1. Operations Research
Lecture 9

2. Operations Research
CPM / PERT

3. FLOATS INDEPENDENT FLOAT
Time by which an activity can expand without affecting other (PREV or SUBSEQ)
I = jE - iL - D
If Negative, take I = 0

4. Cont !
FREE FLOAT
Time by which an activity can expand without affecting subsequent activity.
F = jE - iE - D

5. Cont !
TOTAL FLOAT
Time by which an activity can expand without affecting the overall duration of the project.
T = jL - iE – D

6. Example 8 2 15 Activity 2-8 T = jL – iE – D = 39 – 16 – 15 = 9
F = jE – iE – D = 38 – 16 – 15 = 7
I = jE – iL – D = 38 – 24 – 15 = -1

7. Example 2 5 6 8 1 2 3 4 4 3 7 4 6 8 5 9 6

8. E=11
E=1
E=8
E=6
E=0 2 5 6 8 1 2 3 4
L=12
L=10 4 3 7
E=15
E=21 4 6 8 5 9 6
L=6
L=21
L=15
E=15
L=0
L=10
L=15

9. Cont ! ACT DUR START FINISH FLOAT E L E L T F I 1-2 1 0 9 1 10 9 0 0

10. Cont ! ACT DUR START FINISH FLOAT E L E L T F I 4-5 5 6 7 11 12 1 0 0

11. Cont ! 2 5 4 7 8 1 3 6 E=11 E=1 2 L=12 L=10 1 3 E=15 E=21 E=0 E=6 6 49
L=15 8
L=21
L=0
E=15 4
E=8 5 3 6
L=10
L=15

12. Example 6 4 5 25 40 2 3 4 7 20 5 10 50 55 3 9 2 8 15 30 45 12 35

13. Cont ! E=11 E=17 5 25 40 L=16 L=22 E=26 E=11 E=18 E=0 E=4 2 3 4 7 20 510 50 55
L=23
L=4
L=16
L=0
L=26
E=6 3 9
E=4 2
E=18 8 15 30 45
L=6
L=18
L=4
E=6 12 35
L=6

14. Cont ! 6 4 5 25 40 2 3 4 7 20 5 10 50 55 3 9 2 8 30 15 45 12 35

15. Cont… (Example)
ACTI DUR START FINISH FLOAT
E L E L T F I

16. Cont… (Example) ACTI DUR START FINISH FLOAT E L E L T F I

17. Example: Following table gives the activities of a construction project and duration.
Activity
Duration
1 - 2 20
1 - 3 25
2 - 3 10
2 - 4 12
3 - 4 6
4 - 5

18. Cont !
Draw the network for the project. Find the total, free and independent floats for each activity. Find the critical path.

19. Cont ! 2 12 20 10 10 1 4 5 25 6 3

20. PERT

21. Non Cooperation from the workers Transport not effective
Example
Supply of materials not in time
Non Cooperation from the workers
Transport not effective

22. Duration uncertain

23. Duration uncertain

24. Operations Research
Lecture 9