1. CASE PROBLEM
PERT/CPM
GROUP 3:
SAIFUL BAHRI HJ AHMAD MOKHTAR
MOHD FAUZI MD FADZIL
WAN AISHAH WAN MOHD NOWALID
FARHANAH MOHD NOAH

2. CASE PROBLEM
List of the activities

3. The optimistic, most probable and pessimistic time (in week)

4. Question (a)1
• R.C Coleman’s top management established a
required 40-week completion time for the
project. Can this completion time be
achieved?

5. D I
A
START
C E F K FINISH
H J
B G
Project Network

6. Expected Time
•Optimistic time (a)
The minimum activity time if everything progresses ideally
•Most probable time (m)
The most probable activity time under normal conditions
•Pessimistic time (b)
The maximum activity time if significant delays are
encountered
•Expected time (t)
The average time for the activity
a 4m b
t
6

7. 4 4(6) 8 7 4(10 ) 13 4 4(6) 14
tA tE tI
6 6 6
6 4(8) 16 4 4(6) 8 3 4( 4) 5
tB tF tJ
6 6 6
4 4(6) 20 2 4( 4) 6
2 4( 4) 6 tG tK
tC 6 6
6
8 4(10 ) 24 4 4(6) 8
tD tH
6 6

8. ACTIVITY EXPECTED TIME (WEEKS)
A 6
B 9
C 4
D 12
E 10
F 6
G 8
H 6
I 7
J 4
K 4
TOTAL 76
Expected Time In Weeks

9. D 13 25
12 17 29
A 0 6
6 3 9 I 29 36
7 32 39
C 9 13 E 13 23 K 39 43
START
4 39 43
4 9 13 10 13 23
F 23 29 H 29 35
B 0 9 6 23 29 6 29 35
FINISH
9 0 9
J 35 39
4 35 39
G 13 21
8 21 29
Project Network (Earliest Start, Finish Times, Latest
Start and Finish Times)

10. ACTIVITY ES EF LS LF SLACK
A 0 6 3 9 3
B 0 9 0 9 0 (critical)
C 9 13 9 13 0 (critical)
D 13 25 17 29 4
E 13 23 13 23 0 (critical)
F 23 29 23 29 0 (critical)
G 13 21 21 29 8
H 29 35 29 35 0 (critical)
I 29 36 32 39 3
J 35 39 35 39 0 (critical)
K 39 43 39 43 0 (critical)
Activity Slack Time

11. Critical Path:
B-C-E-F-H-J-K
Project Completion Time:
43 weeks
R.C Coleman’s required 40-week completion
time. This completion time can’t be achieved

12. Question (a)2
Include probability information in your
discussion. What recommendations do you
have if the 40-week completion time is
required?

13. Variance ( 2)
• used to describe the dispersion or variation in the
activity time values
2
b a
2
6

14. ACTIVITY VARIANCE
A 0.44
B 2.78
C 0.44
D 7.11
E 1.00
F 0.44
G 7.11
H 0.44
I 2.78
J 0.11
K 0.44
Variance of Each Activity

15. Variance in the project completion time ( 2)
2 = 2 + 2 + 2 + 2 + 2 2 2
B C E F H+ J + K
= 2.78 + 0.44 + 1.00 + 0.44 + 0.44 + 0.11 + 0.44
= 5.65
Standard deviation ( )
= √5.65
= 2.38

16. Normal Distribution of Project Completion Time
= 2.38
Expected Completion Time
43
Time (weeks)

17. Probability the project will meet the 40-week
completion time
= 2.38
40 43
Time (weeks)

18. At 40 ≤ T ≤ 43
z = (40 – 43) / 2.38 = 1.26
using table,
Pr (40 ≤ T ≤ 43) = 0.3962
Pr (T ≤ 40) = 0.5000 – 0.3962
= 0.103
= 10.38%
 We find that the probability of the project meeting the 40-weeks
deadline is 10.38%. Thus, R.C Collman have a low chance if they
want the project completed at 40-weeks

19. Question (b)
• Suppose that management request that activity
times be shortened to provide an 80 percent chance
of meeting the 40-week completion time. If the
variance in the project completion time is the same
as you found in (a), how much should the expected
project completion time be shortened to achieved
the goal of an 80 percent chance of completion
within 40 weeks?

20. Expected completion time to achieve 80% chance of
completion within 40 weeks
= 2.38
X 40
Time
(weeks)

21. Pr (T ≤ 40) = 0.8000
Pr (x ≤ T ≤ 40) = 0.8000 – 0.5000 = 0.3000
using table,
z (x ≤ T ≤ 40) = 0.84
(40 – x) / 2.38 = 0.84
x = 38
 It shows the project has to be shortened to 38 weeks
to achieve the goal of an 80 % chance of completion
within 40 weeks.

22. Question (c)
• Using the expected completion times as the
normal times and the following crashing
information, determine the activity crashing
decisions and revised activity schedule for the
warehouse expansion project

23. Crash Time and Cost’s Information

24. Maximum possible reduction in time, Mi
M '
i i i
(3)
with i = expected time for activity I
’i = time for activity i under maximum crashing
Crash cost per unit of time, Ki
C' C
K i i
i
M
i
with Ci = cost for activity I
C’i = cost for activity i under maximum crashing

25. TIME COST
ACTIVITY Mj Kj
NORMAL CRASHED NORMAL CRASHED
A 6 4 1000 1900 2 450
B 9 7 1000 1800 2 400
C 4 2 1500 2700 2 600
D 12 8 2000 3200 4 300
E 10 7 5000 8000 3 1000
F 6 4 3000 4100 2 550
G 8 5 8000 10259 3 753
H 6 4 5000 6400 2 700
I 7 4 10000 12400 3 800
J 4 3 4000 4400 1 400
K 4 3 5000 5500 1 500

26. Linear Programming Model

27. EXCEL

28. CRASHING
ACTIVITY TIME (WEEKS)
(WEEKS)
A 6 0
B 7 2
C 4 0
D 12 0
E 10 0
F 5 1
G 8 0
H 6 0
I 7 0
J 3 1
K 3 1
Total Crashing Time 5 weeks
Total Crashing Cost $ 2,250.00
Activity Crashing Decision