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1)Reconsider the network diagram. Suppose that after 12 weeks, activities 1-2, 1-3, and 2-4 have been finished; activity 2-5 is 75 percent finished; and activity 3-6 is half finished. How many weeks after the original start time should the project be finished? |
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Project can be completed in a total of weeks. |
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2)For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project. |
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a. |
Activity-on-arrow diagram |
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Summary: |
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Activity |
ES |
EF |
LF |
LS |
Slack |
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1–2 |
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2–4 |
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4–7 |
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7–10 |
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10–12 |
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2–5 |
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5–8 |
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8–10 |
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1–3 |
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3–6 |
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6–9 |
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9–11 |
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11–12 |
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b. |
Activity-on-node diagram |
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Summary: |
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Activity |
ES |
EF |
LF |
LS |
Slack |
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1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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c.
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Activity |
Immediate |
Estimated Time (days) |
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A |
— |
15 |
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B |
A |
12 |
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C |
B |
6 |
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D |
B |
5 |
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E |
C |
3 |
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F |
— |
8 |
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G |
F |
8 |
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H |
F |
9 |
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I |
G |
7 |
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J |
H |
14 |
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K |
J |
6 |
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End |
D, E, I, K |
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Summary: |
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Activity |
ES |
EF |
LF |
LS |
Slack |
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A |
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B |
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C |
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E |
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D |
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F |
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G |
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I |
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H |
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J |
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K |
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3)For each of the following network diagrams, determine both the critical path and the expected project duration. The numbers on the arrows represent expected activity times. |
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a. |
Activity-on-arrow diagram |
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The critical path is (Click to select) 1–2–5–7–8–9 1–3–7–8–9 1–2–5–8–10–12 1–2–4–7–10–12 1–3–6–9–11–12 . |
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The expected project duration is . |
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b. |
Activity-on-node diagram |
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The critical path is (Click to select) 1–2–5–6–8–9 1–3–6–9–11–12 1–2–4–6–8–9 1–3–7–8–9 1–2–5–7–8–9 . |
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The expected project duration is . |
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c. |
Activity-on-arrow diagram |
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The critical path is (Click to select) 1–2–5–12–16 1–4–8–9–10–11–15–16 1–3–6–13–16 1–3–7–14–16 1–4–8–10–11–15–16 . |
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The expected project duration is . |
4)
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The times required to complete each of eight jobs in a two-machine flow shop are shown in the table that follows. Each job must follow the same sequence, beginning with machine A and moving to machine B. |
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TIME (hours) |
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Job |
Machine A |
Machine B |
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a |
16 |
5 |
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b |
3 |
13 |
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c |
9 |
6 |
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d |
8 |
7 |
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e |
2 |
14 |
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f |
12 |
4 |
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g |
18 |
14 |
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h |
20 |
11 |
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a. |
Determine a sequence that will minimize makespan time. |
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The sequence is (Click to select) a-b-c-d-e-f-g-h b-a-c-d-e-f-g-h e-b-g-h-d-c-a-f . |
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b. |
Find machine B’s idle time. |
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Idle time |
hrs |
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c. |
For the sequence determined in part a, how much would machine B’s idle time be reduced by splitting the last two jobs in half? |
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New idle time hrs, savings of hrs. |
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5)The following table shows orders to be processed at a machine shop as of 8:00 a.m. Monday. The jobs have different operations they must go through. Processing times are in days. Jobs are listed in order of arrival. |
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Job |
Processing |
Due Date |
Remaining Number |
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A |
8 |
20 |
2 |
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B |
10 |
18 |
4 |
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C |
5 |
25 |
5 |
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D |
11 |
17 |
3 |
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E |
9 |
35 |
4 |
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a. |
Determine the processing sequence at the first work center using each of these rules: (1) First come, first served, (2) Slack per operation. |
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Sequence for First come, first served |
(Click to select) A-B-C-D-E B-D-C-A-E C-A-B-D-E D-A-C-B-E E-A-B-C-D |
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Sequence for Slack per operation |
(Click to select) A-B-C-D-E B-D-C-A-E C-A-B-D-E D-A-C-B-E E-A-B-C-D |
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b. |
Compute the effectiveness of each rule using each of these measures: (1) average completion time, (2) average number of jobs at the work center. (Round your answers to 2 decimal places.) |
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First Come, First Served |
Slack per Operation |
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Average completion time |
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Average number of jobs |
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6)Use the assignment method to obtain a plan that will minimize the processing costs in the following table under these conditions: |
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WORKER |
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A |
B |
C |
D |
E |
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1 |
14 |
18 |
20 |
17 |
18 |
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2 |
14 |
15 |
19 |
16 |
17 |
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Job |
3 |
12 |
16 |
15 |
14 |
17 |
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4 |
11 |
13 |
14 |
12 |
14 |
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5 |
10 |
16 |
15 |
14 |
13 |
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a. |
The combination 2-D is undesirable. |
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The sequence is (Click to select) A-B-C-D-E B-A-C-E-D C-A-D-E-B D-A-B-C-E E-A-B-C-D . |
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b. |
The combinations 1-A and 2-D are undesirable. |
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The sequence is (Click to select) E-B-C-D-A B-A-C-D-E C-E-D-B-A D-A-C-E-B E-A-B-C-D . |
7)
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A production process consists of a three-step operation. The scrap rate is 10 percent for the first step and 6 percent for the other two steps. |
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a. |
If the desired daily output is 450 units, how many units must be started to allow for loss due to scrap?(Do not round intermediate calculations. Round up your final answer to the next whole number.) |
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Number of units |
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b. |
If the scrap rate for each step could be cut in half at every operation, how many units would this save in terms of the scrap allowance? (Do not round intermediate calculations. Round up your final answer to the next whole number.) |
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Number of units |
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c. |
If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Part a scrap rate)? (Round your answer to the nearest whole number. Omit the “$” sign in your response.) |
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Cost |
$ |
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7)A company has just negotiated a contract to produce a part for another firm. In the process of manufacturing the part, the inside diameter of successive parts becomes smaller and smaller as the cutting tool wears. However, the specs are so wide relative to machine capabilities that it is possible to set the diameter initially at a large value and let the process run for a while before replacing the cutting tool. |
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The inside diameter decreases at an average rate of .001 cm per part, and the process has a standard deviation of .05 cm. The variability is approximately normal. Assuming a three-sigma buffer at each end, how frequently must the tool be replaced if the process specs are 3 cm and 3.5 cm. Use (Number of shafts) n = 1. |
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Determine how many pieces can be produced before the LCL just crosses the lower tolerance of 3 cm.(Do not round your intermediate calculations.) |
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After pieces the cutting tool should be replaced. |
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8)For each of the accompanying control charts, analyze the data using both median and up/down run tests with z = ± 1.96 limits. |
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a. |
Are nonrandom variations present? Assume the center line is the long-term median. |
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Test |
Conclusion |
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Median |
(Click to select) Random variations are present in the data. Non-random variations are present in the data. |
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Up/Down |
(Click to select) Random variations are present in the data. Non-random variations are present in the data. |
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b. |
Are nonrandom variations present? Assume the center line is the long-term median. |
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Test |
Conclusion |
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Median |
(Click to select) Random variations are present in the data. Non-random variations are present in the data. |
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Up/Down |
(Click to select) Random variations are present in the data. Non-random variations are present in the data. |
9) question (9)
The Cause and Effect diagram can be used to
select
select Define Six-Sigma. Describe the relationship between various causes of a problem and its effect. Improve fit and finish of a product. Reduce costs in a process. Identify the causes for improving productivity.
2.
In the Cause and Effect diagram, the word Category refers to:
select
select A classification system of problems Priority order The rank ordering of quality issues Cost segmentation A group of similar causes
3.
In the Cause and Effect diagram, Effect refers to:
select
select The problem being analyzed Cosmetic quality changes The result of quality improvement Pareto analysis A grouping of causes
4.
The Cause and Effect diagram is also referred to as the “fishbone diagram” because:
select
select It is part of the Six-Sigma process. It is another term for control chart. The shape of the actual diagram resembles a fishbone. It is named after its inventor. Fishbone is a quality management practice.
5.
Which of the following is an alternate name for the Cause and Effect diagram?
select
select Scatter chart Check sheet Ishikawa diagram Pareto chart Control chart
6.
In the Cause and Effect diagram, the word Cause refers to
select
Question 10
1.
A visual representation of the steps in a process is known as a
select
select Pareto chart. cause-and-effect diagram. scatter diagram. control chart. flow chart.
2.
Determining the baseline performance occurs in the Six Sigma DMAIC step known as:
select
select Improve Define Measure Analyze Control
3.
A tool that is commonly used to help facilitate data collection is the:
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select check sheet. cause-and-effect diagram. flow chart. control chart. run chart.
4.
The tool that is used to separate the most important problems regarding a process from problems of less importance is the
select
select fishbone diagram. Pareto chart. flow chart. control chart. quality circle.
5.
Control charts show plotted values of a statistic
select
select with their associated cause. as a flow diagram. on a time-ordered chart. on a check sheet. versus their corresponding Pareto frequency.
6.
Factors that might be causing a problem are grouped into categories such as Methods, Materials, People and Equipment in a
select
11) Question 11
1.
Which of the following sample sizes has the most narrow sampling distribution?
select
select 500 20 100 800 200
2.
In which step of the control process are the characteristics defined?
select
select Correct Define Compare Measure Evaluate
3.
When plotting sample statistics on a control chart, 99.7% of the sample statistic values are expected to fall within plus/minus how many sigma?
select
select 4 1 6 3 2
4.
We measure the following values: 100, 90, 110. What is the range?
select
select 100 10 20 90 110
5.
A customer has specified that a tolerance of 10 to 20 mm is acceptable. Our process has a standard deviation of 2 mm. What is the Cp?
select
select 5 10 22 0.833 2
6.
p-bar is 0.1, n = 20. What is sigma?
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12) Concept Check (question 12)
1.
______ typically is stated in terms of aggregate units for an intermediate-range time horizon.
select
select The job sequence The employee work schedule The sales and operations plan The master production schedule The material requirements plan
2.
The aggregate plan provides input into ___________ and production control systems.
select
select product development scheduling process design corporate strategy forecasting
3.
Aggregation for manufactured goods is typically based on _______________.
select
select customer requests warehouse operators supplier networks groups of similar products marketing considerations
4.
The aggregate plan typically attempts to
select
select minimize the cost of matching supply and demand. produce a supply that exceeds demand in order to keep the sales force busy. determine the firm’s long-term capacity requirements. ensure the supply remains less than demand in order to keep prices up. maximize labor utilization.
5.
Sales and operations planning requires
select
select weekly workforce scheduling. master scheduling. a marketing budget. detailed short-range forecasts. coordination across functional areas.
6.
A production planning strategy that matches supply and demand by hiring and laying off employees as the demand varies is the
select
