# Ihab Saad – Solved Example network constraints

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## AI: Transcript ©

All right, now we're going to look at a salt example on network

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

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

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

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

earlier than day 28

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

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

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

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

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

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

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

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

duration 10 days is going to finish on day 18.

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

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

So far. It's very straightforward, very simple

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

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

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

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

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

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

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

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

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

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

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

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

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

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

day 39

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

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

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

as you can see, very simple calculations and very

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

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

duration. Therefore is going to finish on day 36

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

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

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

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

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

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

plus a duration of,

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

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

relationship to any other activities later on, now going to

activity I.

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

without looking at any numbers coming from any other activity,

we're gonna plug in 33

here and

here as well.

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

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

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

activity. I

now go into activity j

and if it.

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

finish. The early finish is going to be day 44

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

no overlaps. So 36

the duration is

13.

It says

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

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

calculations and the constraint. Therefore the calculation still

holds. So we're going to put here 49

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

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

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

duration of k is

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

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

here we're going to put

49 so and 57

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

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

location.

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

let's just change the color here.

So 57

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

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

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

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

zero.

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

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

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

So here we have

49

minus 13. That's 36

So this, again, is a critical activity.

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

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

second. Activity G is going to be 36

not again,

not the right cell, 36

and 27

so again, this is going to be critical

and zero and zero as total and free floats

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

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

is going to be 27

and 20

zero

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

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

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

and eight

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

critical.

And finally, a is going to be basically

eight

and zero,

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

as well.

So these are my critical activities. I.

E, we have 23

minus the duration, which is 15. So

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

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

F, we have

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

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

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

have eight.

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

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

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

late start,

24

Oh, 24 not 23 so 2324

minus, 15, that would be Nine.

And from F, it would be again,

33 and 2323

minus 13, it would be

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

Therefore is going to be nine

and

24

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

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

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

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

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

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

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

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

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

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

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

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