Name (print, please) _______________________________________________ ID ___________________________
Operations Management I 73-331 Fall 2002
Odette School of Business
University of Windsor
Midterm Exam I Solution
Wednesday, October 16, 10:00 – 11:20 am, in Class, CN G125
Instructor : Mohammed Fazle Baki
Aids Permitted : Calculator, straightedge, and a one-sided formula sheet.
Time available : 1 hour 20 min
Instructions:

This exam has 8 pages including this cover page.

Please be sure to put your name and student ID number on each page.

Show your work.
Grading:
Question
1
Marks:
/10
2
3
/10
/10
4
5
6
/10
/12
/13
Total: /65

Name:_________________________________________________ ID:_________________________
Question 1: (10 points) Circle the most appropriate answer
1.1 Herman Hahn is using a forecasting software for outdoor lights, a seasonal item. He is prompted by the program to input quarterly seasonal factors. Herman estimates that the first-quarter demand for the lights is about 40% below average, the second-quarter demand about 10% below average, the third-quarter demand about average, and the fourth quarter demand about 50% above average. For the 1 st , 2 nd , 3 rd and 4 th quarter seasonal factors he should input respectively a. 0.40, 0.10, 1.00, 0.50 b. 0.40, 0.10, 0.00, 0.50 c.
–0.40,-0.10,0.00,0.50 d. –0.40,-0.10,1.00,0.50 e. 0.60,0.90,1.00,1.50 f. None of the above
1.2 If the forecast errors are normally distributed, then a. both methods MA(6) and ES with
 
0 .
20 will have exactly the same distribution of forecast errors
b. both methods MA(9) and ES with
 
0 .
20 will have exactly the same distribution of c. forecast errors
MA(6) will be more smooth than ES with d. MA(9) will be more smooth than ES with e. MA(9) will be less smooth than ES with






0
0 .
.
20
20
0 .
20 f. None of the above
1.3 Which of the following is true? a. b.
Y
Y
 
 


L
L


Y 14 c. d. e. f.
Y
Y
Y
Y
12
 
 
 
 




L
L
L
L




Y
Y
Y
Y
Y
 
 
 
 
 
 
1.4 If a lead strategy is used
a. Some capacity may be unused b. Some demand may be unfulfilled c. Capacity is added when it is needed d. Capacity is added after it is needed e. All of the above f. None of the above
1.5 Production is initiated by the demand forecast in the following environment a. Assemble-to-stock b. Make-to-stock
c. a and b d. Assemble-to-order e. Make-to-order f. d and e
2

Name:_________________________________________________ ID:_________________________
1.6 Which of the following is more appropriate? a. Dell uses make-to-stock and Compaq assemble-to-order b. Dell uses make-to-order and Compaq assemble-to-stock c. Dell uses assemble-to-stock and Compaq assemble-to-order d. Dell uses assemble-to-order and Compaq assemble-to-stock e. All of the above f. None of the above
1.7 Which of the following is more appropriate? a. Aggregate forecasts are more accurate than disaggregate forecasts b. Disaggregate forecasts are more accurate than aggregate forecasts c. Long term forecasts are more accurate than the short-term forecasts d. Short term forecasts are more accurate than the long-term forecasts
e. a and d f. b and d
1.8 Which of the following demand is more likely to be stationary?
a. Gold, annual b. Cars, annual c. Lawn Mower, quarterly d. Ski equipment, monthly e. Turkey, weekly f. Burgers, hourly
1.9 Double exponential smoothing method is designed for a. stationary series
b. trend c. seasonality d. cyclicity e. random movement f. seasonality with trend
1.10 If the demand demonstrates seasonality with an increasing trend, multiplicative factors a. are more accurate than the additive factors b. yield smoother series than the additive factors
c. provide a higher peak than the additive factors d. provide a lower peak than the additive factors e. a and d f. b and d
3

Name:_________________________________________________ ID:_________________________
Question 2: (10 points)
An analyst predicts that an 80 percent experience curve should be an accurate predictor of the cost of producing a new product. Suppose that the cost of the 2 nd unit is $4,000. Estimate the cost of producing a. (4 points) the 4 th unit.
Answer:
Cost of producing the 2 n th unit = L

(cost of producing the n th unit)
Hence, cost of producing the 4 th unit = L

(cost of producing the 2 nd unit)
Hence, cost of producing the 4 th unit = 0.80

4,000 = $3,200. b. (3 points) the 1 st unit.
Answer:
Cost of producing the 2 n th unit = L

(cost of producing the n th unit)
Hence, cost of producing the 2 nd unit = L

(cost of producing the 1 st unit)
Hence, cost of producing the 1 st unit = cost of producing the 2 nd unit / L = 4,000/0.80 = $5,000. c. (3 points) the 3 rd unit.
Answer: a

$ 5 , 000 (from part b )
Y ( u )
 au
 b
 au



 ln( L ln( 2
)
)



5000 ( 3 )



 ln( 0 .
8 ) ln( 2 )



5000 ( 3 )

0 .
321928 (2 points)

$ 3 , 510 .
52 (1 point)
4

Name:_________________________________________________ ID:_________________________
Question 3: (10 points)
An oil company believes that the cost of construction of new refineries obeys a relationship of the type f ( y )
 ky a
, where y is measured in units of barrels per day and f ( y ) in millions of dollars. a. (5 points) From the past experience, each doubling of the size of a refinery at a single location results in an increase in the construction costs of about 70 percent. Find the value of a .
Answer: f ( 2 y )

1 .
7 f ( y )
k ( 2 y ) a 
1 .
7 k ( y ) a
2 a 
1 .
7
a ln( 2 )
 ln( 1 .
7 )
a
 ln( 1 .
7 ) ln( 2 )

0 .
7655
b. (3 points) If the discount rate for future costs is 20 percent, determine the optimal timing of plant additions. Figure 1-14 is reproduced below.
Figure 1-14
Answer:
1.00
Since a

0 .
7655
0.90
As given by Figure 1-14,
0.80
rx

0 .
51 ( 0.50-0.55) (1 point)
0.70
x
 rx r

0 .
51
0 .
20

2 .
55 years
(2 points, 1 point for unit)
0.60
0.50
0.40
0.30
0 1 u = rx
2 c. (2 points) If a plant size of 5,000 barrels per day costs $25 million, find the value of k .
Answer: f ( 5 , 000 )

25 or, k ( 5 , 000 )
0 .
7655 
25 (1 point) or, k

25
( 5 , 000 )
0 .
7655

0 .
036834 (1 point)
5

Name:_________________________________________________ ID:_________________________
Question 4: (10 points)
Mr. Meadows Cookie Company makes a variety of chocolate chip cookies in the plant in Albion,
Michigan. Based on orders received and forecasts of buying habits, it is assumed that the demand for the next three months is 1300, 1500 and 1100, expressed in thousands of cookies. During a 46day period when there were 100 workers, the company produced 1.955 million cookies. Assume that the numbers of workdays over the three months are respectively 20, 24 and 22. There are currently
130 workers employed, and there is no starting inventory of cookies. Assume that the number of workers hired and fired at the beginning of Months 1, 2 and 3 are as shown below:
Month i
1
Number of workers hired at the beginning of Month
23 i
Number of workers fired at the beginning of Month i
2
3
5
31
Assume that the inventory holding cost is 20 cents per cookie per month, hiring cost $200 per worker, and firing cost $300 per worker. Evaluate the cost of the plan. a. (1 point) Compute the productivity in number of cookies per worker per day
Answer:
Productivity = 1.955

10 6 /100/46 = 425 units/worker/day b. (6 points) Show the number of units produced and ending inventory carried in each of the next three months
Answer:
Month Demand Beginning Number
1
2
3
Total in 000
1300
1500
1100
Inventory in 000
0
0.5
10.1
of days of work
20
24
22
Number of
Workers
Hired
23
23 c. (3 points) Compute the total cost of the plan.
0
0
Number of
Workers Workers
Fired
0
5
31
36
Total
153
148
117
Production in 000
3 points
1300.5
1509.6
1093.95
Ending
Inventory in 000
3 points
0.5
10.1
4.05
14.65
Answer:
Hiring cost = 23

200 = $4,600
Firing cost = 36

300 = $10,800
Inventory holding cost = 14.65

1000

0.20 = $2,930
Total cost = $4,600+10,800+2,930=$18,330
6

Name:_________________________________________________ ID:_________________________
Question 5: (12 points)
Historical demand for a product is: t Month
1
2
3
4
5
January
February
March
April
May
Demand
32
36
37
38
41 a. (4 points) Using a simple three-month moving average, find the April and May forecast. Compute
MAD.
Answer:
F
4
F
5 e
4

32

36


3
35

38


37
3
36

37

38
3 ,
 e
5

35
37

37

41

3 , MAD


3

4

/ 2

3 .
5 b. (2 points) Using a single exponential smoothing with
June forecast
 
0 .
1 and a May forecast = 39, find the
Answer:
F
6
 
D
5


1
 

F
5

   
1

0 .
1
 

39 .
2 c. (4 points) Using a double exponential smoothing method with
G
0

3 , find S
1
and G
1
.
 
0 .
1 ,
 
0 .
1 , S
0

29 , and
Answer:
S
1
 
D
1


1
 

S
0

G
0
    
1

0 .
1

29

3


32
G
1
 

S
1

S
0
 
1
 

G
0

 
32

29
 
1

0 .
1
 

3 d. (2 points) Using S
1
and G
1
found in part ( c ) , find the June forecast made in January.
Answer:
F
1 , 6

S
1

( 6

1 ) G
1

32

5
  
47
7

Name:_________________________________________________ ID:_________________________
Question 6: (13 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
Ice Cream Sales in hundreds, Y 7
2
6
3
4
4
8
5
10
Park Attendees in hundreds, X 11 10 5 17 25 a. (10 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:
Park Attendees Ice Cream Sales in hundreds in hundreds x
11 y
7 xy
77
10
5
17
25
68
6
4
8
10
35
60
20
136
250
543 b

Sum
Average

 xy x
2

 n x y
 n x
2
13.6
543
1160


 
13 .
6
 
 
13 .
6

7
2
7

0.2849
or, using another formula b
 n n

 xy x
2



 x

 
2 y

     
 
1160
  
2

0.2849
a
 y
 b x

7


0 .
2849

13 .
6


3 .
1259
Hence, the regression equation is y

3 .
1259

0 .
2849 x x^2
121
100
25
289
625
1160 b. (3 points) Forecast the ice cream sales in the next month, if the projected number of park attendees in the next month is 3,000
Answer:
Both x and y are in hundreds.
Hence, x

3000 / 100

30 , y

3 .
1259


0 .
2849
 

11 .
67 hundred = 1,167
8