Name (print, please) _______________________________________________ ID ___________________________
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
Name:_________________________________________________
ID:_________________________
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
2
Name:_________________________________________________
ID:_________________________
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
3
Name:_________________________________________________
ID:_________________________
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
EOQ 
Cost, C
2 DS
iC
Feasible
Less than 100 pounds
$40 per pound
EOQ 
2(1200)(30)
 77.5
(0.30)( 40)
Yes
100 pounds to 999 pounds
$38 per pound
EOQ 
2(1200)(30)
 79.5
(0.30)(38)
No
More than 1,000 pounds
$35 per pound
EOQ 
2(1200)(30)
 82.8
(0.30)(38)
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
77.5
$40
100
$38
1000
$35
D
Q
S  iC
Q
2
1200
77.5
TC  (1200)( 40) 
30 
(0.30)( 40)  $48,930
77.5
2
1200
100
TC  (1200)(38) 
30 
(0.30)(38)  $46,530
100
2
1200
1000
TC  (1200)(35) 
30 
(0.30)(35)  $47,286
1000
2
TC  DC 
The best order size is 100 units at a cost of $38 per unit.
4
Name:_________________________________________________
ID:_________________________
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 d  2000 capsules per day, T=14 days, L=5 days,   800 capsules per day, and I  25,000
units.
q M I
 d (T  L)  z T  L  I  d (T  L)  z T  L  I
 2000(14  5)  z (800) 14  5  25000
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
q  2000(14  5)  2.33(800) 14  5  25000  21,125 capsules
5
Name:_________________________________________________
ID:_________________________
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:
Qopt 
2 DS

H
2(5000)10
 408.25 bottles
(0.20)(3)
 L   L  30 3  52 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
R  d L  z L  100(3)  1.645(52)  385.54 bottles
6
Name:_________________________________________________
ID:_________________________
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
20
40
10
30
Requirements
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
2DS
2(1300)(50)

 50 units.
H
52
Hence, order 50 units whenever the net requirement is negative.
Lot-sizing technique: LUC
EOQ 
Order at Week
1
3
Upto Week
1
2
3
4
3
4
Order size 20 60 70 100
10 40
Cumulative Inventory
0 40 60 150
0 30
Carrying cost
0 40 60 150
0 30
Ordering cost 50 50 50 50
50 50
Unit cost 2.50 1.50 1.57 2.00
5.00 2.00
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
7
Name:_________________________________________________
ID:_________________________
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.
Jobs
A
B
C
D
E
1
6
5
7
4
5
Machines
3
12
10
13
16
17
2
11
12
14
15
13
Answer:
8
4
3
7
8
7
11
5
10
9
12
9
12
Name:_________________________________________________
ID:_________________________
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
A
B
C
Machine 1
10
7
5
Machine 2
8
3
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:
Job
C
A
B
Start, Process, End Times
Machine 1
Machine 2
0,5,5
5,6,11
5,10,15
15,8,23
15,6,21
23,3,26
Hence, the last job processed (Job B) is completed at time 26.
9