1. Operations Research
Lecture 7

2. Operations Research
CPM / PERT

3. OR PROCESS OBSERVATION PROBLEM DEFINITION MODEL CONSTRUCTION SOLUTIONH N I Q U S
MODEL CONSTRUCTION
SOLUTION
IMPLEMENTATION

4. Critical Path Method (CPM)
Networks
Critical Path Method (CPM)
Program Evaluation and Review Technique (PERT)
Network Flow

5. Example Obtain Stamp Write a Letter Put in Env. Address & Stamp Post3 8 16 12 14
Obtain
Envelope 7

6. Dummy Activities
There is a need for dummy activities when the project contains groups of two or more jobs which have common predecessors. The time taken for the dummy activities is zero.

7. J A C D B F H D3 D1 D2 E G

8. H 5 7 L D I J A B E G K M 4 1 2 3 6 8 9 10 N F 11 C

9. Looping 8 9 10 9 10

10. Dangling 10 8 9 9 11

11. Merge Node 8 11 9 9 10 10

12. Burst Node 10 5 9 11 12

13. Example
EVENT 16 20
, OR OR
30, OR , OR

14. Cont!
EARLIEST TIME: By Longest Chain
LATEST TIME: Backward Pass
51, 39, 35, 20, 24, 0

15. TIMES (ACTIVITY) EARLIEST START TIME
Earliest possible time at which an activity can start and is given by the earliest time of the Tail Event.

16. TIMES (ACTIVITY) EARLIEST FINISH TIME
Earliest possible time at which an activity can finish and is given by adding the duration time to the earliest start time.

17. TIMES (ACTIVITY) LATEST FINISH TIME
Latest Event Time of the Head Event.

18. TIMES (ACTIVITY) LATEST START TIME
Latest possible time by which an activity start and is given by subtracting the duration time from the Latest Finish Time.

19. Example

20. Cont!
ACTIVITY DURATION START FINISH
E L E L

21. Notations Earliest Time of Tail Event i= iE
Latest Time of Tail Event i = iL
Earliest Time of Head Event j= jE
Latest Time of Head Event j = jL

22. 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

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

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

25. Example 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

26. Example 3 11 4 7 5 10 1 2 5 8 10 6 4

27. Cont ! E=12 L=12 E=23 E=0 E=5 L=5 L=0 L=23 E=13 L=13 3 11 4 7 5 10 1 28 6
E=13 4
L=13

28. For Activity 1 – 3
T = jL - iE – D = = 8
F = jE - iE – D = = 8
I = jE - iL – D = = 8

29. ACTIVITY DURATION FLOATS
T F I
1 – 2 – 3 – 5 !
1 – 2 – 4 – 5 ! CRITICAL PATH

30. Cont ! E=12 L=12 E=23 E=0 E=5 L=5 L=0 L=23 E=13 L=13 3 11 4 7 5 10 1 28 6
E=13 4
L=13

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

32. Example 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

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

34. 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

35. 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

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

37. 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

38. Cont ! ACT DUR START FINISH FLOAT E L E L T F I 5-10 4 0 0 4 4 0 0 0

39. Cont ! ACT DUR START FINISH FLOAT E L E L T F I

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

41. Operations Research
Lecture 7