Critical Path Analysis Worksheet

Start or end of activity Activity A Length of time Activity B Length of time

A network consists of 2 components

•Circles - Nodes which represent the start or end of an activity •Straight line - actual activity. Above the line - name of activity, below the line - estimated time of activity. •Activities are shown as arrows running from left to right. •Their length has no significance.

So, for example… Task A B C D E Preceded by: A B B C, D Duration 2 1 4 3 2

A

2 1

B

4

C D

3

E

2 …a simple network diagram

Rules for drawing networks

1. The network must start and end on a single node 2. No lines should cross each other 3. Nodes should be numbered 4. There must be no lines that are not activities 5. Due to the need to write figures in the nodes, it is helpful to draw networks with large circles and short lines.

• • •

Earliest start times and latest finishing times

The EST shows the earliest time at which following activities can be started.

The LFT shows the time by which an activity must be completed and the latest finishing time of preceding activities.

ESTs are calculated from left to right and LFTs are calculated from right to left.

Node number Nodes show: e arliest s tart t ime

1

EST LFT l atest f inishing t ime

EST and

simultaneous

activities

ESTs provide 2 key pieces of information:

1. The earliest date certain resources will be needed. Avoids tying up working capital.

2. The earliest completion date for the whole project (the EST on the final node).

LFTs provides 3 pieces of information:

1. The deadlines that must be met in order for the project to be completed on time.

2. Helps to identify the activities that have ‘float time’.

3. It identifies the critical path.

The Critical Path

• • • • The critical path comprises the activities that take the longest to complete.

They determine the length of the whole project.

In our example the critical path is… These activities cannot be delayed by even one day.

Float Time

• Definition: the amount of time that non critical activities within a project can be delayed without affecting the deadline for completion of the project as a whole.

•

Total float for an activity = LFT – EST – duration of the activity.

Exercise – baking a loaf of bread

Activity

A weigh ingredients

Preceded by

-

Elapsed time (minutes)

1 B mix ingredients A 3 C dough rising time D prepare tins E pre-heat oven F knock back dough and place in tins G 2nd dough rising time H cooking time B C&D F E & G 60 1 10 2 15 40

Bread baking – Complete the Critical path (easy)

D 1 1 0 A 1 2 1 1 B 3 C 3 4 60 4 64 F 2 5 G 15 H 6 81 45 7 E 10

1

Bread baking – Complete the Critical Path (hard)

D 1 A 1 2 B 3 3 C 60 4 F 2 5 G 15 6 H 45 7 E 10

Bread baking – Answers

D 1 1 0 0 A 1 2 1 1 B 3 4 3 4 C 60 64 4 64 F 2 66 5 66 G 15 81 6 81 H 45 126 7 126 E 10