Name (print, please) _______________________________________________ ID ___________________________
Operations Management I 73-331 Fall 2001
Faculty of Business Administration
University of Windsor
Midterm Exam I
Wednesday, October 17, 5:30 – 6:50 pm
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.
Time available: 1 hour 20 min
Instructions:
 This exam has 7 pages including this cover page.
 Please be sure to put your name and student ID number on each page.
 Show your work.
Grading:
Question
Marks:
1
/10
2
/7
3
/7
4
/10
5
/6
Total:
/40
Name:_________________________________________________
ID:_________________________
Question 1: (1 point each  10 = 10 points)
Questions 1.1 and 1.2: Suppose that the Travel EZ Corporation believes that a learning curve
accurately describes the evolution of its production costs for a new line of handbags.
1.1 Suppose that the first unit costs $200, and the second unit $160. What is the rate of learning?
a. 160%
b. 125%
c. 80%
d. 40%
e. None of the above
1.2 Let u be the unit number and Y (u ) be the cost incurred to produce the u  th handbag. Which of
the following relationship is expected to be linear?
a. u vs. Y (u )
b. ln(u) vs. ln(Y(u))
1.3 The learning curve parameter a represents
a. intercept
b. slope
c. –slope
d. the time/cost required by the first unit
e. the rate of learning
1.4 The Capacity Utilization Ratio is found by dividing Best Operating Level by Capacity Used.
a. True
b. False
1.5 The economies of scale dictates that the cost of adding capacity y , f  y   kya where
a. a < 1
b. a  1
c. a  1
d. none of the above
1.6 Which of the following is correct?
a. Moving average lags behind the trend, but exponential smoothing does not
b. Exponential smoothing lags behind the trend, but moving average does not
c. Both moving average and exponential smoothing lag behind the trend
d. None of the above
1.7 Holt’s method is a type of double exponential smoothing designed to track
a. stationary time series
b. time series with trend
c. time series with trend and seasonality
d. none of the above
2
Name:_________________________________________________
ID:_________________________
1.8 Aggregate planning methodology is designed to translate demand forecasts into a blueprint for
planning staffing and production levels for the firm over a predetermined planning horizon.
a. True
b. False
1.9 _____________________ are those costs that accrue as a result of changing the production
levels from one period to the next are called
a. Smoothing costs
b. Holding costs
c. Shortage costs
d. Regular time costs
e. Overtime and subcontracting costs
f. Idle time costs
1.10 Matching the production rate to the demand rate by hiring and laying off employees as the
demand rate varies is which of the following Production Planning Strategies?
a. Constant workforce plan
b. Chase
c. Level
d. Mixed
e. None of the above
3
Name:_________________________________________________
ID:_________________________
Question 2: (7 points)
Based on past experience, an oil company estimates that the construction cost of new refineries
obeys the law f  y   0.03 y 0.73 , where y is measured in barrels per day and f  y  in millions of dollars.
Demand is growing at a constant rate of 2 million barrels per year (assume 365 days per year) and
the discount rate for future costs is 30 percent.
a. (2 points) If the size of the refinery is doubled, what is the percentage increase in the construction
costs?
Answer:
f 2 y  0.032 y 

 2 0.73  1.6586 (1 point)
0.73
f y
0.03 y 
0.73
Hence, the cost increases by 65.86% (1 point)
b. (2 points) Determine the optimal timing of plant additions. Figure 1-14 is reproduced below.
Answer:
Figure 1-14
a  0.73 Hence, from Figure 1-14, rx  0.6 (0.5 point)
r
rx 0.6

 2 years (1.5 points, 0.5 point for unit)
r
0.3
1.00
0.90
0.80
c. (1 point) Determine the optimal size of each plant addition.
Size of each plant addition,
xD  22  4 million barrels (1 point, 0.5 point for unit)
0.70
Function = a
Answer:
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0
1
2
3
4
5
u = rx
d. (2 points) Determine the optimal cost of each plant addition.
4,000,000
 10959 barrels per day (0.5 point)
365
Answer: Size of each capacity addition =
Hence, cost, f  y   0.03 y 0.73  0.0310959
0.73
 26.68 million dollars (1.5 points, 0.5 point for unit)
4
6
Name:_________________________________________________
ID:_________________________
Question 3: (7 points)
Historical demand for a product is:
Month
t
Demand
1
January
30
2
February
31
3
March
34
4
April
36
a. (2 points) Using a simple three-month moving average, find the May forecast
Answer:
F5 
31  34  36
 33.67
3
b. (2 points) Using a single exponential smoothing with   0.2 and an April forecast = 11, find the
May forecast
Answer:
F5  D4  1   F4  0.236  1  0.211  16
c. (2 points) Using a double exponential smoothing method with   0.1,   0.1, S 0  20, and
G0  2 , find S1 and G1 .
Answer:
S1  D1  1   S 0  G0   0.130  1  0.120  2  22.8
G1   S1  S 0   1   G0  0.122.8  20  1  0.12  2.08
d. (1 point) Using S1 and G1 found in part (c ) , find the May forecast made in January.
Answer:
F1,5  S1  (5  1)G1  22.8  42.08  31.12
5
Name:_________________________________________________
ID:_________________________
Question 4: (10 points)
Hy and Murray are planning to set up an ice cream stand in Shoreline Park. After five months of
operation, the observed sales of ice cream and the number of park attendees are:
Month
1
2
3
4
5
Ice Cream Sales in hundreds, Y
3
4
2
6
8
Park Attendees in hundreds, X
9
10
5
18
20
a. (9 points) Determine a regression equation treating ice cream sales as the dependent variable
(on the vertical axis) and park attendees as independent variable (on the horizontal axis).
Answer:
Sum
Average
Park Attendees
in hundreds
x
9
10
5
18
20
62
12.4
Ice Cream Sales
in hundreds
y
3
4
2
6
8
23
4.6
xy
27
40
10
108
160
345
x2
81
100
25
324
400
930
 xy  n x y  345  512.44.6  0.3710 or, using another formula
930  512.4
 x  nx
n xy   x y 5345  6223
b

 0.3710
5930  62
n x   x 
b
2
2
2
2
2
2
a  y  b x  4.6  0.371012.4  0
Hence, the regression equation is y  0  0.3710 x  0.3710 x
b. (1 point) Forecast the ice cream sales in the next month, if the projected number of park
attendees in the next month is 2,400
Answer:
Both x and y are in hundreds. Hence, x  2400 / 100  24 , y  0.371024  8.90 hundred = 890
Major mistakes:

3 points off for taking logarithms of x and y

0.5 off in Part b for using incorrect x value
6
Name:_________________________________________________
ID:_________________________
Question 5: (6 points)
The Windsor Paint Company is planning labor force requirements over the next 3 quarters. The
demand forecast over the next 3 quarters, the inventory in the beginning of Quarter 1 and the
inventory required in the end of Quarter 3 are shown below:
Quarter
1
2
3
Demand Forecast
(in thousands of gallons)
480
600
210
Beginning inventory
(in thousands of gallons)
80
Ending inventory
(in thousands of gallons)
20
There are currently 300 employees with the company. Each employee produces 1000 gallons per
quarter. Employees are hired for at least one full quarter. The company will use a constant workforce
over the next 3 quarters. So, workers may be hired or fired in Quarter 1, but no worker will be hired or
fired in Quarters 2 or 3. The company would like to meet all the demand (i.e., shortages are not
allowed). Does the company need to hire some workers? If so, determine the minimum number of
workers hired.
Answer:
Quarter Demand Beginning Ending
Production Cumulative
Inventory Inventory Requirement Production
Required
Requirement
1
2
3
480
600
210
80
20
400
600
230
400
1000
1230
Number
Cumulative Workers
of units
units
Required
produced
produced
per worker per worker
1
1
400
1
2
500
1
3
410
Since the maximum workers required is 500, the company must employ at least 500 workers to avoid
shortages.
Hence, the number of workers to hire = 500 – 300 = 200.
Marking scheme: 1 point for each of the following
 adjustment of beginning and ending inventory
 finding cumulative production requirement
 finding cumulative units produced per worker
 finding workers required in various quarters
 finding number of workers needed
 finding number of workers to hire
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