# Ihab Saad – PDM Solved Example

The speakers discuss various problems in construction management, including overlap and contiguous duration, and the network activities of various activities. They explain how the network works and the critical path, emphasizing the importance of the total float and the critical path in determining the optimal level of activity. They also discuss the importance of the critical path and how it will be different for each successor, emphasizing the importance of understanding the math in calculating PDM.
00:00:06 --> 00:00:08

Foreign welcome again to

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

problems in construction management, and today we're going

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

to talk about some PDM solved examples, presence Diagramming

00:00:18 --> 00:00:21

Method, as we have discussed it in the previous lecture. So let's

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

have a quick look at this example. Here, very simple problem. As you

00:00:25 --> 00:00:29

can see, the activities are represented by boxes. Each box has

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

the name of the activity and its duration, and then we have the

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

links, or the relationships between the activities. Some of

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

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

here. Some of them are start to start with lag. Some of them are

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

finished to start with overlap, which is a negative lag, and so

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

on.

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

Now we're going to assume contiguous duration for the

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

activity, which means once the activity starts, it should keep

00:00:58 --> 00:01:02

going without any interruption. As you may notice, here in this

00:01:02 --> 00:01:07

network, we have activity B with an open end from the finish side.

00:01:07 --> 00:01:10

So we're going to see. How does that affect the calculations? Now,

00:01:10 --> 00:01:14

starting the calculations, we're going to start from the start side

00:01:14 --> 00:01:18

of the activity A, which is the absolute left of the network.

00:01:19 --> 00:01:23

And as we assume, the network's going to start on day zero.

00:01:24 --> 00:01:27

So it's going to start on day zero, and as the duration is 12,

00:01:27 --> 00:01:32

then it's going to end on day 12. Looking at the activities B, C and

00:01:32 --> 00:01:37

D, they have a finish to start relationship with activity A. So

00:01:37 --> 00:01:45

all of these activities are going to start on day 12. So and with

00:01:45 --> 00:01:48

their respective durations. Activity B has eight days, so it's

00:01:48 --> 00:01:52

going to finish on day 20. Activity C, 15 days ending on day

00:01:52 --> 00:01:56

27 and activity D, 14 days ending on day 26

00:01:57 --> 00:02:00

now looking at the following activities, activity e has only

00:02:00 --> 00:02:04

one immediate predecessor, which is b. So from B, we're going to

00:02:04 --> 00:02:08

take the 12 to get the start of activity e. It's a relationship of

00:02:08 --> 00:02:12

start to start, but it has four days of lag. Therefore the start

00:02:12 --> 00:02:17

of activity e is going to be 12, plus four days of lag here, which

00:02:17 --> 00:02:23

is going to be 16, with a duration of 11 is going to end on day 27

00:02:24 --> 00:02:29

for activity f, it has one immediate predecessor. C finished

00:02:29 --> 00:02:32

to start with two days of overlap, which is the negative lag here,

00:02:33 --> 00:02:37

which means activity f is going to start two days before the

00:02:37 --> 00:02:40

completion of activity c. Therefore the expected start for f

00:02:40 --> 00:02:46

is going to be 27 plus negative two, which is 27 minus two, that's

00:02:46 --> 00:02:50

25 its duration is seven days. So it's going to be expected to

00:02:50 --> 00:02:51

finish on day 32

00:02:52 --> 00:02:57

activity G has only one immediate predecessor. D finished to start,

00:02:57 --> 00:03:01

no lag, no overlap. Therefore it's going to start on day 26 with a

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

duration of 10 days, is going to end on day 36

00:03:05 --> 00:03:10

going to activity h, it has two immediate predecessors, E and F.

00:03:10 --> 00:03:16

And the dates coming from E are 27 and from F, 32 this is the forward

00:03:16 --> 00:03:19

pass. We're moving forward. Therefore we're going to take the

00:03:19 --> 00:03:22

larger of the two numbers. So for the start of activity, h is going

00:03:22 --> 00:03:27

to be day 32 with the duration of 16 is going to end on day 48

00:03:29 --> 00:03:34

activity I also has two immediate predecessors, but it's quite

00:03:34 --> 00:03:37

interesting here, because the immediate predecessors link at two

00:03:37 --> 00:03:41

different locations. So let's look at the dates coming to the start

00:03:41 --> 00:03:46

of I from these two respective activities. From F, we have 32 no

00:03:46 --> 00:03:51

lag, no overlap. So if it had only F as a predecessor, it should

00:03:51 --> 00:03:55

start on day 32 but it has another predecessor, which is G. We

00:03:56 --> 00:04:01

notice that the relationship with G is finish to finish. Look at the

00:04:01 --> 00:04:06

connecting points on the relationship finish to finish with

00:04:06 --> 00:04:11

five days of lag, which means I should finish five days after the

00:04:11 --> 00:04:15

completion of G. Now let's calculate the two dates going to

00:04:15 --> 00:04:20

the start and the finish of this activity. If we were going to use

00:04:20 --> 00:04:27

32 from f. It would be 32 at the start, plus 18, that would give 50

00:04:27 --> 00:04:31

at the end, at the end of activity i, if we were to take only

00:04:31 --> 00:04:36

activity G, it would be 36 plus five, that would be 41 so the

00:04:36 --> 00:04:40

larger of two numbers comes comes from activity f. Therefore we can

00:04:40 --> 00:04:45

say that activity f is the one that drives activity I, therefore

00:04:45 --> 00:04:46

we're going to take the 32

00:04:48 --> 00:04:50

plus 18, that's 50.

00:04:52 --> 00:04:56

Now looking at activity j, the last activity in the network. We

00:04:56 --> 00:04:59

we have two immediate predecessors with the numbers 48 and 50.

00:05:00 --> 00:05:03

Coming from H and I respectively. We're going to take the larger

00:05:03 --> 00:05:06

number, since we are still in the forward pass, so it's going to be

00:05:06 --> 00:05:13

50 plus nine, and the early finish of this network is day 59 now we

00:05:13 --> 00:05:16

are done with the forward pass again. What did we do in the

00:05:16 --> 00:05:21

forward pass? We moved from left to right, adding the durations,

00:05:21 --> 00:05:25

00:05:25 --> 00:05:29

two, if you notice what I said here, plus negative two, which is

00:05:29 --> 00:05:34

the same as minus two. So we just keep moving from left to right,

00:05:34 --> 00:05:40

adding the durations and the legs and the overlaps until we reach

00:05:40 --> 00:05:43

the end of the network, and that gives the early finish of the

00:05:43 --> 00:05:47

network. Now we're going to start the trip backwards. So we're going

00:05:47 --> 00:05:52

to start from the end of activity j and the early finish is 59 it's

00:05:52 --> 00:05:55

going to be the same as the late finish. So we're going to drop

00:05:55 --> 00:05:59

here, 59 minus nine. Now we're moving backwards, so we're going

00:05:59 --> 00:06:06

to subtract, which gives 50 at the late start of activity J. The

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

first thing to notice is that the early start and the late start are

00:06:10 --> 00:06:14

exactly the same. The early finish and the late finish are the same.

00:06:15 --> 00:06:19

Therefore, what's the total float of activity J? Basically it's

00:06:19 --> 00:06:23

zero, which means activity j is critical. And this is something

00:06:23 --> 00:06:27

that we can conclude, and we can expect, usually in a network like

00:06:27 --> 00:06:31

this, starting with one activity and ending with one activity,

00:06:31 --> 00:06:34

usually the first and the last activities are going to be

00:06:34 --> 00:06:38

critical, since there's going to be one continuous path linking

00:06:38 --> 00:06:41

these two activities from beginning to end, therefore

00:06:42 --> 00:06:44

they're going to fall on that critical path, or that longest

00:06:44 --> 00:06:48

path in the network. Now we have to move back and see which other

00:06:48 --> 00:06:51

activities are going to be critical and where's the critical

00:06:51 --> 00:06:55

path going to be. So this 50 is going to be transferred, basically

00:06:56 --> 00:07:00

to the finish of activity h and the finish of activity i, and then

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

we're going to subtract the durations, and we have here 50

00:07:04 --> 00:07:09

minus 16, that's 34 at the late start of H, and 50 minus 18,

00:07:09 --> 00:07:14

that's 32 at the late start of i, we notice again for activity I,

00:07:15 --> 00:07:20

the dates are exactly the same at both sides. So early start, late

00:07:20 --> 00:07:24

start, early finish and late finish, the early and late dates

00:07:25 --> 00:07:28

are pretty much the same. Therefore this is another critical

00:07:28 --> 00:07:33

activity. But looking at activity h, we notice that the late finish

00:07:33 --> 00:07:36

is different from the early finish and the late start is the

00:07:36 --> 00:07:41

different different from the late from the early start, which means

00:07:41 --> 00:07:44

this is going to be what we call the total float. Total float is

00:07:44 --> 00:07:48

late minus early, either from the start or the finish for the time

00:07:48 --> 00:07:52

being. So late finish minus early finish, or late start minus early

00:07:52 --> 00:07:56

start. So the total float for activity h is going to be two

00:07:56 --> 00:08:01

days. Now, remember the sad method that I told you about when we try

00:08:01 --> 00:08:05

to calculate the free float of activity h we said that the free

00:08:05 --> 00:08:10

float of an activity is going to be its total float minus the total

00:08:10 --> 00:08:14

float of its immediate successor, or the largest total float of any

00:08:14 --> 00:08:17

of its immediate successors if it has more than one immediate

00:08:17 --> 00:08:21

successor. So looking here, this is an activity that has two days

00:08:21 --> 00:08:26

of total float with only one immediate successor which has zero

00:08:26 --> 00:08:30

days of total float. Therefore, the free float for activity h is

00:08:30 --> 00:08:34

going to be exactly the same as its total float, which is also

00:08:34 --> 00:08:38

equal to two days activity I of course, since it's critical, and

00:08:38 --> 00:08:43

by default, any critical activity has zero total float and zero free

00:08:43 --> 00:08:48

float as well. Now let's move back going to, for example, activity e,

00:08:49 --> 00:08:52

we're going to find that it has only one immediate successor,

00:08:52 --> 00:08:56

therefore that 34 is going to be transferred here as is, because

00:08:56 --> 00:08:58

there's no lag or overlap.

00:08:59 --> 00:09:04

And for activity f, which has two immediate successors. We have 34

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

coming from H, 32 coming from I remember, this is the backward

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

pass. So we take the smaller number. Therefore we're going to

00:09:13 --> 00:09:18

take, here the 32 so let's look at the numbers here. For example, we

00:09:18 --> 00:09:24

have 50 minus five, which is the lag. So it's going to end on day

00:09:24 --> 00:09:30

45 minus the duration 10 is going to start on day 35 and here we

00:09:30 --> 00:09:35

have the 32 which is the smaller of the two numbers, 32 and 3432

00:09:36 --> 00:09:41

minus seven. That's 25 and here we're going to have 34 and 2334

00:09:42 --> 00:09:44

minus 11. That's 23

00:09:46 --> 00:09:49

as you notice, we are moving one column at a time. We're not moving

00:09:49 --> 00:09:52

to the whole beginning of the network. We're taking it one

00:09:52 --> 00:09:53

column at a time.

00:09:55 --> 00:09:58

All right now if we move back to activity D, for example, it has

00:09:58 --> 00:09:59

only one immediate success.

00:15:00 --> 00:15:03

Minus nine, which gives 30 at the beginning. But here from E, we

00:15:03 --> 00:15:10

have 3033 plus negative two, which gives 31 larger than the 30. So e

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

is driving G, therefore it's going to be 31 and nine is 40 activity.

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

H is going to be here we have again, 33 and 30. We're going to

00:15:19 --> 00:15:21

take the larger number, the 33 plus 841,

00:15:23 --> 00:15:27

again, looking at activity, I we have numbers coming from both

00:15:27 --> 00:15:35

sides. If we look at G, is going to be 40 plus 12, that's 52 if we

00:15:35 --> 00:15:39

look at H, it's going to be 41 plus nine. That's 50 at the end.

00:15:39 --> 00:15:45

So at the end we have from G 52 from H 50 we're going to take the

00:15:45 --> 00:15:48

larger number. So here we're going to have 40 and 52

00:15:49 --> 00:15:53

that's the forward pass. Very simple, very straightforward. We

00:15:53 --> 00:15:57

add the numbers as we are moving from left to right now starting

00:15:57 --> 00:16:01

the backward pass again, the late finish is going to be the same as

00:16:01 --> 00:16:06

the early finish. So it's going to be 52 minus 12. That's 40 again.

00:16:06 --> 00:16:10

Network starts with one activity ends with one activity. We should

00:16:10 --> 00:16:13

expect the first and the last activities to be on the critical

00:16:13 --> 00:16:18

path. Now think about it for a second. Where is the longest path?

00:16:18 --> 00:16:22

Which path gives the largest numbers. Someone might get

00:16:22 --> 00:16:28

confused and say, well, H is 41 and g is 40 so h is longer. No,

00:16:28 --> 00:16:32

that's a trick, because h goes to the end, but G goes to the

00:16:32 --> 00:16:35

beginning. And we found out that G is the one that drives I,

00:16:36 --> 00:16:39

therefore g must be the one that's critical. So it's going to be

00:16:40 --> 00:16:45

here. We're gonna have 52 minus nine. That's 43 minus 835,

00:16:46 --> 00:16:48

and here we're gonna have

00:16:50 --> 00:16:51

00:16:53 --> 00:16:54

same path.

00:16:56 --> 00:16:58

Here we have the 40 and the 31

00:16:59 --> 00:17:04

now going to activity e, we have, what's the number coming to E,

00:17:04 --> 00:17:09

from G and H, from H, what do we have? We have 35

00:17:10 --> 00:17:17

from G. What do we have? 31 No, it's 31 minus negative two, which

00:17:17 --> 00:17:22

is 31 which is 31 plus two, therefore it's 33 so 33 from G and

00:17:22 --> 00:17:26

35 from H, this is backward pass we take the smaller number. So

00:17:26 --> 00:17:31

we're going to take the 33 minus nine, that's 24 so obviously the

00:17:31 --> 00:17:37

critical path is going to be I, G, E, and then tracing backward.

00:17:37 --> 00:17:41

We're not sure yet whether it's going to be B or C. We're gonna

00:17:41 --> 00:17:46

see in a minute. Here, we're gonna have 40 minus six going to the

00:17:46 --> 00:17:50

end. We did not take a number from the beginning, because we don't

00:17:50 --> 00:17:54

have a relationship here. So 40 minus six, that's 34 minus 14,

00:17:54 --> 00:18:00

that's 20 now here at C, we have 24 coming from E,

00:18:01 --> 00:18:07

and we have 35 minus seven, which would be a 28 coming to the end of

00:18:07 --> 00:18:13

C, we're going to take the smaller number. So here we have 24 and at

00:18:13 --> 00:18:17

B, also we're going to have 24 and 13. So obviously B is going to be

00:18:17 --> 00:18:23

the critical activity. Moving back to activity. A, here we have 11.

00:18:23 --> 00:18:28

And from C, we have nine. Again, no, it's nine minus negative

00:18:28 --> 00:18:32

three, which is nine plus three. Therefore the number coming from C

00:18:32 --> 00:18:36

is 12. From B is 11. We take the smaller number, so it's going to

00:18:36 --> 00:18:40

be 11 and zero. And here's our critical path.

00:18:43 --> 00:18:47

Looking at the total and free floats again, for activity D,

00:18:47 --> 00:18:49

obviously we have a total float of one,

00:18:50 --> 00:18:53

its immediate successor is critical. So according to the SAT

00:18:53 --> 00:18:56

method, the free float for D is also one.

00:18:58 --> 00:19:02

Activity H has a total float of two, immediate successor,

00:19:02 --> 00:19:07

critical, therefore the free float is also two. Activity f has total

00:19:07 --> 00:19:11

float of two. Immediate successor has also a total float of two. So

00:19:11 --> 00:19:13

the free float here is going to be zero.

00:19:14 --> 00:19:17

Activity C has a total float of one,

00:19:18 --> 00:19:22

immediate successors. One is critical. One has a total float of

00:19:22 --> 00:19:25

two. We're going to take the largest of the total floats of the

00:19:25 --> 00:19:30

immediate successors. So one minus two gives us negative one. We

00:19:30 --> 00:19:34

agreed before that we cannot have a negative free float. So whenever

00:19:34 --> 00:19:38

you get a negative free float, just put zero, and that would be

00:19:38 --> 00:19:42

the free float. So the free float for activity c is zero, its total

00:19:42 --> 00:19:43

float is one.

00:19:45 --> 00:19:48

As you can see, the calculations are not that hard at all. I hope

00:19:48 --> 00:19:53

that these two examples illustrate the calculations for PDM. The only

00:19:53 --> 00:19:57

thing that you have to pay attention to is, where are the

00:19:57 --> 00:19:59

relationship points starting and finishing?

00:20:00 --> 00:20:03

Is it a finish to start? Is it a start to start? Is it a finish to

00:20:03 --> 00:20:08

finish? Do we have any lags? Do we have an overlaps? And how are

00:20:08 --> 00:20:12

these going to be factored in our calculations? And again, apart

00:20:12 --> 00:20:15

from that, is just very simple math. One of the very common

00:20:15 --> 00:20:19

mistakes that I usually see on assignments, on exams, is errors

00:20:19 --> 00:20:24

in that very simple math like 19 plus 14 equals 34 or 35 or

00:20:24 --> 00:20:27

something like that. Take your time with these initial

00:20:27 --> 00:20:30

calculations, because this is what makes most of the mistakes on

00:20:30 --> 00:20:34

these problems. The math, as you can see, is very simple and very

00:20:34 --> 00:20:37

straightforward. I'll see you later in another lecture and in

00:20:37 --> 00:20:38

another example.

00:20:41 --> 00:20:42

You.

Share Page