6. (18 points)
A copy business operates with a single copier. It is now the beginning of the fourth (4th) hour. The jobs listed in the following table are waiting to be processed. The due date is the end of that hour. For example, Job 1 is due at the end of hour 42.
Job | Job Processing Time (Hours) | Due Date (in Hours) from Time 0 |
1 | 20 | 42 |
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2 | 18 | 24 |
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3 | 25 | 70 |
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4 | 32 | 90 |
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5 | 30 | 65 |
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a) Determine the sequence of jobs using the following rules as these were defined during our weekly assignments:
· Critical ratio rule (CR)
· Slack time
b) Prioritize (rank) the rules used in a) based on average flow time measured from now.
c) Prioritize (rank) the rules used in a) based on average lateness with no credit for completing any job early.
d) Prioritize (rank) the rules used in a) based on average early time with no penalty for completing any job late (in other words, the early time would be set at zero if a job is late).
7. (17 points)
First City Bank orders cash from the Federal Reserve Board to meet daily transaction needs. Linda Davis, the operations manager, estimates that $5,000,000 in cash will be needed next month. She has estimated that the cost to order, receive, and store each shipment of cash from the Federal Reserve Board will be $675 per shipment. First City Bank is open for business 250 days each year. These are considered its working days for the year. The bank’s related carrying cost for cash is 0.65 percent per month. That is, each dollar held in the bank’s vault costs $0.0065 per month in foregone profits.
a) How much should Linda order from the Federal Reserve Board each time a cash order is placed if she wants to minimize her cost?
b) What is the expected total annual holding cost plus ordering cost?
c) If the lead time is 3 days what is the reorder point? Also, what is the inventory position immediately after reordering?
d) If it is against First City Bank’s policy to order more than $750,000 when placing a cash order. How much should it order each time? Explain or support your answer.
8. (10 points)
It costs a total of $2,000 to perform preventive maintenance (PM) on five identical production machines. If one of the machines malfunctions between PM inspections, this breakdown cost averages $5,000. Following is the historical breakdown for the machines.
PM every n months | Average Number of Breakdowns between PM Inspections |
2 | 0.1 |
3 | 0.5 |
4 | 1.6 |
5 | 3.2 |
a) Which PM policy provides the minimum cost strategy based on the information provided?
b) With everything else the same, what is the average breakdown cost that results in the same total cost for a 3-month PM strategy and a 4-month PM strategy?
9. (8 points)
USA Company’s current switch design is composed of two components, A and B, in series. The company wants to upgrade the reliability of the switch. As one option, the company is considering the switch option shown below. The reliability of A is 0.9, and the reliability of B is also 0.9.
What will be the improved reliability should USA upgrade to the Switch Option shown above? Provide the reliability of this option.
10. (16 points)
The estimated times and immediate predecessors for the activities in a project at John Black’s company are given in the following table. Assume that the activity times are independent. All times are in weeks.
Activity | Predecessors | Optimistic Time (a) | Most Likely Time (m) | Pessimistic Time (b) |
A | -- | 2 | 4 | 6 |
B | -- | 1 | 2 | 9 |
C | A | 2 | 4 | 6 |
D | B | 5 | 8 | 17 |
E | C | 3 | 4 | 11 |
a) What is the critical path? You may use any method to determine this.
b) What is the expected completion time of the project?
c) What is the probability of completing the project in 16 weeks or more?
10 years ago
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