activities that you

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need to do, and it's not necessarily in order. It does not

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show any dependency among these activities, and it does not show

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any duration for these activities. So it's just a matter of listing

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the activities, and once you've done each one of them, you check

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it with a check mark. So at the end, it can be used as a planning

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tool and as a control tool by looking at the checked activities.

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But again, as you can see, the drawbacks of this technique. It

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does not show duration, does not show dependency or order of the

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activities. Another technique was the Gantt chart, or the bar chart,

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which was a great development, because now it showed in a

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graphical format, the different activities, which showed on two

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axes, a vertical axis showing the activities, and horizontal axis is

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a time line, showing when does each activity start and finish. So

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you can trace a bar or a line representing the duration of the

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activity. So the activities are drawn in a scale that shows their

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relative duration, however, and that's that technique, by the way,

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is still very commonly used today in construction projects and any

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other project as well. The main drawback of that technique is that

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it does not show the dependency among the activities. Yes, it

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shows when each one should start and when each one is expected to

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finish or plan to finish, but it does not show what the

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interrelationship among these activities? What if one of them

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was delayed? How is that going to affect the others? That is not

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shown on the Gantt chart? Trying to do that, as we're going to see

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something that's really hard to to read. So someone started thinking

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about a new graphical method of representing the activities. How

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are we going to develop that schedule? And they started

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thinking about the flow of water, for example, from the source until

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it reaches your house, how it goes from a large plant through a

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smaller one, through pipes and popping stations and so on. And

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these pipes start branching from a main pipe to a secondary pipe,

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until they reach the very fine pipes that are in your house. And

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then finally, once this water is used and you need to collect it

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back the used water, it's done in a reverse way, again, from smaller

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pipes to larger ones, until they reach the sewage treatment plant.

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So we have junctions, we have pipes, we have connections, and

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they show the dependency. If, for example, there's no water in this

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pipe, then the following one's not going to have any water either. So

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the activity on aero is the first developed networking method, like

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a network of water distribution or collection. This is basically what

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we have. It's also called the IJ, or Arrow Diagramming Method. Why

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is it called the IJ? Because each activity is going to be

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represented by two nodes, the start node of the activity and the

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finish node of the activity, and the activity itself is going to be

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the line, or the arrow connecting between these two nodes. So in

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this case, the activity is going to be represented by a node i,

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representing its start, and a node j, representing its finish. And

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the activity itself is ij, the line that bridges between these

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two nodes. Each activity is represented by an arrow spanning

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between two nodes representing the start and finish events of the

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activity.

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So the activities are linked from the finish of one activity to the

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start of

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the next one through a node. Therefore the finish of one

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activity, the node representing the finish of one activity, is

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exactly the same as.

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Is the node representing the start of the activity that follows it.

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So activities are stated on the arrow. The name of the activity,

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or the description of the activity is going to be mentioned or

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written on the arrow, so we know what activity ij means. Nodes have

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no duration and use no resources. The node is just a date. It does

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not have a duration. It's an event. This is the start event.

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This is the finish event. The i node marks the beginning of the

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activity, whereas the j node marks its completion. And the network

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always remember that very well. The network always flows from left

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to right. Therefore, even if you have in these nodes numbers, let's

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say node three, five or 712, or whatever. The number itself does

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not mean anything. It's just a matter of order. And you can have,

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for example, the numbers in reverse order or any other order,

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as long as we know that the network flows from left to right.

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This is how we read the network as we are progressing. So here, for

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example, we have the node i, we have the finished node j, and the

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arrow, or the activity itself, representing

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whatever description that might be. And underneath the arrow we're

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going to put the duration of that activity.

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J should be bigger than I when we're talking about dates, then

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this date is going to be later than that one or sometimes it

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might be the same date as we're going to see very shortly.

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Activities are related to each other through nodes. Activity

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2030, cannot start until activity 1020 is complete. Here, for

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example, we have activity 1020 which is also known as activity A,

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and activity 2030 which is also known as activity B. Activity A

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has a duration of five days, B has a duration of 10 days. What if

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activity 1020 or a has not started, then definitely 2030

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cannot start either. So we say in this case that activity 2030

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depends on activity 1020,

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now can there be more than one activity depending on one? Yes. So

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for example, we can have a starting node, node 10, and from

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this node we have three activities starting at the same time. So

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these activities have the same start date, but they might have

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different finish dates. Activity A is going to finish on day 5b, is

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going to finish on day 10, and C is going to finish on day 12. So

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all of these started from the same node. Similarly, several

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activities can merge into one node as well.

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So when two or more activities merge into a node, here we have,

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for example, activity, 2040, 3040, and 4040,

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of course, there should be that. That's a probably a typo. We

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should have put here 50 instead of 40, because you should not have 40

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and 40 as the start and finish of the same activity. So this is a

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typo. This should be either 4050, or 5040,

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once the dependencies have been established among the activities

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and network diagram can be constructed. That's why the first

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effort is not going to be to draw the network. The first effort

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first is going to be to analyze the activities, to define what

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these activities are, and then to start thinking logically about

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their dependencies and about their order of occurrence. Once we have

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established that, we can start drawing the network,

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the former activity is called a predecessor or preceding activity,

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whereas the dependent activity is called the successor or succeeding

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activity. So in the previous examples, for example, we had

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three nodes, 1020, and 30. Activity. 1020

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is a predecessor to activity 2030,

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or is also called a preceding activity to activity 2030 and also

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activity 2030 is going to be called a successor to activity

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1020 or a succeeding activity to activity 1020 so from now on,

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we're not going to say the activity before or the activity

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after. We're going to use the new lingo, which we're gonna represent

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it as either predecessors and successors to a certain activity.

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A network should start with a single node and end with a single

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node. That's another convention of drawing the network like it flows

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from left to right. Another issue here is that it's gonna have one

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starting node and one finishing node. So we're going to have

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several activities, maybe merging emerging from one node, and

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several activities merging into one node at the end.

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To look at an example here, activity on arrow network

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dependency. So what we have, what you as a project manager, do, is

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develop.

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Is, and putting them in the logical sequence is looking at

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determining the activity resources, what kind of resources

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are going to be needed, and the availability rates of these

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resources. So these resources can be material, can be equipment, can

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be subcontractor, or simply, can be money that's going to pay for

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all of the above,

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once we have developed the resource pool and the resource

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availability, now we can establish a duration for each activity. And

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the duration for the activity is going to be very simple. That's

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going to be one universal equation used to determine the duration of

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the activity. And that's a very simple equation. It's Q divided by

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p or q over p, q is the quantity of work for that activity, and P

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is the production rate of the resources used in the activity.

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What if one activity has more than one resource with different

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production rates? The slowest resource the one

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with the lowest production rate is going to be the control effect.

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So if, for example, I have to place concrete, and placing the

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concrete is going to involve mixing the concrete and the batch

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plant,

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transporting the concrete to the construction site,

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pouring the concrete into the bucket of a tower crane, lifting

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the concrete to the seventh floor and then placing that concrete

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through a group of personnel of people later.

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Now, the production of the batch plant can be 200 cubic yards. An

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hour of these 200 cubic yards, I can only transport 50 cubic yards.

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An hour of these 50 cubic yards an hour, I can only lift

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with the tower crane 30 cubic yards an hour. Of these 30 cubic

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yards, I can only place and finish 20 cubic yards an hour. Therefore,

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we have seen several resources with different production rates.

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The controlling production rate is going to be this the lowest one,

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the 20 cubic yards an hour. Therefore, if I have 100 cubic

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yards to place, it's going to take five hours. 100 divided by 20,

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that gives five pounds. So that's going to be the duration of the

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activity. Once we have established the durations of the activities.

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Now we can start talking about network calculations and the

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dates, when should the activity start? When Should it finish? And

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so on and so forth. So the objectives here are going to be to

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calculate the duration to establish what's called the

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critical path, which is, I'm just going to give you a heads up here,

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the definition of the critical path is the longest continuous

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path through the network. Listen to the two critical words here,

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longest and continuous. It has to be, it will be the longest path,

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and it has to be a continuous path through the network. And then

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we're going to talk about the activity float. We're going to

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define what float is. And then talk about two different types of

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floats, total float and free float. The calculations are going

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to be done in two phases. One is going to be a motion from left to

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right, from the beginning of the network to the end, which is going

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to be called following the natural flow of the network. Therefore

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it's going to be called forward pass. And then once we reach the

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end of the network, we're going to go back to the beginning, so we're

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going to be retracing our steps backwards, and that's going to be

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moving from right to left against the flow of the network. And

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that's going to be called the backward pass. The combination of

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the forward pass and the backward pass is going to give us the

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network calculations to calculate the different dates for the

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different activities.

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Let's talk about the forward pass. The forward pass establishes the

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early start and the early finish dates of each activity and or the

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early node times for each activities. Remember, we mentioned

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that the nodes represent dates, events, start, event, finish,

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event, and each of these events has a date.

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So

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the earliest start, which means the activity cannot start any

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earlier than that,

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and the early finish, sometimes also called earliest finish, means

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that the activity cannot finish any earlier than that.

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So to calculate the early dates, te

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i is the early time at the node i of an activity ij. So we have an

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activity ij, which is in this case, 3743

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so Tei is the earliest time activity, 3743

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can start the earliest time event. I, which is 37 can happen. And

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similarly, Tej is the earliest.

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Possible time for that activity to finish, or the earliest date at

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node 43

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looking at this network here, we have several activities, several

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predecessors to this activity,

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and we might have different dates coming to these activities.

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So, for example, I have activity 2237

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activities 2737

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and activity 3237

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each one of them might be ending at a certain date.

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However, for node 37 to start.

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I have to wait for all the predecessors to happen. So if, for

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example, this activity here ended on day 10 and this one ended on

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day 12 and this one ended on day 14, I cannot start this one at day

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10 because these two are not done yet. I cannot start at day 12

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either, because this one has not started again and has not finished

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yet. So I have to wait until day 14 for all of these to be

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concluded in order to start this following activity. Therefore the

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earliest start date for node 37 in this case, would be day 14.

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If the duration of this activity is five days, then the finish is

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going to occur five days after the start. If the start was 14, then

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the finish is going to be day 19. It's as simple as that, very

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simple math.

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So the whole trick here is that when we are talking about the

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earliest start is going to be the latest date of

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completion of the predecessor activities again, 1012, and 14. We

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The early start of activity. JK

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is going to be basically the same as the finish of activity. Ij,

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the early finish is going to be the early start plus the duration.

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So what we said here, this is the early start. There's a duration

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here, five days. So the early finish is going to be early start

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plus duration.

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Now, talking about the forward pass, the forward pass establishes

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the early start and the early finish. The early start is going

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to be designated as es, and the early finish is going to be

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designated as EF, dates for each activity and or the early node

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times for each activity. It's basically the same thing. So Tei

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is the early time at the i node of an activity ij, and Tej is the

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early time at its j node.

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As we mentioned here,

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Tej maximum is equal to the early finishes of all the activities

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that terminate at node j. So here, for example, if we have several

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activities, then this is going to be the latest of all of these

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dates.

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The TE of the first node of the network should be zero. So the

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start of the network is going to be at Day Zero, not day one. One

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of the common mistakes is to start at day one. We're always going to

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start at day zero, where nothing has been done. All the

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relationships among activities are finished to start. There's no lag

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or delay, which means activity 2030, cannot start until activity

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1020 has been fully complete. That's one of the drawbacks of the

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Arrow Diagramming Method, as we're going to see.

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So again, now the same network that we have drawn, what I want

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you to do is to add durations to this network and to start, solving

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for the early start and the early finish of the different

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activities.

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And here's an example.

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So here we have activity, 1020,

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2100,

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2050,

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1040, and so on. Each activity has a name. So this is activity A,

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activity e, activity f, and each activity has a duration. The

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duration is going to be underneath the arrow, so activity 1020, or

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activity A has a duration of 10 days. Notice that we have some

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dummy activity. So we have here, for example, 2050, is a dummy

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activity. Therefore we did not put a duration, since the duration is

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going to be zero, same here for 9100, and same for 6070, any

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activity that does not have a duration is going to be denoted by

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a dotted line or dashed line, and that means it's a dummy activity.

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Now looking at the calculation.

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Here we're going to put a zero at the start of all of these three

00:30:02 --> 00:30:08

activities. So zero at node 10, which means zero at 1020 zero at

00:30:08 --> 00:30:10

1040, and zero at 1030,

00:30:11 --> 00:30:15

at the node 20, we started with zero, and we have a duration of 10

00:30:15 --> 00:30:19

days. Therefore the early finish of activity 1020, is going to be

00:30:19 --> 00:30:24

day 10, which means that at node 20, the date is 10, which means

00:30:24 --> 00:30:28

that any activity that starts after node 20 is going to start

00:30:28 --> 00:30:32

with 10. So here 20 100 is going to start on day 10, and so would

00:30:32 --> 00:30:33

activity 2050,

00:30:35 --> 00:30:39

activity 1040, has four days of duration. Therefore zero plus

00:30:39 --> 00:30:42

four, we're going to have four at the end of node 40

00:30:44 --> 00:30:45

and activity 1038,

00:30:46 --> 00:30:51

days duration. So basically, we're going to have a an early finish of

00:30:51 --> 00:30:55

day eight. Therefore we're going to start here with eight plus 14.

00:30:55 --> 00:31:00

That's 22 we're going to have 22 here and here, 22 plus four,

00:31:00 --> 00:31:01

that's 2622

00:31:02 --> 00:31:05

plus zero, that's 22 and so on and so forth.

00:31:07 --> 00:31:12

I'd like you to keep doing this, noting that if I have two dates on

00:31:12 --> 00:31:14

coming to a node, I take the larger number.

00:31:16 --> 00:31:19

So here we have two merging activities. Here we have two

00:31:19 --> 00:31:23

merging activities. And so we have here, here we have four merging

00:31:23 --> 00:31:28

activities. So the completion of the project at the end after node

00:31:28 --> 00:31:31

110 is going to be the largest number coming from all of these

00:31:31 --> 00:31:32

four activities.

00:31:35 --> 00:31:38

And this is going to be the forward pass that's going to give

00:31:38 --> 00:31:41

us the early dates of the activities to reverse that we're

00:31:41 --> 00:31:44

going to do the backward pass. The backward pass is the exact

00:31:44 --> 00:31:47

opposite of the forward pass. Whatever we did in forward, we're

00:31:47 --> 00:31:50

going to reverse in backward. So in forward, we move from left to

00:31:50 --> 00:31:53

right, adding the durations of the activities.

00:31:54 --> 00:31:58

And in case we had two activities merging into one node, we took the

00:31:58 --> 00:31:59

larger number

00:32:00 --> 00:32:03

on the backward pass, we're going to do the exact opposite, starting

00:32:03 --> 00:32:07

from right to left, subtracting the durations of the activities.

00:32:08 --> 00:32:11

If two numbers merge into one node in the backward pass, we're going

00:32:11 --> 00:32:15

to take the smaller number to proceed backwards. So the backward

00:32:15 --> 00:32:19

pass indicates the earliest dates on which each activity can be

00:32:19 --> 00:32:20

accomplished.

00:32:21 --> 00:32:24

The backward pass provides the late start and late finish dates

00:32:24 --> 00:32:27

for each activity without affecting the overall duration of

00:32:27 --> 00:32:31

the project. These dates are used in conjunction with the early

00:32:31 --> 00:32:35

dates to determine the criticality of each activity and its float, if

00:32:35 --> 00:32:36

any, as we're going to see in a moment.

00:32:39 --> 00:32:44

So the backward pass begins at the terminal or last activity works

00:32:44 --> 00:32:49

backward toward backwards toward the beginning the late finish,

00:32:49 --> 00:32:54

which is the late time at the no K node of activity, JK, the late

00:32:54 --> 00:32:58

start is going to be late finish minus duration, the opposite of

00:32:58 --> 00:32:59

what we did in the forward pass.

00:33:01 --> 00:33:06

The late date at node k is going to be the minimum of the late

00:33:06 --> 00:33:10

starts of all activities following the node k. So if we have two

00:33:10 --> 00:33:13

activities merging into node k, we're going to take the smallest

00:33:13 --> 00:33:17

number, smaller number, and that's going to be transferred backward

00:33:18 --> 00:33:23

the TL, the late dates of the last node of the network should be

00:33:23 --> 00:33:28

equal to the TE of the last node. So if we started the network with

00:33:28 --> 00:33:31

zero in the forward pass, we should end with zero in the

00:33:31 --> 00:33:33

backward pass. That's basically what it is.

00:33:37 --> 00:33:40

We're going to find that some activities have

00:33:41 --> 00:33:42

the same dates,

00:33:43 --> 00:33:47

and some activities have different dates. We're going to see that in

00:33:47 --> 00:33:49

a in a numerical example, in a moment.

00:33:50 --> 00:33:54

So for example, if activity just looking at the numbers, if

00:33:54 --> 00:33:56

activity 5070,

00:33:57 --> 00:33:59

00:34:00 --> 00:34:07

early, start of 15, duration of 10 days, early finish of 25 remember

00:34:07 --> 00:34:14

these numbers 15 and 25 early start, 15, early finish, 25 in the

00:34:14 --> 00:34:17

backward pass. However, we got a different number. We got an early,

00:34:18 --> 00:34:19

late finish of 28

00:34:21 --> 00:34:25

duration, is still 10. Therefore the early start is going to be 18

00:34:26 --> 00:34:31

in the forward pass, it was 15 and 25 in the backward pass, it was 18

00:34:31 --> 00:34:35

and 28 so what we're saying here is that activity, this activity,

00:34:35 --> 00:34:38

can start as early as day 15

00:34:39 --> 00:34:44

or as late as day 18. It can start any time in between these two

00:34:44 --> 00:34:48

days. If it starts on day 15, that's fine. If it starts on day

00:34:48 --> 00:34:53

1617, or 18, that's fine. The project's still going to finish on

00:34:54 --> 00:34:57

time. Therefore, this activity has some flexibility, or some leeway,

00:34:58 --> 00:34:59

and that leeway or flexibility.

00:35:00 --> 00:35:06

We usually call float, or to be more accurate, total float. To the

00:35:06 --> 00:35:10

total float is the leeway or the flexibility, and it's the amount

00:35:10 --> 00:35:14

of time by which a non critical activity can be delayed, without

00:35:14 --> 00:35:18

delaying the project completion. Why are we saying noncritical?

00:35:18 --> 00:35:22

Because, again, if that activity has this flexibility is not

00:35:22 --> 00:35:24

critical. Therefore, what is a critical activity? A critical

00:35:24 --> 00:35:29

activity is one that has the exact same days. The early start is 15,

00:35:29 --> 00:35:33

the early finish is 25 the late start is also 15, and the late

00:35:33 --> 00:35:37

finish is also 25 so looking at the total float, in this case,

00:35:37 --> 00:35:38

it's zero.

00:35:39 --> 00:35:44

It has to start on day 15 has to finish on day 25 in order for the

00:35:44 --> 00:35:47

project to be completed on time. Therefore we call this activity

00:35:47 --> 00:35:51

critical. Therefore the definition of a critical activity is an

00:35:51 --> 00:35:54

activity that has zero total float.

00:35:56 --> 00:36:00

The free float, on the other hand, is a subset of the total float,

00:36:00 --> 00:36:03

which means it can never exceed the total float. It's part of the

00:36:03 --> 00:36:09

total float. A part can, at its maximum, be equal to the whole so

00:36:09 --> 00:36:12

at its maximum, the free float can be equal to the total float, but

00:36:12 --> 00:36:17

it cannot exceed the total float. Therefore, the free float is the

00:36:17 --> 00:36:20

amount of time look at the definition of total float and the

00:36:20 --> 00:36:22

slight difference with free float.

00:36:23 --> 00:36:26

In case of total float, we said amount of time a non critical

00:36:26 --> 00:36:30

activity can be delayed without delaying, the project completion.

00:36:30 --> 00:36:34

In case of free float, we say it's exactly the same first line,

00:36:34 --> 00:36:37

amount of time a non critical activity can be delayed without

00:36:37 --> 00:36:40

delaying. And here's the difference any of its immediate

00:36:40 --> 00:36:43

successors. We're not looking as far as the completion of the

00:36:43 --> 00:36:46

project. We're just looking at the following activity, the immediate

00:36:46 --> 00:36:49

successor. Is it going to be delayed by the delay of this

00:36:49 --> 00:36:53

activity or not? If it's going to be delayed, therefore the free

00:36:53 --> 00:36:56

float is zero, even if the activity has total float. If it's

00:36:56 --> 00:37:00

not going to be delayed, then in this case, the free float has

00:37:00 --> 00:37:01

certain positive value.

00:37:02 --> 00:37:06

The free float, by the way, can never be negative. The minimum

00:37:06 --> 00:37:09

free float is zero. The maximum is going to be the exact amount of

00:37:09 --> 00:37:10

the total float.

00:37:12 --> 00:37:16

So for the calculations, again, the total float is equal to the

00:37:16 --> 00:37:20

late finish minus the early finish. Or it can also be equal to

00:37:21 --> 00:37:26

late start minus early start. So it's always late minus early at

00:37:26 --> 00:37:29

the same end of the activity. If we look at the start side, it's

00:37:29 --> 00:37:33

late start, minus start minus early start. If we look at the

00:37:33 --> 00:37:37

finish side, it's late finish minus early finish. Free float, on

00:37:37 --> 00:37:42

the other hand, is equal to the earliest, early start of the

00:37:42 --> 00:37:46

activity, minus of the success of the successor, minus the early

00:37:46 --> 00:37:49

finish of the activity. So, for example, if our activity has an

00:37:49 --> 00:37:51

early finish of day 25

00:37:53 --> 00:37:57

and the early start of its successor is day 28 How come?

00:37:58 --> 00:38:01

Because there was another activity that ended on day 28 and merged in

00:38:01 --> 00:38:06

the same node. So now we have two activities, one, finishing on day

00:38:06 --> 00:38:11

25 one finishing on day 28 merging in the same node. When should the

00:38:11 --> 00:38:14

successor start? We take the larger number. So we take 28

00:38:14 --> 00:38:20

therefore for the first one that ends on day 25 it has three days

00:38:20 --> 00:38:24

of free float by which it can be delayed without delaying the start

00:38:24 --> 00:38:27

of its immediate successor. That's how free float works.

00:38:31 --> 00:38:34

There's something called interfering float. We're not going

00:38:34 --> 00:38:37

to focus on it, on it too much. It's basically the difference

00:38:37 --> 00:38:41

between the total float and the free float. It's that simple. We

00:38:41 --> 00:38:43

are not going to address it at all. I just wanted to inform you

00:38:43 --> 00:38:46

00:38:46 --> 00:38:50

it has pretty much no practical use, something called the

00:38:50 --> 00:38:51

interfering float.

00:38:53 --> 00:38:56

Now, with the same exercise that we've done before, I'd like you to

00:38:56 --> 00:38:57

draw the network.

00:39:00 --> 00:39:02

We have the dependencies. In the third column, we have the

00:39:02 --> 00:39:07

durations. And now I'd like you to calculate the early start, early

00:39:07 --> 00:39:10

finish, late start, late finish. Total float, free float and

00:39:10 --> 00:39:13

interfering float for that network. So what you're gonna do

00:39:13 --> 00:39:17

after drawing the network and make doing the calculations, you're

00:39:17 --> 00:39:21

gonna draw the table, and in that table you're gonna add these seven

00:39:21 --> 00:39:24

columns, early start, early finish. Late start, late finish.

00:39:25 --> 00:39:27

Total float, free float and interfering float.

00:39:31 --> 00:39:34

Now let's start looking at some of the limitations of the activity on

00:39:34 --> 00:39:39

arrow networks. One of the major limitations that it shows only one

00:39:39 --> 00:39:43

type of relationships, which means one activity has to finish for its

00:39:43 --> 00:39:47

successor to start. You cannot have a lag. You cannot have an

00:39:47 --> 00:39:51

overlap between the activities. Therefore, it's all finished to

00:39:51 --> 00:39:52

start.

00:39:53 --> 00:39:57

And the issue of dummy activities sometimes it might be a little bit

00:39:57 --> 00:39:59

confusing if you're not used to it. So.

00:40:00 --> 00:40:03

So these are some of the limitations, or the main drawbacks

00:40:03 --> 00:40:07

on activity on arrows. And by the way, activity on arrows are no

00:40:07 --> 00:40:12

longer used on a large scale, as we're going to see later on in the

00:40:12 --> 00:40:15

next lecture about another scheduling technique, another type

00:40:15 --> 00:40:19

of networks. This is the one that's more commonly used, but you

00:40:19 --> 00:40:22

00:40:22 --> 00:40:25

as we're going to see that the calculations are pretty much the

00:40:25 --> 00:40:25

same.

00:40:27 --> 00:40:30

The question now is, that's a very important question, by the way.

00:40:30 --> 00:40:34

It's both a legal question and a technical question. Who owns the

00:40:34 --> 00:40:38

float? So if we say that an activity can be delayed by three

00:40:38 --> 00:40:43

days or five days or 10 days, who can delay it? Is it the owner? Is

00:40:43 --> 00:40:46

it the Arctic engineer? Is it the construction manager? Is it the

00:40:46 --> 00:40:50

general contractor? Is it the subcontractor? Is it the supplier,

00:40:50 --> 00:40:54

who can delay the activity, or basically, who can utilize, or who

00:40:54 --> 00:40:55

can use this float?

00:40:57 --> 00:41:01

The second answer is it's on a first come, first served. Basis,

00:41:02 --> 00:41:05

whoever needs it first can use it first,

00:41:06 --> 00:41:11

but each time you use part of the float, you leave less for someone

00:41:11 --> 00:41:15

else. So if, for example, the activity has 10 days of total

00:41:15 --> 00:41:19

float the owner used three, then for all the other parties that are

00:41:19 --> 00:41:24

left, we only have seven days. If the engineer uses four, then we

00:41:24 --> 00:41:29

have only three remaining days. If the contractor used one, then we

00:41:29 --> 00:41:32

have only two days left for subcontractor, suppliers, etc.

00:41:33 --> 00:41:37

So the ownership of float should be carefully examined in every

00:41:37 --> 00:41:42

contract for equitable risk allocation, we're going to say

00:41:42 --> 00:41:46

that the float is a shared property, and it's a property of

00:41:46 --> 00:41:51

the project. Any party involved with the project can use the

00:41:51 --> 00:41:54

float, as long as we still have some of it,

00:41:58 --> 00:42:00

an example of contract provisions.

00:42:01 --> 00:42:06

So the general statement is that the project owns the float, unless

00:42:06 --> 00:42:12

otherwise stated in the contract. Here, for example, is a is an

00:42:12 --> 00:42:16

example contract provision or clause float, sometimes referred

00:42:16 --> 00:42:20

to, also as slack, is defined as the amount of time between the

00:42:20 --> 00:42:23

early start date and the late start date, or the early finish

00:42:23 --> 00:42:26

date and the late finish date of any of the activities in the

00:42:26 --> 00:42:32

schedule float is not time for the exclusive use or benefit of either

00:42:32 --> 00:42:36

of the owner of the contract. Extension of time for performance

00:42:36 --> 00:42:40

required under the contract clauses entitled changes differing

00:42:40 --> 00:42:44

site conditions, termination for default damages, for delay time,

00:42:44 --> 00:42:49

extensions or suspension of work will be granted only to the extent

00:42:49 --> 00:42:52

that equitable time adjustments for the activity or activities

00:42:52 --> 00:42:55

affected exceed the total float or slack

00:42:56 --> 00:43:00

in simple English, the owner is Not going to grant you any

00:43:00 --> 00:43:04

extension of time as long as the activity has flowed,

00:43:06 --> 00:43:10

the owner is only gonna grant you an extension of time if the full

00:43:10 --> 00:43:14

float has been consumed and the activity has become critical, and

00:43:14 --> 00:43:18

that was the fault of the owner or any of his agents. In this case,

00:43:18 --> 00:43:20

the owner is gonna give the contractor an extension of time.

00:43:21 --> 00:43:21

However,

00:43:23 --> 00:43:26

if the contract has been delayed, the activity has been delayed, and

00:43:26 --> 00:43:29

therefore the project has been delayed due to an error of the

00:43:29 --> 00:43:35

general contractor or any of his agents, then in this case, the

00:43:35 --> 00:43:38

owner is not going to give the contractor any extension of time.

00:43:38 --> 00:43:42

On the other hand, the contractor may have to pay liquidated damages

00:43:42 --> 00:43:43

for the delay to the project.

00:43:45 --> 00:43:50

Some contractors submit late start time, thus hiding part of the

00:43:50 --> 00:43:54

float for their own use. So basically, the contract would have

00:43:54 --> 00:43:58

several versions of the same schedule. On one version, they

00:43:58 --> 00:44:00

would give the owner that this activity is going to take 10 days

00:44:00 --> 00:44:01

to finish

00:44:03 --> 00:44:06

on the inside for their own internal use. They know that this

00:44:06 --> 00:44:10

activity is going to take only six days, so they have embedded four

00:44:10 --> 00:44:13

days of total float inside the activity without showing it to the

00:44:13 --> 00:44:17

owner. It is legal, but slightly unethical.

00:44:20 --> 00:44:23

Now, based on the

00:44:24 --> 00:44:29

Arrow Diagramming Method, someone said, Okay, why not add

00:44:30 --> 00:44:35

lines to the Gantt charts showing because we mentioned that the

00:44:35 --> 00:44:39

Gantt chart, or the bar chart, does not show dependencies. So

00:44:39 --> 00:44:42

someone thought, why not show the dependencies through lines

00:44:42 --> 00:44:46

connecting the activities, as we did with the network, and that

00:44:46 --> 00:44:50

should solve the issue. Now we have a graphical representation

00:44:51 --> 00:44:54

drawn to scale. By the way, the network is not drawn to scale, so

00:44:54 --> 00:44:57

the length of the arrow does not represent anything whatsoever. You

00:44:57 --> 00:44:59

can have two activities with exactly the same.

00:45:00 --> 00:45:03

Length on the arrow with two totally different durations, but

00:45:03 --> 00:45:07

in the Gantt chart, they are drawn to scale. So the time scaled

00:45:07 --> 00:45:12

network is a time scaled diagram combining the principal features

00:45:12 --> 00:45:16

of the bar chart and the activity on arrow diagram. The bar chart

00:45:16 --> 00:45:21

that shows the activity is drawn as a bar with a relative length

00:45:21 --> 00:45:25

drawn to scale and the aspect from the activity on arrow showing the

00:45:25 --> 00:45:27

links or the relationships between the activities.

00:45:29 --> 00:45:31

The problem is that once you have a

00:45:32 --> 00:45:33

500 schedule,

00:45:34 --> 00:45:39

500 activity schedule, which is a relatively medium sized schedule,

00:45:39 --> 00:45:43

it's going to be impossible to navigate through the lines. It's

00:45:43 --> 00:45:47

going to be a big spaghetti bowl. The project is plotted on the

00:45:47 --> 00:45:51

horizontal time scale with arrows vectors and nodes representing

00:45:51 --> 00:45:54

activities, and with Arrow lengths representing time. That's the

00:45:54 --> 00:45:59

difference between time scale and arrow. It's seldom used due to its

00:45:59 --> 00:46:03

illegibility for complex projects. Once again, you get to a complex

00:46:03 --> 00:46:07

project, it's very hard to read. That's how it looks. So basically,

00:46:07 --> 00:46:12

we have a time scale like the the Gantt chart, and we have the nodes

00:46:12 --> 00:46:18

like the Arrow Diagramming Method, and then we have here the links

00:46:18 --> 00:46:23

connecting the activities and so on. So again, here we have made

00:46:23 --> 00:46:27

basically about what seven activities. Imagine if that were

00:46:27 --> 00:46:30

500 activities would be totally impossible to read it, especially

00:46:30 --> 00:46:33

when the lines start intersecting and things like that.

00:46:36 --> 00:46:39

That's another representation of that time scale network. And

00:46:39 --> 00:46:42

again, once you have so many activities, going to be really

00:46:42 --> 00:46:42

00:46:46 --> 00:46:50

For someone who might consider it advantageous over the Arrow

00:46:50 --> 00:46:54

Diagramming, it shows the activity sequence and order and it shows

00:46:54 --> 00:46:58

the relative duration of the activities. The project plan and

00:46:58 --> 00:47:01

schedule can be shown together graphically. Project progress can

00:47:01 --> 00:47:03

be represented graphically as well.

00:47:05 --> 00:47:09

Disadvantages, use of dummy activities may be cumbersome, not

00:47:09 --> 00:47:13

easily modified, very awkward for large and complex projects, and

00:47:13 --> 00:47:17

still allows for only one type of relationships, which is finished

00:47:17 --> 00:47:21

to start. And that's the main drawback of Arrow Diagramming that

00:47:21 --> 00:47:26

so we did not solve it in the time scaled diagram. Therefore, we are

00:47:26 --> 00:47:29

not going to worry at all about the time scale network. We're not

00:47:29 --> 00:47:31

going to discuss it any further. We're just going to put an end to

00:47:31 --> 00:47:32

it right there.

00:47:34 --> 00:47:38

Now, if you want to go through the exercise and draw the timescale

00:47:38 --> 00:47:43

network to see the interaction among the lines linking the

00:47:43 --> 00:47:44

different activities.

00:47:46 --> 00:47:49

And now we come to another sort of a philosophical discussion that

00:47:49 --> 00:47:52

has very practical implications on our schedule,

00:47:53 --> 00:47:57

the units of time. The units of time depend on the type of the

00:47:57 --> 00:47:58

project.

00:47:59 --> 00:48:01

In most of the projects, especially construction projects,

00:48:01 --> 00:48:06

the minimum increment unit of time is going to be a day. Therefore

00:48:06 --> 00:48:09

we're going to say that this activity has a duration of seven

00:48:09 --> 00:48:14

days, nine days, 21 days, etc. However, on some

00:48:15 --> 00:48:20

very unique activities or some very unique projects, you might

00:48:20 --> 00:48:25

have the duration in minutes or in hours rather than days,

00:48:26 --> 00:48:30

especially if the project has a very short duration, or in case,

00:48:30 --> 00:48:33

the liquidated damages are very high. To give you an example

00:48:35 --> 00:48:40

for the resurfacing of the main runway at O'Hare Airport, and

00:48:40 --> 00:48:42

that's a project that took place several years

00:48:43 --> 00:48:45

ago. O'Hare Airport is one of the busiest airports in the world.

00:48:47 --> 00:48:51

The contractor you cannot shut off the the whole airport just to

00:48:51 --> 00:48:57

surface, resurface the the runway. So it was divided into segments,

00:48:58 --> 00:49:01

allowing for parallel runways to be operating temporarily until you

00:49:01 --> 00:49:05

fix the main one. The contractor was given

00:49:07 --> 00:49:09

14 days to finish the project, and

00:49:10 --> 00:49:15

the contractor was only allowed to work from midnight to 6am where

00:49:15 --> 00:49:18

the traffic is less dense than the rest of the day.

00:49:20 --> 00:49:23

The liquidated damages for that project were \$25,000

00:49:24 --> 00:49:28

an hour. So if the project is late by one hour, the contractor pays

00:49:29 --> 00:49:29

\$25,000.02

00:49:30 --> 00:49:36

hours, \$50,000 so imagine the contractor cannot plan based on

00:49:36 --> 00:49:42

days. A day is too long. A day is 25 times six hours. That's 150,000

00:49:42 --> 00:49:42

hours. That's \$150,000.06

00:49:44 --> 00:49:47

hours, because they only work six hours from midnight to 6am

00:49:48 --> 00:49:53

you cannot even schedule by the hour, because, again, \$25,000 is a

00:49:53 --> 00:49:58

big chunk. So the activities were drawn by the minute. This activity

00:49:58 --> 00:49:59

is going to take 12 minutes. This one's.

00:50:00 --> 00:50:02

Want to take 15 minutes. It's one seven minutes and so

00:50:04 --> 00:50:07

on. So in turn around or plan shut down work, that's another example.

00:50:08 --> 00:50:11

Durations might be set in terms of shifts or even hours and minutes.

00:50:12 --> 00:50:16

If the schedule is conceptual, durations might be staged or

00:50:16 --> 00:50:20

stated in longer units, such as weeks, months or even years. So I

00:50:20 --> 00:50:22

want to develop a new city

00:50:24 --> 00:50:27

now. The new city is going to take seven years to develop, or

00:50:27 --> 00:50:31

something like the Olympic Games. I am planning for the Olympic

00:50:31 --> 00:50:36

Games eight years in advance. I'm not going to say that on such and

00:50:36 --> 00:50:41

such day. I'm going to install the light switch in the dressing room

00:50:42 --> 00:50:46

of the swimming pool, for example. I cannot do that at the very

00:50:46 --> 00:50:51

beginning, but I would say that the swimming pool should start in

00:50:51 --> 00:50:54

such on such and such date and finish on such and such date,

00:50:54 --> 00:50:57

without putting much detail in between. I just want some

00:50:57 --> 00:51:01

milestones or major events. So in this case, the duration might be

00:51:01 --> 00:51:03

in months or even in weeks.

00:51:05 --> 00:51:07

For most typical construction schedules, we're going to use days

00:51:08 --> 00:51:08

as a unit of time.

00:51:12 --> 00:51:13

CPM days

00:51:15 --> 00:51:17

are work days plus one.

00:51:19 --> 00:51:23

So the CPM day is also referred to as the morning of the project

00:51:23 --> 00:51:29

workday, and also known as the ordinal dates. And that brings us

00:51:29 --> 00:51:33

back to the discussion, why do we start the project on day zero and

00:51:33 --> 00:51:34

not on day one?

00:51:35 --> 00:51:40

And if an activity has a duration of seven days and starts on day

00:51:40 --> 00:51:45

zero, it ends on zero plus seven. That's seven days. Shouldn't the

00:51:45 --> 00:51:49

following activity start the following day? Because we have

00:51:49 --> 00:51:53

reached the end of day seven, we cannot do anything yet, so we're

00:51:53 --> 00:51:57

going to wait until the morning of day eight. Therefore the start of

00:51:57 --> 00:52:00

the following activity is going to be on day eight. That's going to

00:52:00 --> 00:52:03

be really confusing, because when you look at one activity ending on

00:52:03 --> 00:52:06

day seven, the following one starting on day eight, where did

00:52:06 --> 00:52:10

they they go? So from now on, we're always gonna discuss we're

00:52:10 --> 00:52:14

gonna always calculate it based on the start of the day.

00:52:15 --> 00:52:20

If we start on the morning of Day Zero, add seven days, let's count

00:52:20 --> 00:52:22

together zero, that's day. 01234567,

00:52:29 --> 00:52:30

how many is that?

00:52:33 --> 00:52:34

Eight?

00:52:35 --> 00:52:36

So let's do it again.

00:52:37 --> 00:52:38

0123456,

00:52:42 --> 00:52:47

basic, basically, we miscounted. Let's do the counting again. We

00:52:47 --> 00:52:50

start on day zero with the duration of seven days. So

00:52:50 --> 00:52:50

0123456,

00:52:56 --> 00:53:00

how many fingers? Seven fingers. What's the last number? I counted

00:53:00 --> 00:53:06

six. So how come zero plus seven is six? No zero plus seven is

00:53:06 --> 00:53:10

seven. But we're saying that this is the end of day number six,

00:53:10 --> 00:53:14

which is the same as the beginning of day number seven. So we're

00:53:14 --> 00:53:17

always going to count from the beginning of the days. So end of

00:53:17 --> 00:53:21

day six same as beginning of day number seven. Therefore zero plus

00:53:21 --> 00:53:25

seven is seven. We ended the activity on the beginning of day

00:53:25 --> 00:53:28

number seven. We're going to start it successor on the beginning of

00:53:28 --> 00:53:32

day number seven. So the number at the end node is seven. The number

00:53:32 --> 00:53:35

of the start of the following node is also seven.

00:53:36 --> 00:53:39

So make sure you all you always measure from the start of the day

00:53:40 --> 00:53:41

to the start of the following day.

00:53:42 --> 00:53:47

Now these numbers that we are calculating are in workdays,

00:53:48 --> 00:53:52

because we did not include any holidays, any weekends. However,

00:53:53 --> 00:53:56

sometimes the schedule, or most of the time the schedule, is

00:53:56 --> 00:53:58

represented in calendar days,

00:53:59 --> 00:54:03

so we need to make some modification. If I have, for

00:54:03 --> 00:54:05

example, a five

00:54:06 --> 00:54:11

day working week and the activity duration is 10 days, then we're

00:54:11 --> 00:54:15

talking about two weeks. So that's the conversion between calendar

00:54:15 --> 00:54:17

days and work days.

00:54:19 --> 00:54:21

What is a work day?

00:54:22 --> 00:54:25

Unless otherwise specified, the contractor will be permitted. This

00:54:25 --> 00:54:29

is an exemplary contract clause. The contractor will be permitted

00:54:29 --> 00:54:32

to do the work between the hours of 7:45am to 4:30pm

00:54:33 --> 00:54:37

Monday through Friday. Federal holidays that fall within the work

00:54:37 --> 00:54:41

week will not be considered work days prior to the contractor

00:54:41 --> 00:54:45

performing any work during hours other than those specified, the

00:54:45 --> 00:54:48

contractor shall submit an overtime request to the owner's

00:54:48 --> 00:54:52

representative for review and approval. Overtime requests shall

00:54:52 --> 00:54:52

be submitted

00:54:54 --> 00:54:58

no less than 24 hours prior to the time the contractor designs

00:54:58 --> 00:54:59

desires to work.

00:55:00 --> 00:55:04

It so again, if you want to work out of the traditional work week,

00:55:04 --> 00:55:07

out of the traditional work day, you have to submit a request to

00:55:07 --> 00:55:08

the engineer for their proof.

00:55:12 --> 00:55:14

00:55:16 --> 00:55:20

So if we were supposed to work but there was a storm, for example,

00:55:20 --> 00:55:20

that

00:55:22 --> 00:55:23

forced us to shut down the work.

00:55:24 --> 00:55:28

It may be broadly defined to exclude weekends.

00:55:30 --> 00:55:34

Work Day may be broadly defined to exclude weekends, holidays and

00:55:34 --> 00:55:37

those days on which no work can be performed. So for example,

00:55:38 --> 00:55:42

something like a storm that forced us to close every all the work on

00:55:42 --> 00:55:46

site. Then in this case, it's excluded from the calculations of

00:55:46 --> 00:55:50

the workdays. What constitutes a day on which no work can be

00:55:50 --> 00:55:54

performed, a national holiday weekend, unless stated otherwise,

00:55:55 --> 00:55:58

and other designated non work days for maintenance and other

00:55:58 --> 00:56:01

purposes. So for example, we have the Fourth of July, Christmas Day,

00:56:01 --> 00:56:06

Thanksgiving, sometimes New Year's Day. These are these would be

00:56:06 --> 00:56:10

designated initially as non work days in the calendar of the

00:56:10 --> 00:56:13

project, so that you wouldn't include them in your workday

00:56:13 --> 00:56:14

calculations.

00:56:17 --> 00:56:21

Work days versus calendar days. Now, when the owner says, you have

00:56:21 --> 00:56:24

200 days to finish this project. Are we talking about work days or

00:56:24 --> 00:56:29

calendar days in most of the cases, unless stated otherwise,

00:56:29 --> 00:56:32

we're talking about calendar days. So you have to make that

00:56:32 --> 00:56:35

conversion. You have to retranslate these 200 work leads

00:56:35 --> 00:56:39

200 days into their work equivalent by subtracting all the

00:56:39 --> 00:56:43

holidays and the weekends and so on. In general, if a project is

00:56:43 --> 00:56:46

vulnerable to the weather, or if the weather can dramatically

00:56:46 --> 00:56:50

impact work progress, scheduling with work days is favorable, then

00:56:51 --> 00:56:54

the owner might say, I'm going to give you 200 work days because we

00:56:54 --> 00:56:57

don't know we're going to be working in winter. We might have

00:56:57 --> 00:57:02

some interruptions. I can, I cannot determine the number of the

00:57:02 --> 00:57:06

exact date. So I'm going to give you 200 work days in heavy

00:57:06 --> 00:57:09

construction site work may be a significant component of the

00:57:09 --> 00:57:12

project and susceptible to adverse weather as well as soil

00:57:12 --> 00:57:13

conditions, etc.

00:57:15 --> 00:57:17

Building Construction may be less susceptible to weather, because

00:57:17 --> 00:57:20

once you're done with the skeleton, most of the activities

00:57:20 --> 00:57:23

that take place indoors can be done any time of the day, any time

00:57:23 --> 00:57:24

of the year.

00:57:25 --> 00:57:29

Use of workdays or calendars. The calendar days may be guided by the

00:57:29 --> 00:57:32

contract. So the contract is going to say whether that number of days

00:57:32 --> 00:57:38

is calendar days or work days, if not mentioned, it means calendar

00:57:38 --> 00:57:42

days. Certain project durations may be defined by a specific

00:57:42 --> 00:57:45

calendar date or milestone date, again, that's going to be

00:57:45 --> 00:57:49

specified in the segment or the section in this in the

00:57:49 --> 00:57:51

00:57:54 --> 00:57:58

the work days usually can be converted to calendar days or

00:57:58 --> 00:57:59

calendar days to work days.

00:58:02 --> 00:58:06

Pros and concerns of using work they scheduled is the project on

00:58:06 --> 00:58:10

track? Is the project not on track? We will have to look at

00:58:10 --> 00:58:14

that one once we start performing calculations in the following

00:58:14 --> 00:58:14

lectures.

00:58:17 --> 00:58:22

And now here's a problem for practice. You have to draw a

00:58:22 --> 00:58:24

network and arrow network for the following project. You have the

00:58:24 --> 00:58:28

activities dependencies, or IPAs, and they have, you have the

00:58:28 --> 00:58:32

durations of the activities. You have to now, you are given the

00:58:32 --> 00:58:38

activity as only one designator, which is basically an i j. So you

00:58:38 --> 00:58:41

are given the name on the arrow and not the nodes. You have to

00:58:41 --> 00:58:43

come up with the names of the nodes.

00:58:45 --> 00:58:48

So calculate the duration of the project and calculate early start,

00:58:48 --> 00:58:52

early finish. Late start, late finish, total float and free float

00:58:52 --> 00:58:53

on each activity.

00:58:55 --> 00:58:58

That's basically our discussion for today. You're going to find

00:58:58 --> 00:59:01

some solved examples on the web as well that show you how to solve

00:59:01 --> 00:59:02

these problems. So.

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