# Ihab Saad – Solved Example network constraints

The speaker discusses the network's three constraints: activity E, activity F, and activity J, and how they will be solved. They also discuss the duration of each activity and how it will affect the network's performance. The importance of activity J and activity K is highlighted, along with the importance of marked critical activities. The speakers outline the critical activities and encourage the audience to try solving the problem of finding the right critical path, while also mentioning a new class and asking for the audience to try solving the problem of finding the right critical path.
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All right, now we're going to look at a salt example on network

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constraints. So here we have a network that we're going to fill,

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we're going to solve, and we're going to fill this table with the

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dates, noticing that this network has three constraints. One of them

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is a start no earlier than constraint on activity e, start no

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earlier than day 28

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and one is start on day 33 on activity I, and the third one is

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finish no earlier than this is a start, no later than day 28 This

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is start on and this is finished no earlier than day 49 for

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activity j, so let's go ahead and start solving this network. Here

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are the durations for the different activities. We're going

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to start with activity A, it's going to start on day zero

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with a duration of eight, so it's early finishes day eight.

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Activity B, no lag, no overlap, is going to start on day eight, and

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duration 10 days is going to finish on day 18.

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Activity C, again, no lags, no overlaps, is going to start on day

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eight again, and it's going to end on day 23.

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So far. It's very straightforward, very simple

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for activity. D, we had a finish to finish relationship with the

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lag of nine days. So it's going to finish nine days after the

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completion of B. B ends on day 18, so D is going to end on day 27

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assuming contiguous duration. It's gonna end. It's gonna start on day

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20, which is seven days earlier, because the duration is seven

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now going to activity. E, from C, we have no lag, no overlap, finish

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to start. So from C, we have day 23 what should we put at the start

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of E the constraint says, Start no later than day 28 so what should

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we put here 23 or 28 first of all, this is a late date constraint, so

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it does not have any effect whatsoever in the forward pass. So

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in the forward pass as if it does not exist, because the left side

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of the triangle is white, is not shaded. So we're going to follow

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the calculations, therefore we're going to have 23 for the start of

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activity e, its duration is 16 days. So it's going to finish on

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day 39

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activity f starts 13 days after the start of C. C started on day

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eight, so f is going to start 13 days later on day 21 duration 10

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days. So it's going to finish on day 31

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as you can see, very simple calculations and very

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straightforward so far. Now moving to activity. G finished to start

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with D, D ends on day 27 so G is going to start on 27 nine days of

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duration. Therefore is going to finish on day 36

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activity. H, we have two numbers. The number coming from E was the

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early finish for E is 39 so 39 and the duration of H is 17. So it

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should finish on the on day 50. But from D, we have 27 minus

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three, which would be 24 so we're going to take the larger number,

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of course, because we're moving the forward pass, therefore E is

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going to be driving H. So we're going to have from E 39

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plus a duration of,

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yeah, E was 39 duration of 17 days. So that's 56 so

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is notice that activity is open ended. It does not have any

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relationship to any other activities later on, now going to

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activity I.

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Activity i has an on constraint start on day 33 so immediate, even

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without looking at any numbers coming from any other activity,

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we're gonna plug in 33

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here and

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here as well.

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Because again, this is Start no earlier than start no later than

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which means start on 33 so we put Early Start 33 and late start is

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33 as well. And that's going to create a critical point here in

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activity. I

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now go into activity j

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and if it.

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Starts on day 33 it has a duration of 11 days. So it's going to

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finish. The early finish is going to be day 44

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going to activity J, finish to start with G, so we have no lags,

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no overlaps. So 36

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the duration is

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13.

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It says

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finish no earlier than day 49 which is exactly the date that

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comes from the calculations. So there's no conflict between the

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calculations and the constraint. Therefore the calculation still

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holds. So we're going to put here 49

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and finally activity K. We have two numbers coming to K. We have

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either from the start, we have 49 coming from J, or from the finish,

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we have 44 plus 12, which is 56 coming to the end of K. The

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duration of k is

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eight days. So 49 plus eight is 57 which is going to be larger than

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the number coming from i, so j is going to be driving activity k. So

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here we're going to put

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49 so and 57

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and that's our forward pass. Now we're gonna put 57

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as the late finish of activity. Oops. That's not the proper

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location.

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We're gonna put late finish of activity K as 57

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let's just change the color here.

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So 57

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and going backwards, the duration is eight, so the late start is

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going to be 49 so obviously activity K, as we can see, is

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going to be critical. So we're going to just mark it as critical.

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Okay, and if it's critical, total float is zero and free float is

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zero.

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Now going back to activity J. Activity J is the one that drove

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activity i. So most likely, as we can see, the longest path is going

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to be here at the top activity j is going to be critical as well.

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So here we have

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49

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minus 13. That's 36

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So this, again, is a critical activity.

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So any critical activity, zero. Total float, zero, free float,

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going to activity G, I'm just skipping the other ones here for a

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second. Activity G is going to be 36

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not again,

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not the right cell, 36

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and 27

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so again, this is going to be critical

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and zero and zero as total and free floats

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going to activity D again, we can imagine that the critical path is

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going to go through D and B and A. So D

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is going to be 27

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and 20

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zero

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and zero. And here is going to be critical as well.

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Activity B, we have 20 here, 20 minus nine.

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No, we have 27 at the end. 27 minus nine is going to give us 18

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and eight

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and zero and zero for the total and free floats. And again, B is

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critical.

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And finally, a is going to be basically

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eight

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and zero,

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and here we have zero and zero and again, A is going to be critical

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as well.

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So these are my critical activities. I.

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E, we have 23

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minus the duration, which is 15. So

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the early start of activity C, coming from E is going to be 23

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minus 15, which is eight, looking at the numbers coming from F, from

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F, we have

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the finish, the start of F, late start of F was 21 minus 13, so

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it's going to give eight. So in both cases, going to be eight,

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therefore we don't have any problem. So here we're going to

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have eight.

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And the duration for C is 15. So it is 23

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very interesting here again. What about active let's, let's just

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make sure that these numbers are correct. So here at E, we had

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late start,

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24

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Oh, 24 not 23 so 2324

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minus, 15, that would be Nine.

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And from F, it would be again,

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33 and 2323

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minus 13, it would be

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10. So we have 10 coming from F and we have nine coming from E.

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Therefore is going to be nine

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and

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24

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looking at the total float for activity c is going to be one day.

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Free float for E was also one day, therefore the total, the free the

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total float for E is one day, therefore the free float for C is

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zero. And here's our network with all the calculations. Here are the

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critical activities. And we have a half critical activity here in i,

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which is a something that we haven't seen before, and that's

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all because of this constraint. I hope this example helps you

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understand how the constraints work when they are in effect, I

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would like you to try to solve this problem again without looking

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at our answer. Just copy the problem and try solving it on your

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own, and then compare your answers to the one that you have here in

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this presentation. I'll see you in another class. You.

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