Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd1 Chapter 15...

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 1

Chapter 15

Critical path analysis


Activity on node

A B5 2

Activity identifier

Durations


EST EFT

LFTLST

A

10

Earliest Start Time

Latest Start Time

Earliest Finish Time

Latest Finish Time


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.


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.


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


Start A2

B5

C10

D6

E4

F2

G4

H2

I4

END


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


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


• 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


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.


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).


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.


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.


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)


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?


JH

G

C

AStart F

B

End

2

6

2

1

1

5 2I3

E

D

2

1


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


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.


Gantt chart0 5 10 15 20

Weeks

A 5 C 3

B 1

D1

E 2

F1 H 4 I 5 J 5

G2


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


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


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


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


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.

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd1 Chapter 15...

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