QB250

Tutorial and Lab Session Week 1.4 Tutor Guidelines (Please do not give out to the students but do discuss with them, once they have attempted it)

Network Diagrams, Critical Path Method and Gantt Charts

In order to construct a network diagram, we will use the Activity-on Arrow convention in these notes. If you use MS Project software, it will build a network diagram for you using the alternative convention, Activity-on-Node. Here, as shown in the key below, activities are shown on arrows and events are shown at nodes. A node is the start/end of one or more activities.

An event:

An Activity:

A network diagram is constructed from a list of activities, taking into account the logical sequence. For example, to build a house, we might have the following activities together with the likely length of time in days each would take. The dependencies for each activity are also shown, so we know the logical order in which each activity must take place.

Activity Id

Activity Name

Duration

Depends on

Staff Resources

A

Lay foundations

10

-

5

B

Build walls

12

A

5

C

Install plumbing

5

B

3

D

Install electricity supply

4

B

3

E

Install bath & shower unit

3

C

1

F

Install electric cooker

2

D

1

G

Tile bathroom

6

E

1

H

Paint interior

7

G, F, I

6

I

Put on roof

5

B

3

We can calculate when each activity will start, see which activities can run in parallel, and how long the project will take overall.Forward Pass across Network

The first step is to determine the EET (earliest event time) based on the duration of each activity. We do this by making a forward pass, from left-to-right, over the network. Notice that where activities G, I and F converge on to event 70, the longest time is taken, as this is the earliest time at which the next activity (H) will be able to start. It would not be possible for activity H to start as soon as activity I finished (time 27), or when activity F has finished (time 28), because activity H cannot begin until activities G, I and F have all finished, and that means waiting until activity G has finished (time 36).

EventThe start or end of an activity

ActivitySomething that consumes time and/or resources

Dummy Depicts precedence where no activity is present

Critical pathThe currently most costly path to the end of project. To determine the critical path: Most of the time all that you need to do is follow the route where EET = LET (and use a bit of common sense where there are two possibilities).

EETThe EET of the first event = 0. The EET for the following event is the sum of the EET of the first event + the activity duration ( EET: 0 +10 = 10)

Backward Pass across Network

The next step is to make a backward pass, from right-to-left, working out the LET (latest event time) for each event. Where the LET is later than the EET, it means that it is possible for an activity to be delayed without making the whole project late: this "spare" time is known as float. Sometimes the LET will be the same as the EET; this means that there is zero float, as the activity has to start as soon as the activities on which it depends have finished, or the whole project will be delayed. Note that where several activities converge, we can only have one LET, but there can still be float on some of the activities from this point.

Working backwards, from event 80 to the start, the earliest latest event time needs to be taken.

In this way, the LET for activity H is 36 (time 43 at event 80 minus duration time of 7). Similarly, the LET for activity G is 30 (time 36 at event 70 minus duration time of 6), LET for activity E is 27 (time 30 at event 50 minus duration time of 3), and the LET for activity F is 34 (time 36 at event 70 minus 2). Note that the LET at event 30 is time 22. You might expect the LET at event 30 to be at time 31 (looking at activity I with duration 5), or at time 30 (with activities D and F having a combined duration of 6). We need to choose the earliest latest event time of these three candidates, otherwise the project would overrun.

We choose H G E C for event 30, which is the earliest.

LET = last event activity duration e.g. 43 7 = 36 We go backwards.

Finding the Critical Path

We now know the earliest and latest event times for each activity on the network diagram. The critical path is the route through the network with zero float (i.e. there is no difference between the EET and the LET). Critical path ( EET=LET

Note that although activity I has the same values for its EET and LET, we can see that it is not on the critical path because the EET for the subsequent activity (activity H) is 36. This means that activity I can start at any time between time 22 (the EET) and time 31 (the EET of activity H, minus the duration of activity I). Activity I therefore does have float (or, strictly speaking, "slack"), but it is not shown on the nodes of the network diagram because the convergence of three different paths through the network.

The critical path through the network is shown dotted in red. This shows the activities D, F and I could be delayed within their float time without the project as a whole overrunning, but if any of the other activities is delayed, the entire project will finish late.

Event label

120

25,22

Earliest event time (EET)

Latest event time (LET)

Activity id

Q

12

Duration of activity

A

10

B

12

I

5

H

7

E

3

C

5

G

6

D

4

F

2

10

20

30

60

40

50

70

80

A

10

B

12

I

5

H

7

E

3

C

5

G

6

D

4

F

2

10

0

20

10

30

22

60

26

40

27

50

30

70

36

80

43

A

10

B

12

I

5

H

7

E

3

C

5

G

6

D

4

F

2

10

0,0

20

10,10

30

22,22

60

26,34

40

27,27

50

30,30

70

36,36

80

43,43

A

10

B

12

I

5

H

7

E

3

C

5

G

6

D

4

F

2

80

43,43

70

x,x

50

30,30

40

27,27

60

26,34

30

22,22

20

10,10

10

0,0

1

1