1- R. C. Coleman’s top management established a required 40-week completion time for the
project. Can this completion time be achieved? Include probability information in your
discussion. What recommendations do you have if the 40-week completion time is required?
-
Optimistic time (a)
the minimum activity time if everything progresses ideally
-
Most probable time (m)
The most probable 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
immediate optimistic
Activity
predecessors
time
A
B
C
D
E
F
G
H
I
J
K
Activity
A
B
C
D
E
F
G
H
I
J
K
AB
C
C
E
C
DFG
DF
H
IJ
ES
0
0
9
13
13
23
13
29
29
35
39
Critical Path: B-C-E-F-H-J-K
4
6
2
8
7
4
4
4
4
3
2
EF
6
9
13
25
23
29
21
35
36
39
43
most
likely
time
6
8
4
10
10
6
6
6
6
4
4
pessimistic
time
expected
time
variance
8
16
6
24
13
8
20
8
14
5
6
6
9
4
12
10
6
8
6
7
4
4
0.44
2.78
0.44
7.11
1
0.44
7.11
0.44
2.78
0.11
0.44
LS
3
0
9
17
13
23
21
29
32
35
39
LF
9
9
13
29
23
29
29
35
39
39
43
Slack
3
0 Critical
0 Critical
4
0 Critical
0 Critical
8
0 Critical
3
0 Critical
0 Critical
Project completion time: 43 weeks
Therefore, the 40-week completion time cannot be achieved.
= 2.78+ 0.44+ 1+0.44+0.44+0.11+0.44 = 5.65
z-score = 40-43/5.65 *0.5 = -1.26
z score of -1.26 = 0.1038
Therefore, the probability of the project meeting the 40-week deadline is 10.38%.
2- Suppose that management requests that activity times be shortened to provide an 80%
chance of meeting the 40-week completion time. If the variance in the project completion
time is the same as you found in part (1), how much should the expected project completion
time be shortened to achieve the goal of an 80% chance of completion within 40 weeks?
Pr (T<=40) = 0.8000
Pr (0.8000- 0.5000 = 0.3000
Using table
Z(x<= T <=40)= 0.84
(40 – x)/ 2.38 = 0.84
x= 38
Therefore, the project has to be shortened to 38 weeks to achieve the goal of an 80% chance of
completion within 40 weeks.
3- Using the expected activity times as the normal times and the following crashing information,
determine the activity crashing decisions and revised activity schedule for the warehouse
expansion project
Activity
Normal
time
crash
time
Normal
cost
crash cost
time to be
crashed
cost of
crash
cost of crash
per period
A
6
4
1,000.00
1,900.00
2
900.00
450.00
B
C
D
E
F
G
H
I
J
K
9
4
12
10
6
8
6
7
4
4
7
2
8
7
4
5
4
4
3
3
1,000.00
1,800.00
1,500.00
2,700.00
2,000.00
3,200.00
5,000.00
8,000.00
3,000.00
4,100.00
8,000.00 10,250.00
5,000.00
6,400.00
10,000.00 12,400.00
4,000.00
4,400.00
5,000.00
5,500.00
45,500.00 60,650.00
2
2
4
3
2
3
2
3
1
1
800.00
1,200.00
1,200.00
3,000.00
1,100.00
2,250.00
1,400.00
2,400.00
400.00
500.00
400.00
600.00
300.00
1,000.00
550.00
750.00
700.00
800.00
400.00
500.00
potential path
length
A-C-D-I-K
A-C-D-H-J-K
A-C-E-F-I-K
A-C-E-F-H-J-KA-C-G-H-J-K
B-C-D-I-K
B-C-D-H-J-KB-C-E-F-I-K
B-C-E-F-H-J-K
B-C-G-H-J-K
cost
Total crashing
cost
Total crashing
week
33
36
37
40
32
36
39
40
43
35
crash J 1week
33
35
37
39
31
36
38
40
42
34
400
crash B 2 weeks
33
35
37
39
31
34
36
38
40
32
800
2250
5
crash K 1 week
32
34
36
38
30
33
35
37
39
31
500
crash F 1 week
32
34
35
37
30
33
35
36
38
31
550