Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 1
Chapter 15
Critical path analysis
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 2
Activity on node
A B5 2
Activity identifier
Durations
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 3
EST EFT
LFTLST
A
10
Earliest Start Time
Latest Start Time
Earliest Finish Time
Latest Finish Time
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 4
Objectives of the method
1. Find the total time that the project will take.
2. Identify the activities that are critical to the project.
3. Identify those activities that can be delayed without delaying the completion of the project.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 5
Procedure
1. Break down project into a number of activities.
2. Estimate duration of each activity.
3. Decide on the logical sequence of activities (i.e. the immediate predecessors for each activity).
4. Draw the diagram.
5. Make a forward pass through the network, calculating the earliest start time (EST) and the earliest finish time (EFT) for each activity.
6. Make a backward pass through the network, calculating the latest start time (LST) and the latest finish time (LFT) for each activity.
7. Determine the minimum time that the project can be completed in, the critical path and the floats of all the non-critical activities.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 6
Example
Activity Description Duration Immediate (weeks) Predecessors A Set objectives 2 - B Design TV advertising 5 A C Design new packaging 10 A D Design newspaper campaign 6 B E Film TV advertisements 4 B and C F Arrange Graphics 2 D G Run campaign in local TV region 4 E and F H Assess results 2 G I Arrange national campaign 4 H
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 7
Start A2
B5
C10
D6
E4
F2
G4
H2
I4
END
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 8
Start A2
B5
C10
D6
E4
F2
G4
H2
I4
END
7
2
2 7 13
0
13 15
2 12 12 16 16 20 20 22 22 26 26
Forward pass
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 9
Start A2
B5
C10
D6
E4
F2
G4
H2
I4
END
7
2
2 7 13
0
13 15
2
14
12 16 16 20 20 22 22 26 260 2
3 8
2 12 12 16 16 20 20 22 22 26
8
12
14 16
Backward pass
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 10
• Total time for the campaign is 26 weeks
• Float of an activity is the difference between the latest start time and earliest start time i.e. LST – EST
A: 0; B: 1; C: 0; D: 1; E: 0;
F: 1; G: 0; H: 0; I: 0
• Critical activities are A, C, E, G, H, I
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 11
Critical path
• The critical activities form a critical path.• The critical path is the longest path through the
network. (A–C–E–G–H–I).• There can be more than one critical path.• Any delay to a critical activity will automatically
delay the project.• If you delay a non-critical activity by more than
its float the project will again be delayed.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 12
Other important points
• A project can have more than one start and end. An END node is essential to avoid having ‘dangling’ nodes!
• Always draw the network in pencil so that you can amend it easily.
• Try and avoid crossing lines (sometimes unavoidable).
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 13
Gantt charts
• A CPA chart tells you how activities are related to each other.
• Gantt charts show you when activities occur and if resource problems are likely to occur.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 14
Example 2
A small market research company consists of 6 people who are all adept at dealing with the many and varied problems associated with conducting surveys, such as designing the necessary computer software, briefing interviewers, etc. The company hires interviewers for its surveys and the 6 permanent staff never carry out interviews themselves. Recently, the company was asked to conduct a market research survey for a food manufacturer, and details of the activities which the survey will involve are given below.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 15
Activity Description Preceding Estimated No. of staff* Activities Duration required per week (weeks) A Design survey 6 5 B Print questionnaire A 2 1 C Engage interviewers A 2 3 D Prepare interviewer instruction sheets, etc. A 1 1 E Set up computer software A 2 2 F Brief interviewers C and D 1 1 G Test computer software E 1 2 H Supervise fieldwork B and F 5 4 I Analyse results G and H 3 5 J Prepare report I 2 5
(* excluding interviewers)
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 16
1. Draw a network to represent the project.2. For each activity, calculate the earliest and latest start and finish
times and the total float.3. What is the critical path?4. Ignoring for the moment any possible staff shortages, how long will
it take to complete the survey?5. Draw a Gantt chart to represent the project.6. Calculate the number of permanent staff (i.e. excluding
interviewers) who will be required for each week of the project, assuming that each activity starts as early as possible.
7. Given the number of staff required, can the project be completed in the time calculated in (4)?
8. If one member of staff is ill from weeks 7 to 14, would the
completion of the survey be delayed?
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 17
JH
G
C
AStart F
B
End
2
6
2
1
1
5 2I3
E
D
2
1
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 18
JH
G
C
AStart F
B
End
2
6
2
1
1
5 2
0 6
6 8
I3
E
D
2
1
6 7
6
6
8
8 8 9
8 9 9 14 14 17 17 19
9 14 14 17 17 19
14131311
98
87
6 8
7 9
0 6
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 19
Solutions:(3) The critical path is A–C–F–H–I–J.(4) The project will take 19 weeks.(5) To draw a Gantt chart we use rectangles to
represent the activities. Floats are represented by dotted rectangles.
Each activity starts at its earliest start time.Keep the critical activities together in one line.Add the resources required for each activity in the rectangles.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 20
Gantt chart0 5 10 15 20
Weeks
A 5 C 3
B 1
D1
E 2
F1 H 4 I 5 J 5
G2
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 21
Resource histogramNumber of Staff Required
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Week
Nu
mb
er o
f S
taff
Req
uir
ed
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 22
Resource requirements
• 5 staff required for the first 6 weeks• 7 staff required the next week (week no. 6 )• 6 staff required for the next week (week no. 7)• 3 staff required for the next week (week no. 8)• 4 staff required for the next 5 weeks (9 to 14)• 5 staff required for the remainder of the time
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 23
Smoothing resources• Only 6 staff available but 7 required during
week 6
• Either activity B could be delayed for 1 week
• Or activity E and G could be delayed by 1 week
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 24
Smoothed histogramNumber of Staff Required
0
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Week
Nu
mb
er o
f S
taff
Req
uir
ed
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 25
If one member of staff were ill from weeks 7to 14, would the completion of the survey
bedelayed ? Yes, as there is no way we can delay
activitiesto need only 5 staff.