Last Name _________________________ First Name _________________________ ID ________________________
Operations Management I 73-331 Winter 2005
Odette School of Business
University of Windsor
Midterm Exam I Solution
Thursday, February 17, 10:00 – 11:20 am
Last Name A-L: Classroom OB B02 (Odette)
Last Name M-Z: Education Building ED 1123
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.
Time available: 1 hour 20 min
Instructions:
 This solution has 7 pages.
 Please be sure to put your name and student ID number on each page.
 State your answers up to four decimal places.
 Show your work.
Grading:
Question
Marks:
1
/10
2
/10
3
/10
4
/10
5
/12
6
/13
Total:
/65
Name:_________________________________________________
ID:_________________________
Question 1: (10 points) Circle the most appropriate answer
1.1 The learning curve captures the phenomenon that as more and more units are produced
a. the rate of learning increases
b. the rate of learning decreases
c. the time required to produce each unit increases
d. the time required to produce each unit decreases
1.2 Which of the following is a fixed cost?
a. Cost of material
b. Installation cost of machines
c. Hourly wages
d. b and c
1.3 Which of the following is true?
a. Long term forecasts are more accurate than short term forecast and aggregate forecasts are
more accurate than disaggregate forecasts
b. Long term forecasts are more accurate than short term forecast and disaggregate forecasts
are more accurate than aggregate forecasts
c. Short term forecasts are more accurate than long term forecast and aggregate
forecasts are more accurate than disaggregate forecasts
d. Short term forecasts are more accurate than long term forecast and disaggregate forecasts
are more accurate than aggregate forecasts
1.4 The forecast series is more smooth if
a. simple moving average method is used with a higher N
b. exponential smoothing method is used with a higher 
c. both
d. none
1.5 Which of the following method(s) correspond to the stationary series?
a. Double exponential smoothing
b. Weighted moving average
c. Simple moving average
d. b and c
1.6 If multiplicative seasonal factor for a period is 0.90, the demand for the period is
a. 90% less than the annual demand
b. 0.10 less than the annual demand
c. 10% less than the average demand per period
d. 0.90 more than the average demand per period
1.7 Which of the following is a part of the smoothing cost?
a. Cost to interview job candidates
b. Cost of breakage, spoilage, deterioration and obsolescence
c. Backorder cost
d. b and c
2
Name:_________________________________________________
ID:_________________________
1.8 Which strategy requires less hiring/firing?
a. Chase strategy
b. Level strategy
c. The strategy obtained by applying linear programming
d. All strategy requires the same amount of hiring/firing
1.9 A lead strategy
a. is a forecasting strategy that requires production before demand forecast
b. is an aggregate production planning strategy and alternative to the chase strategy and the
level strategy
c. maintains a capacity more than or equal to demand
d. maintains a capacity less than or equal to demand
1.10
a.
b.
c.
d.
What is backorder?
The units of sales lost when demand exceeds inventory on hand
The units ordered when demand exceeds inventory on hand
Finished goods inventory
Work-in-process inventory
Question 2: (10 points)
An analyst predicts that a 70 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 $4,200. Estimate the cost of
producing
a. (3 points) the 4th unit.
L
Y 2n 
Y n 
So, Y 2n  Y nL
Or, Y 4  Y 2L  4,200  0.70  $2,940
b. (3 points) the 1st unit.
L
Y 2n 
Y n 
So, Y n  
Y 2n 
L
Or, Y 2  
c. (4 points) the 3rd unit.
a  Y 1  $6,000 (from part b )
Y (u )  au b
 au
 ln(L ) 

 
 ln(2 ) 
 6000(3)
 ln(0.7 ) 

  
 ln(2 ) 
 6000(3) 0.5146
 $3,409.08
(3 points)
(1 point)
3
Y 4  4,200

 $6,000
L
0.7
Name:_________________________________________________
ID:_________________________
Question 3: (10 points)
A major oil company is considering the optimal timing for the construction of new refineries. From
past experience, each doubling of the size of a refinery at a single location results in an increase in
the construction costs of about 85 percent. Furthermore, a plant of size 6,000 barrels per day costs
$30 million.
a. (5 points) Find the value of a assuming a relationship of the form f  y   ky a .
Since doubling capacity increases cost by 85%, f 2 y   f  y   0.85 f  y  
f 2 y 
 1.85
f y
f 2 y  k 2 y 
k 2a y a
Again,


 2a
a
a
f y
ky
ky
a
Hence, 2 a  1.85
So, a 
ln 1.85 0.6152

 0.8875
ln 2
0.6931
b. (3 points) Find the value of k assuming a relationship of the form f  y   ky a . Assume that y is in
units of barrels per day.
f  y   kya
So, k 
f y
30

 0.0133049124
a
y
6000 0.8875
c. (2 points) Find the cost of adding a plant of size 7,500 barrels per day.
f  y   kya
So, f 7500  0.01330491247500
0.8875
 $36.570331 million
4
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 600, 800 and 450, expressed in thousands of cookies. During a 50-day
period when there were 80 workers, the company produced 2.4 million cookies. Assume that the
number of workdays in each month is 25. There are currently 70 workers employed, and there is no
starting inventory of cookies.
a. (6 points) What is the minimum constant workforce (level strategy) required to meet demand
(shortages not allowed) over the next three months?
Productivity = 2,400,000 cookies / 80 workers / 50 days = 600 cookies per worker per day (1 point)
Monthly production = 600 × 25 = 15,000 cookies per worker
Month
Production Cumulative Net
Monthly
Cumulative
Number of Workers
Required
Production
Production Production
Needed
(000 units)
Required
per Worker per Worker
(2 points)
(000 units)
(000 units) (000 units)
(2 points)
A
B
C
D
E
F = E/C
1
600
600
15
15
600/15=40=40
2
800
1400
15
30
1400/30=46.67=47
3
450
1850
15
45
1850/45=41.11=42
Hence, the minimum constant workforce = max (40, 47, 42) = 47 (1 point)
b. (4 points) Assume that the inventory holding cost is 5 cents per cookie per month, hiring cost is
$400 per worker, and firing cost is $600 per worker. Evaluate the cost of the plan derived in a.
Number of workers to fire = 70-47=23. Firing cost = 23 × 600 = $13,800. (1 point)
To compute holding cost, first compute ending inventory in each period.
Month
Beginning
Inventory
0
Actual Production
(1 point)
(47)(15,000)=705,000
Ending Inventory
1
Production
Required
600,000
2
800,000
105,000
(47)(15,000)=705,000
10,000
3
450,000
10,000
(47)(15,000)=705,000
265,000
Total
105,000
380,000
Inventory holding cost = 380,000(0.05) = $19,000 (1 point)
Total cost = $13,800 + $19,000 = $32,800 (1 point)
5
Name:_________________________________________________
ID:_________________________
Question 5: (12 points)
Historical demand for a product is:
Month
t
Demand
1
January
40
2
February
43
3
March
45
4
April
48
5
May
50
a. (4 points) Using a simple three-month moving average, find the April and May forecast. Compute
MAD.
40  43  45
 42.6667
3
43  45  48
F5 
 45.3333
3
e4  42.6667  48  5.3333, e5  45.3333  50  4.6667, MAD  5.3333  4.6667  / 2  5
F4 
b. (2 points) Using a single exponential smoothing with   0.20 and a May forecast = 49, find the
June forecast
F6  D5  1   F5  0.250  1  0.249  49.2
c. (4 points) Using a double exponential smoothing method with   0.1,   0.25, S 0  38, and
G0  2.5 , find S1 and G1 .
S1  D1  1   S 0  G0   0.140  1  0.138  2.5  40.45
G1   S1  S 0   1   G0  0.2540.45  38  1  0.252.5  2.4875
d. (2 points) Using S1 and G1 found in part (c ) , find the June forecast made in January.
F1, 6  S1  (6  1)G1  40.45  52.4875  52.8875
6
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
2
3
4
5
Ice Cream Sales in hundreds, Y
8
6
5
8
9
Park Attendees in hundreds, X
18
16
12
20
24
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).
xy
Park Attendees
Ice Cream Sales
x2
In Hundreds
In Hundreds
y
x
18
8
144
324
16
6
96
256
12
5
60
144
20
8
160
400
24
9
216
576
Sum
90
36
676
1700
Average
18
7.2
 xy  n x y  676  5187.2  28  0.35 or, using another formula
 x  n x 1700  518 80
n xy   x y 5676  9036 140
b


 0.35
51700  90 400
n x   x 
b
2
2
2
2
2
2
a  y  b x  7.2  0.3518  0.90
Hence, the regression equation is y  0.90  0.35 x
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.
Both x and y are in hundreds.
Hence, x  3000 / 100  30 , y  0.90  0.3530  11.4 hundred = 1,140
7