1. Operations Research
Lecture 8

2. Operations Research
CPM / PERT

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

4. … OVERHAUL Plant, Equipment, Vehicle CONSTRUCTION
Flats, Houses, Offices
CIVIL ENGINEERING
Bridges, Roadways
TOWN PLANNING
Control of design procedures …

5. MARKETING
Product launching
SHIP BUILDING
Designing and Production
DESIGNING
Car, Machine Tools
OFFICE PROCEDURE
CONSULTANCY, etc.

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

7. Example:A project has the following relationships among the activities
Example:A project has the following relationships among the activities. Construct the network.   A is the first operation. B and C can be performed parallel and are immediate successors to A. D,E and F follow B. G follows E. H follows D, but it cannot start till E is complete. I and J succeed G. F and J precede K. H and I precede L. M succeeds L and K. The last operation N succeeds M and C.

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

9. A is the first operation.
The last operation N succeeds M and C.
A is the first operation. 7 H 5 4 F E D L 8 I J 2 1 A 3 B 6 G 9 K 10 M 11 N C
B and C can be performed parallel and are immediate successors to A.
H follows D, but it cannot start till E is complete.
D,E and F follow B.
G follows E
I and J succeed G.
F and J precede K.
H and I precede L
M succeeds L and K.

10. 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. 1 2 7

11. 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. 1 2 7

12. TIMES (ACTIVITY) LATEST FINISH TIME
Latest Event Time of the Head Event. 1 2 7

13. 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. 1 2 7

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

15. Cont ! 5 2 3 4 7 8 6 E=11 E=1 E=8 E=6 E=0 2 6 8 1 L=12 L=10 4 3 E=159 6
L=6
L=21
L=15
E=15
L=0
L=10
L=15

16. 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

17. 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

18. 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

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

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

21. Operations Research
Lecture 8