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

2. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd2 Activity on node

3. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd3 Earliest Start Time Latest Start Time Earliest Finish Time Latest Finish Time

4. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd4 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.

5. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd5 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.

6. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd6 Example

7. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd7 StartA2A2 B5B5 C 10 D6D6 E4E4 F2F2 G4G4 H2H2 I4I4 END

8. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd8 StartA2A2 B5B5 C 10 D6D6 E4E4 F2F2 G4G4 H2H2 I4I4 END 7 2 27 13 0 15 2 12 16 20 22 26 Forward pass

9. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd9 StartA2A2 B5B5 C 10 D6D6 E4E4 F2F2 G4G4 H2H2 I4I4 END 7 2 2 7 13 0 15 2 14 12 16 20 22 26 02 38 212 16 20 22 26 8 12 1416 Backward pass

10. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd10 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

11. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd11 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.

12. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd12 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).

13. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd13 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.

14. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd14 Example 2

15. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd15

16. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd16 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?

17. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd17

18. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd18

19. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd19 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.

20. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd20 Gantt chart

21. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd21 Resource histogram

22. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd22 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

23. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd23 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

24. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd24 Smoothed histogram

25. Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd25 If one member of staff were ill from weeks 7 to 14, would the completion of the survey be delayed ? Yes, as there is no way we can delay activities to need only 5 staff.