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7/11/23, 1:07 AM 407 Week 4: Homework#4 - MNS407 Management Science, Summer 1 2023 | WebAssign
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MNS407 Management Science, Summer 1 2023
407 Week 4: Homework#4 (Homework) INSTRUCTOR
Karen Joiner
National University, La Jolla CA
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QUESTION
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SUN, JUL 30, 2023
11:59 PM MST
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This quiz covers material in Chapter 9. . You have 5 attempts to get this
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7/11/23, 1:07 AM 407 Week 4: Homework#4 - MNS407 Management Science, Summer 1 2023 | WebAssign
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Norton Industries is installing a new computer system. The activities, the activity times, and the project network are as follows.
Activity Time
A 3
B 6
C 2
D 5
E 4
F 3
G 9
H 3
The critical path calculation shows B-D-E-F-H is the critical path, and the expected project completion time is 21 weeks. After viewing this information, management requested overtime be used to complete the project in 16 weeks. Thus, crashing of the project is necessary. The following information is relevant.
Time (weeks) Cost ($)
Activity Normal Crash Normal Crash
A 3 1 900 1,700
B 6 3 2,000 4,100
C 2 1 500 1,000
D 5 3 1,800 2,400
E 4 3 1,500 1,850
F 3 1 3,000 3,900
G 9 4 8,000 9,800
H 3 2 1,000 2,000
ℹ
1. [–/1.33 Points] ASWMSCI15 9.E.020.DETAILS MY NOTES ASK YOUR TEACHER
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(a) Formulate a linear programming model that can be used to make the crashing decisions for this project. (The objective function should be the additional cost of crashing. Let the finish time for activity i and the amount of time activity i is crashed where i = A, B, C, D, E, F, G, and H.)
Min
s.t. constraint A
constraint B
C depends on A
D depends on C
D depends on B
E depends on D
F depends on E
G depends on C
G depends on B
H depends on G
H depends on F
x =i y =i
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finish time for H
maximum crashing for A
maximum crashing for B
maximum crashing for C
maximum crashing for D
maximum crashing for E
maximum crashing for F
maximum crashing for G
maximum crashing for H
(b) Solve the linear programming model and make the minimum cost crashing decisions. What is the amount of crash time (in weeks) for each activity?
Activity Crash Time
A
B
C
D
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E
F
G
H
What is the added cost (in dollars) of meeting the 16-week completion time?
$
(c) Develop a complete activity schedule based on the crashed activity times.
Activity Earliest
Start Latest Start
Earliest Finish
Latest Finish
Slack Critical Activity
A ---Select---
B ---Select---
C ---Select---
D ---Select---
E ---Select---
F ---Select---
G ---Select---
H ---Select---
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A cookie recipe gives the following numbered steps.
1. Preheat oven. 2. Grease cookie sheets. 3. Cream shortening and sugar. 4. Mix eggs and flavoring into the cream. 5. Measure and sift dry ingredients. 6. Add dry ingredients to mixture. 7. Drop the completed mixture by spoonfuls onto sheets and bake for 10 minutes.
Although the steps are numbered, they do not always reflect immediate precedence relationships. Develop a table that lists the immediate predecessors for each activity. (Enter your answers as comma-separated lists. If an activity does not have immediate predecessors, enter NONE.)
Activity Immediate Predecessor
1
2
3
4
5
6
7
2. [–/1.33 Points] CAMMIMS16 9.TB.049.DETAILS MY NOTES ASK YOUR TEACHER
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You may need to use the appropriate technology to answer this question.
Use the following network with activities and times estimated in days to answer the questions.
Activity Optimistic Most Probable Pessimistic
A 2 5 6
B 1 3 7
C 7 8 11
D 5 12 14
E 3 4 5
F 9 10 13
G 4 6 8
H 3 6 8
I 5 7 12
J 11 12 13
K 1 3 4
(a) What are the critical path activities? (Enter your answers as a comma-separated list.)
ℹ
3. [–/1.33 Points] CAMMIMS16 9.TB.055.DETAILS
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(b) What is the expected time (in days) to complete the project?
days
(c) Based only on the critical path, what is the probability the project will take more than 26 days to complete? (Round your answer to four decimal places.)
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A project network is shown in the figure.
Use a forward and a backward pass to determine the critical path, and then fill out the following table. Activity times are in weeks. (For the precedence activities, enter your answers as comma-separated lists. If an activity does not have immediate predecessors, enter NONE.)
Activity Precedence Activities Activity Time
(weeks) ES LS EF LF Slack Critical Path?
A ---Select---
B ---Select---
C ---Select---
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4. [–/1.33 Points] CAMMIMS16 9.TB.051.DETAILS
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D ---Select---
E ---Select---
F ---Select---
G ---Select---
H ---Select---
I ---Select---
Now assume that the times listed are only the expected times instead of being fixed times. Is the probability of being finished in fewer than 28 weeks more or less than 50%?
The probability is less than 50% because 28 weeks is less than the expected time for the project.
The probability is more than 50% because 28 weeks is less than the expected time for the project.
The probability is less than 50% because 28 weeks is more than the expected time for the project.
The probability is more than 50% because 28 weeks is more than the expected time for the project.
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A project network is shown in the figure.
For the project represented above, determine the earliest and latest start and finish times for each activity.
Activity Duration ES LS EF LF Slack
A 7
B 5
C 7
D 3
E 7
F 3
G 7
H 9
Determine the expected overall completion time.
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5. [–/1.33 Points] CAMMIMS16 9.TB.057.DETAILS
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You may need to use the appropriate technology to answer this question.
Consider the PERT/CPM network with estimated times in weeks shown in the following figure. The project is scheduled to begin on May 1.
The three-time estimate approach was used to calculate the expected times and the following table gives the variance for each activity.
Activity Variance
A 1.0
B 0.6
C 1.1
D 0.7
E 0.2
F 0.5
G 0.5
H 1.1
(a) Give the expected project completion date and the critical path. (Enter your critical path as a comma-separated list.)
The expected project completion is weeks from May 1 with a critical path of
.
(b) Based only on the critical path, by what date are you 99% sure the project will be completed? (Round your answer to one decimal place.)
weeks from May 1.
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6. [–/1.35 Points] CAMMIMS16 9.TB.058.DETAILS
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