MSci 261 Managerial and Engineering Economics W96



Production Management 73-604 Fall 2000

Faculty of Business Administration

University of Windsor

Midterm Exam 2

Thursday, November 16

Instructor: Mohammed Fazle Baki

Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.

Time available: 2 hours

Instructions:

This exam has 10 pages.

Please be sure to put your name and student ID number on each page.

Show your work.

Grading:

Question Marks:

1. /6

2. /6

3. /6

4. /6

5. /8

6. /4

7. /4

Total: /40

Question 1: (6 points)

Multiple Choice Questions

1.1 Which of the following are related to JIT?

a. A philosophy of waste reduction

b. Pull production

c. Multi-skilled workers

d. Strong supplier relations

e. All of the above

1.2 Suppose we want to set up a kanban control system and want to determine the number of kanbam card sets needed. If the expected demand during lead time is 50 per hour, the safety stock is 20% of the demand during lead time, the container size is 4, and the lead time to replenish an order is 4 hours, what is the number of kanban card sets?

a. 60

b. 50

c. 30

d. 20

e. 10

1.3 You have just used the Capability Index formulas to compute the two values “min[2,2.5].” Which of the following is the interpretation of these numbers?

a. The true Capability index Value is 2.5

b. The mean of the production process has shifted towards the LCL

c. The mean of the production process has shifted towards the UCL

d. The mean has not shifted at all

e. None of the above

1.4 Quality control charts usually have a central line and upper and lower control limit lines. Which of the following are reasons why the process that is being monitored with the chart should be investigated?

a. Plots fall outside the upper or lower limit lines

b. Normal behavior

c. A large number of plots are on or near the central line

d. No real trend in any direction

e. All of the above

1.5 The costs of quality include which of the following?

a. Appraisal costs

b. Prevention costs

c. Internal failure costs

d. External failure costs

e. All of the above

1.6 Which of the following is the ISO 9000 form of certification that requires that a “qualified” national or international standards or certifying agency serve as an auditor?

a. First party

b. Second party

c. Third party

d. All of the above

e. None of the above

Question 2 (6 points)

A particular raw material is available to a company at three different prices, depending on the size of the order:

Less than 100 pounds $40 per pound

100 pounds to 999 pounds $38 per pound

More than 1,000 pounds $35 per pound

The cost to place an order is $30. Annual demand is 1,200 pounds. Holding or carrying cost is 30 percent of the material price. What is the economic order quantity to buy each time?

Answer:

|Quantity Range |Cost, C |[pic] |Feasible |

|Less than 100 pounds |$40 per pound |[pic] |Yes |

|100 pounds to 999 pounds |$38 per pound |[pic] |No |

|More than 1,000 pounds |$35 per pound |[pic] |No |

Therefore, calculate total cost at (i) Q=77.5, C=$40, (ii) Q=100, C=$38, and (iii) Q=1000, C=$35

|Q |C |[pic] |

|77.5 |$40 |[pic] |

|100 |$38 |[pic] |

|1000 |$35 |[pic] |

The best order size is 100 units at a cost of $38 per unit.

Question 3 (6 points)

University Drug Pharmaceuticals orders its antibiotics every two weeks (14 days) when a salesperson visits from one of the pharmaceutical companies. Tetracycline is one of its most prescribed antibiotics, with average daily demand of 2,000 capsules. The standard deviation of daily demand was derived from examining prescriptions filled over the past three months and was found to be 800 capsules. It takes five days for the order to arrive. University Drug would like to satisfy 99 percent of the prescriptions. The salesperson just arrived, and there are currently 25,000 capsules in stock. How many capsules should be ordered?

Answer:

We have [pic]capsules per day, T=14 days, L=5 days, [pic]capsules per day, and [pic] units.

[pic]

We have service level = 0.99. Look for area = 0.99-0.50=0.49 in the Standard Normal Distribution table. We get z=2.33

[pic]

Question 4 (6 points)

Gentle Ben’s Bar and Restaurant uses 5,000 quart bottles of an imported wine each year. The effervescent wine costs $3 per bottle and is served only in whole bottles because it loses its bubbles quickly. Ben figures that it costs $10 each time an order is placed, and holding costs are 20 percent of the purchase price. It takes three weeks for an order to arrive. Weekly demand is 100 bottles (closed two weeks per year) with a standard deviation of 30 bottles. Ben would like to use an inventory system that minimizes inventory cost and will provide a 95 percent service probability. Determine the order quantity and reorder point.

Answer:

[pic]bottles

[pic]bottles

We have service level = 0.95. Look for area = 0.95-0.50=0.45 in the Standard Normal Distribution table. We get z=1.645

[pic]bottles

Question 5 (8 points)

An item has a setup cost of $50 and a weekly holding cost of $1.00 per unit. Currently, there is no item in the inventory. The gross requirements are as follows:

| |Week |

| |1 |2 |3 |4 |

|Gross Requirements |20 |40 |10 |30 |

a) What should the lot sizes be using economic order quantity (EOQ) and the least unit cost (LUC)?

Answer:

Lot-sizing technique: EOQ

From the 4-week data, annual demand, D=(20+40+10+30)(52/4)=1300 units.

Annual holding cost per unit = $1.00(52) = $52.00

[pic]units.

Hence, order 50 units whenever the net requirement is negative.

Lot-sizing technique: LUC

The above worksheet shows that if an order is placed in Week 1, the unit cost is minimum if the order is placed for Weeks 1 and 2. If order is placed in Week 3, the unit cost is minimum if the order is placed for Weeks 3 and 4. Hence, 2 orders are placed; one in Week 1 of size 60 and the other in Week 3 of size 40.

Lot-sizing technique: EOQ Lot-sizing technique: LUC

|Week |1 |2 |3 |4 | |Week |1 |2 |3 |4 |

|Gross Requirement |20 |40 |10 |30 | |Gross Requirement |20 |40 |10 |30 |

|Beginning Inventory |0 |30 |40 |30 | |Beginning Inventory |0 |40 |0 |30 |

|Net Requirements |20 |10 |0 |0 | |Net Requirements |20 |0 |10 |0 |

|Planned Order receipt |50 |50 |0 |0 | |Planned Order receipt |60 |0 |40 |0 |

|Ending inventory |30 |40 |30 |0 | |Ending inventory |40 |0 |30 |0 |

b) What is the total cost associated with each lot-sizing technique?

Answer: EOQ: Cost = ordering cost+holding cost = (50(2))+ (30(1)+40(1)+30(1)+0(1))=$200

LUC: Cost = ordering cost+holding cost = (50(2))+ (30(1)+40(1)+30(1)+0(1))=$170

Question 6 (4 points)

The following matrix contains the costs (in dollars) associated with assigning Jobs A, B, C, D, and E to Machines 1, 2, 3, 4, and 5. Assign jobs to machines to minimize costs.

| |Machines |

|Jobs |1 |2 |3 |4 |5 |

|A |6 |11 |12 |3 |10 |

|B |5 |12 |10 |7 |9 |

|C |7 |14 |13 |8 |12 |

|D |4 |15 |16 |7 |9 |

|E |5 |13 |17 |11 |12 |

Answer:

[pic]

Question 7 (4 points)

a) Schedule the following 3 jobs through two machines in sequence to minimize the completion time of the last job processed using Johnson’s rule:

| |Operations Time |

|Job |Machine 1 |Machine 2 |

|A |10 |8 |

|B |7 |3 |

|C |5 |6 |

Answer:

Minimum operation time is 3 units for Job B on Machine 2. Since the minimum occurs on Machine 2, schedule Job B in the end.

Among the remaining jobs A and C, the minimum operation time is 5 units for Job C on Machine 1. Since the minimum occurs on Machine 1, schedule job C in the beginning.

The remaining job, Job A is scheduled after Job C and before Job B.

Hence, the sequence is C, A, B on both machines.

b) For the schedule in Part a, what is the completion time of the last job processed?

Answer:

| |Start, Process, End Times |

|Job |Machine 1 |Machine 2 |

|C |0,5,5 |5,6,11 |

|A |5,10,15 |15,8,23 |

|B |15,6,21 |23,3,26 |

Hence, the last job processed (Job B) is completed at time 26.

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