Question
In: Operations Management
Consider the following precedence chart: ACTIVITY PRECEDING ACTIVITIES OPTIMISTIC TIME (days) MOST LIKELY TIME (days) PESSIMISTIC...
Consider the following precedence chart:
| ACTIVITY | PRECEDING ACTIVITIES | OPTIMISTIC TIME (days) | MOST LIKELY TIME (days) | PESSIMISTIC TIME (days) |
| A | - | 5 | 10 | 15 |
| B | - | 10 | 12 | 14 |
| C | - | 10 | 10 | 10 |
| D | B,C | 2 | 4 | 6 |
| E | A | 4 | 8 | 12 |
| F | A | 4 | 8 | 12 |
| G | D,E | 10 | 12 | 14 |
| I | F | 4 | 8 | 12 |
| J | G | 2 | 4 | 6 |
The total slack for activity C is __________
| a. |
0 |
|
| b. |
2 |
|
| c. |
8 |
|
| d. |
4 |
Solutions
Expert Solution
The expected durations of each activity are presented below :
|
Task |
Optimistic (O) |
Most likely ( m) |
Pessimistic(P) |
Expected duration |
|
A |
5 |
10 |
15 |
10.00 |
|
B |
10 |
12 |
14 |
12.00 |
|
C |
10 |
10 |
10 |
10.00 |
|
D |
2 |
4 |
6 |
4.00 |
|
E |
4 |
8 |
12 |
8.00 |
|
F |
4 |
8 |
12 |
8.00 |
|
G |
10 |
12 |
14 |
12.00 |
|
I |
4 |
8 |
12 |
8.00 |
|
J |
2 |
4 |
6 |
4.00 |
Expected duration = ( Optimistic duration + 4 x Most likely duration + Pessimistic duration) / 6
The precedence diagram of activities as follows :
|
A |
B |
C |
|
|
F |
E |
D |
|
|
I |
G |
||
|
J |
|||
The possible parallel paths and their expected durations as follows :
A-F-I = 10 + 8 + 8 = 26
A-E-G-J = 10 + 8 + 12 + 4 = 34
B-D-G-J = 12 + 4 + 12 + 4 = 32
C-D-G-J = 10 + 4 + 12 + 4 = 30
Since A-E-G-J has the longest Expected duration, it forms the critical path.
Slack for activities C, D
= Duration A-E-G-J – Duration C-D-G-J
= 34 – 30 DAYS
= 4 days
|
TOTAL SLACK FOR ACTIVITY C = 4 DAYS |
keosha answered 1 year agoRelated Solutions
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Consider the following precedence chart:
ACTIVITY
PRECEDING ACTIVITIES
OPTIMISTIC TIME (days)
MOST LIKELY TIME (days)
PESSIMISTIC TIME (days)
A
-
5
10
15
B
-
10
12
14
C
-
10
10
10
D
B,C
2
4
6
E
A
4
8
12
F
A
4
8
12
G
D,E
10
12
14
I
F
4
8
12
J
G
2
4
6
The total slack for activity C is __________
Consider the following precedence chart: ACTIVITY PRECEDING ACTIVITIES OPTIMISTIC TIME (days) MOST LIKELY TIME (days) PESSIMISTIC...
Consider the following precedence chart:
ACTIVITY
PRECEDING ACTIVITIES
OPTIMISTIC TIME (days)
MOST LIKELY TIME (days)
PESSIMISTIC TIME (days)
A
-
5
10
15
B
-
10
12
14
C
-
10
10
10
D
B,C
2
4
6
E
A
4
8
12
F
A
4
8
12
G
D,E
10
12
14
I
F
4
8
12
J
G
2
4
6
The total slack for activity F is __________
a.
8
b.
4
c.
2
d.
0
Times (days) Activity Optimistic Most Likely Pessimistic Preceding Tasks 1 8 10 13 - 2 5...
Times (days)
Activity
Optimistic
Most Likely
Pessimistic
Preceding Tasks
1
8
10
13
-
2
5
6
8
-
3
13
15
21
2
4
10
12
14
1,3
5
11
20
30
4
6
4
5
8
5
7
2
3
4
5
8
4
6
10
7
9
2
3
4
8,6
Draw the AON Network Diagram
Compute the expected activity time
Using the expected activity times, compute the early start,
early finish, late start, late finish, and...
Activity Optimistic Time Estimate (weeks) Most Likely Time Estimates (weeks) Pessimistic Time Estimates (weeks) Immediate Predecessor(s)...
Activity
Optimistic Time Estimate
(weeks)
Most Likely Time Estimates (weeks)
Pessimistic Time Estimates (weeks)
Immediate Predecessor(s)
A
3
6
9
none
B
3
5
7
A
C
4
7
12
A
D
4
8
10
B
E
5
10
16
C
F
3
4
5
D, E
G
3
6
8
D, E
H
5
6
10
F
I
5
8
11
G
J
3
3
3
H, I
A.)Using the information given, construct a network diagram
using AON notation....
QUESTION 7 [18 MARKS) In the following table, optimistic, most likely and pessimistic time estimates have...
QUESTION 7
[18 MARKS)
In the following table, optimistic,
most likely and pessimistic time estimates have been given for each
activity for a project.
Task
Immediate
Predecessor(s)
Time (days)
Optimistic (a)
Most Likely (m)
Pessimistic (b)
A
None
5
7
12
B
None
8
8
8
C
A
2
6
10
D
A,B
12
14
19
E
C,D
6
6
12
F
B,E
3
12
18
G
F
6
8
10
Construct an activity on node network diagram for this...
activity follows optimistic duration most likely direction pessimistic duration A - 4 6 14 B A,C...
activity
follows
optimistic duration
most likely direction
pessimistic duration
A
-
4
6
14
B
A,C
3
4
5
C
-
3
5
13
D
A,E
12
18
24
E
-
8
10
18
F
A,E
4
6
8
G
B,F
7
8
9
H
G
10
12
14
I
G
5
6
7
J
D,I
5
7
9
Calculate the probability of completing the project between 35
and 40 weeks? [4 pts]
f Answer the project manager’s question:...
Activity Predecessor Optimistic Most Likely Pessimistic A 4 7 10 B 2 9 10 C A,B...
Activity
Predecessor
Optimistic
Most Likely
Pessimistic
A
4
7
10
B
2
9
10
C
A,B
2
5
8
D
C
16
19
28
E
C
6
9
24
F
E
1
7
13
G
C
4
10
28
H
D,F
2
5
14
I
G,F
5
8
17
J
H,I
2
5
8
Determine the expected completion
time for each activity.
Construct the AON network for the
activities of this contract and determine the critical path for the
project.
Use the following table to answer questions. Activity a (Optimistic Time Estimate) m (Most Likely Estimate)...
Use the following table to answer
questions.
Activity
a (Optimistic Time Estimate)
m (Most Likely Estimate)
b (Pessimistic Time Estimate)
A
3
8
13
B
3
6
9
C
4
6
8
D
7
9
11
E
5
7
12
What is the expected time for activity c?
5.167
3
4.28
6
What is the variance for activity A?
3.33
2.77
5.31
.674
Assume there is one critical path of (A, B, C, E) what is the
project variance?
5.583...
A project has the following activities, precedence relationships, and time estimates in weeks: Activity Immediate...
A project has the following activities, precedence
relationships, and time estimates in weeks:
Activity
Immediate Predecessor
Activities
Optimistic
Time (to)
Most Likely Time (tm)
Pessimistic
Time (tp)
A
—
15
20
25
B
—
8
10
12
C
A
25
30
40
D
B
15
15
15
E
B
22
25
27
F
E
15
20
22
G
D
20
20
22
a. Compute the expected time and variance for
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b. Determine the critical path and the expected...
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A network consists of the following list. Times are given in
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Activity
Preceding
Optimistic
Probable
Pessimistic
A
--
5
11
14
B
-
3
3
9
C
--
6
10
14
D
A, B
3
5
7
F
C
6
8
13
G
D, E
2
4
6
H
F
3
3
9
Calculate the probability that the project will be completed in
less than 25 weeks.
NOTE
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