Tutorial 11- Network diagrams and CPM PDF

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Tutorial 11- Network diagrams and CPM...

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COMP1821 Critical Path Method Network Diagrams, Critical Path Method

Tutorial: 1. Please use the information provided below to create a network diagram – activity on arrow method.

2. Calculate when each activity will start, see which activities can run in parallel, and how long the project will take overall. 3. Identify the activities that are on the critical path. Activity Id

Activity Name

Duration

A

Lay foundations

10

-

B C D E

Build walls Install plumbing Install electricity supply Install bath & shower unit

12 5 4 3

A B B C

Acknowledgements to Mrs Aditi Rawal for tutorial exercise and solution

Depends on

1

F G H I

Install electric cooker Tile bathroom Paint interior Put on roof

2 6 7 5

D E G, F, I B Solution

Event The start or end of an activity Activity Something that consumes time and/or resources Critical path The 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). The 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. The LET of the last event = EET of the last event. To calculate the LET for the following event you subtract the LET of the last event – the activity duration.

Note that where several activities converge, we can only have one EET and one LET, but there can still be float on some of the activities from this point. When there is a convergence of a number of activities to an event, we calculate the EET and LET as follows:  For EET, we calculate the EETs of all activities. We then take the longest time, as this is the earliest time at which the next activity will be able to start. o For example, 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).  For LET, we calculate the LETs of all activities. We then take the shortest time, otherwise the project would overrun.

Acknowledgements to Mrs Aditi Rawal for tutorial exercise and solution

2

E 40 27,27

50 30,30

3

G

C 6 A 10 0,0

B 20 10,10

10

5

I

H

30 22,22 12

70 36,36 D

4 Finding the Critical Path

5

F

80 43,43 7

2

60 26,34

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

Acknowledgements to Mrs Aditi Rawal for tutorial exercise and solution

3

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. Activity I does have float, but it is not shown on the nodes of the network diagram because the convergence of three different paths through the network. E 40 27,27

3

50 30,30 G

C 6 A 10 0,0

B 20 10,10

10

5

I

H

30 22,22 12

70 x,x D

4

5

60 26,34

F

80 43,43 7

2

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.

Acknowledgements to Mrs Aditi Rawal for tutorial exercise and solution

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