Name (print, please) _______________________________________________ ID ___________________________
Operations Management I 73-331 Fall 2003
Odette School of Business
University of Windsor
Midterm Exam I Solution
Thursday, October 9, Education Gym
Section 1: 10:00 am – 11:20 am
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
/12
3
/13
4
/20
5
/10
Total:
/65
Name:_________________________________________________
ID:_________________________
Question 1: (10 points) Circle the most appropriate answer
1.1 If multiplicative seasonal index of the winter quarter is 0.70
a. the expected demand of winter is 30 units less than the average quarterly demand
b. the expected demand of winter is 70% of the annual demand
c. the expected demand of winter is 30% less than the average quarterly demand
d. the expected demand of winter is 70% more than the average quarterly demand
1.2 The additive seasonal index of the winter quarter for lawn mower is expected to be
a. positive
b. negative
c. positive, but less than 1.00
d. zero
1.3 If the rate of learning, L = 0.90 and the time required by the 4 th unit is 100 hours, then the time
required by the 16th unit is
a. 4 hours
b. 16 hours
c. 90 hours
d. 81 hours
1.4 Cost of too infrequent capacity additions includes cost of
a. capital
b. too many installations
c. too many training programs
d. a and b
1.5 Advantage of chase strategy includes
a. minimum inventory
b. minimum hiring/firing
c. minimum outsourcing
d. b and c
1.6 Hiring cost includes all of the following except the cost of
a. advertising
b. interviewing
c. training
d. salary/wages
1.7 In the exponential smoothing method, the forecast series is more smooth if the smoothing
constant,  is
a. 2 / N  1 , where N is the length of season
b. large
c. small
d. does not matter
2
Name:_________________________________________________
ID:_________________________
1.8 Component of a stationary time series includes
a. average, trend, seasonality, cyclicity and autocorrelation.
b. an average, but no trend, seasonality, cyclicity and autocorrelation.
c. an average and a trend, but no seasonality, cyclicity and autocorrelation.
d. an average, a trend, a seasonality, but no cyclicity and autocorrelation.
1.9 Suppose that the cost of capacity addition follows an equation, f  y   kya , where y is the size
the capacity to be added. If there is economy of scale, a is
a. negative
b. positive but less than 1.00
c. 1.00
d. more than 1.00
1.10
a.
b.
c.
d.
Which of the following is true about forecast?
Some forecasting software can always forecast correctly
Long term forecasts are more accurate than short term forecasts
Aggregate forecasts are more accurate than the disaggregate forecasts
b and c
Question 2: (12 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 4 th unit is $4,900. Estimate the cost of
producing
a. (4 points) the 8th unit.
Cost of producing the 2 n th unit = L  (cost of producing the n th unit)
Hence, cost of producing the 8th unit = L  (cost of producing the 4th unit)
Hence, cost of producing the 8th unit = 0.70  4900 = $3,430.
b. (4 points) the 1st unit.
Cost of producing the 2 n th unit = L  (cost of producing the n th unit)
Hence, cost of producing the 4th unit = L  (cost of producing the 2nd unit)
= L  ( L  cost of producing the 1st unit) = L2  (cost of producing the 1st unit)
Hence, cost of producing the 1st unit = cost of producing the 4th unit / L2 = 4,900/0.702 = $10,000.
c. (4 points) the 5th unit.
a  $10,000 (from part b) (1 point)
Y (u )  au
b
 10,000(5)
 au
 ln(L ) 

  
 ln(2 ) 
 ln(0.7 ) 

  
 ln(2 ) 
 10,000(5) 0.5146
(2 points)
 $4,368.46
(1 point)
3
Name:_________________________________________________
ID:_________________________
Question 3: (13 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. (4 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 77 percent. Find the value of a .
f (2 y )  1.77 f ( y )
or, k (2 y ) a  1.77k ( y ) a
or, 2a  1.77
(2 points)
or, a ln( 2)  ln( 1.77)
ln( 1.77)
or, a 
 0.8237
ln( 2)
(2 points)
b. (3 points) If the discount rate for future costs is 25 percent, determine the optimal timing of plant
additions. Figure 1-14 is reproduced below.
Figure 1-14
Since a  0.8237
1.00
As given by Figure 1-14, rx  0.375
(1 point)
x
rx 0.375

 1.5 years
r
0.25
0.90
Function = a
(acceptable: rx from 0.33 to 0.42)
0.80
0.70
0.60
0.50
0.40
(2 points, 1 point for unit)
0.30
0
1
u = rx
c. (3 points) If a plant size of 6,000 barrels per day costs $30 million, find the value of k .
f (6,000)  30
(1 point)
or, k (6,000)0.8237  30
30
or, k 
 0.023177
(6,000)0.8237
(1 point)
(1 point)
d. (3 points) Compute the cost of adding a plant of size 9,000 barrels per day.
f  y   kya
or, f 9,000  0.0231779,000
 $41.8954 million
0.8237
(1 point)
(2 points, 1 for unit)
4
2
Name:_________________________________________________
ID:_________________________
Question 4: (20 points)
The 7-11 store at the corner of Wyandotte and Patricia street observes that the coffee sales are high
in fall and winter terms when more students take courses in the University of Windsor. The sales are
low in the 12-week period from May to August. The following are the sales in $000 during 2001 and
2002:
Term, 2001
Period
Sales ($000)
Term, 2002
Period
Sales($000)
Winter
1
12
Winter
4
15
12-Week
2
7
12-Week
5
8
Fall
3
11
Fall
6
13
a. (4 points) Compute the 3-period moving average forecasts of winter, 12-week period and fall of
2002. Find the Mean Absolute Deviation (MAD).
12  7  11
7  11  15
11  15  8
 10, F5 
 11, F6 
 11.33 (3 points, 1 for each forecast)
3
3
3
Each of the above forecast is in ($000)
e4  10  15  5, e5  11  8  3, e6  11.33  13  1.67
F4 
MAD  5  3  1.67 / 3  3.2233 (1 point)
b. (2 points) Forecast sales of 12-week period of 2001 using exponential smoothing method, a sales
forecast of winter 2001 of $11,000 and a smoothing constant   0.20 .
F2  D1  1   F1  0.212  1  0.211  11.2
Hence, forecast sales is $11,200
c. (4 points) Using double exponential smoothing method with S 0  9 , G0  2 ,   0.20 and
  0.10 compute S1 and G1
S1  D1  1   S0  G0   0.212  1  0.29  2  11.2
(2 points)
G1   S1  S0   1   G0  0.111.2  9  1  0.12  2.02
(2 points)
d. (2 points) Using the results of part c, forecast sales in fall, 2001
F1,3  S1  (3  1)G1  11.2  22.02   15.24
Hence, forecast sales is $15,240
5
Name:_________________________________________________
ID:_________________________
e. (8 points) Suppose that the multiplicative seasonal factors are 1.2, 0.70 and 1.10 of winter, 12week period and fall respectively. Forecast sales in fall, 2003. Use the regression method on
deseasonlaized demand.
Term
Period
x
Sales
(copied
from p.5)
Seasonal
Factor
Deseasonalized
Demand
y
xy
x2
Winter
2001
1
12
1.2
10
10
1
12-Week
2001
2
7
0.7
10
20
4
Fall
2001
3
11
1.1
10
30
9
Winter
2002
4
15
1.2
12.5
50
16
12-Week
2002
5
8
0.7
11.42857143
57.14285714
25
Fall
2002
6
13
1.1
11.81818182
70.90909091
36
Sum
21
-----
-----
65.74675325
238.0519481
91
Average
3.5
-----
-----
10.95779221
-----
-----
8
 8  8 
6 xi yi    xi   yi 
 i 1  i 1   6(238.0519)  (21)(65.7468)  0.4536
Slope  i 1
2
8
6(91)  (21) 2
 8 
2
6 xi    xi 
i 1
 i 1 
Intercept  y  slope( x)  10.9578  0.4536(3.5)  9.3701
(1 point for slope, 1 for intercept)
Projection: forecast deseasonalized series in fall, 2003 (period 9):
Y = a + bx= 9.3701 + 0.4536 (9) = 13.4527
(1 point)
Reseasonalization: forecast sales in fall, 2003 = 13.4527 × 1.1 = 14.7980 (1 point)
Hence the forecast sales in fall, 2003 is $14,798
6
Name:_________________________________________________
ID:_________________________
f. (8 points) Suppose that the multiplicative seasonal factors are 1.2, 0.70 and 1.10 of winter, 12week period and fall respectively. Forecast sales in fall, 2003. Use the regression method on
deseasonlaized demand.
Term
Period
x
Sales
(copied
from p.5)
Seasonal
Factor
Deseasonalized
Demand
y
xy
x2
Winter
2001
1
12
1.2
10
10
1
12-Week
2001
2
7
1.1
6.363636364
12.72727273
4
Fall
2001
3
11
0.7
15.71428571
47.14285714
9
Winter
2002
4
15
1.2
12.5
50
16
12-Week
2002
5
8
1.1
7.272727273
36.36363636
25
Fall
2002
6
13
0.7
18.57142857
111.4285714
36
Sum
21
-----
-----
70.42207792
267.6623377
91
Average
3.5
-----
-----
11.73701299
-----
-----
8
 8  8 
6 xi yi    xi   yi 
 i 1  i 1   6(267.6623)  (21)(70.4221)  1.21058
Slope  i 1
2
8
6(91)  (21) 2
 8 
2
6 xi    xi 
i 1
 i 1 
Intercept  y  slope( x)  11.7370  1.2106(3.5)  7.5
(1 point for slope, 1 for intercept)
Projection: forecast deseasonalized series in fall, 2003 (period 9):
Y = a + bx= 7.5 + 1.2106 (9) = 18.3952
(1 point)
Reseasonalization: forecast sales in fall, 2003 = 18.3952 × 0.7 = 12.8766 (1 point)
Hence the forecast sales in fall, 2003 is $12,877
7
Name:_________________________________________________
ID:_________________________
Question 5: (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 701, 803 and 452, expressed in thousands of cookies. During a 40-day
period when there were 100 workers, the company produced 2 million cookies. Assume that the
numbers of workdays in a month is 20. There are currently 60 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 = 2,000,000 cookies / 100 workers / 40 days = 500 cookies per worker per day (1 point)
Monthly production = 500 × 20 = 10,000 cookies per worker (1 point)
Month
t
A
1
2
3
Demand
In Month
t
(000
units)
B
701
803
452
Cumulative
Demand up to
Month t
(000 units)
(1 point)
C
701
1504
1956
Production
per Worker
in Month t
(000 units)
Cumulative
Production up to
Month t per Worker
(000 units) (1 point)
D
10
10
10
E
10
20
30
Number of Workers
Needed
To avoid shortage at the
end of Month t
(1 point)
F = E/C
701/10 = 70.1 = 71
1504/20 = 75.2 = 76
1956/30 = 65.2 = 66
Hence, the minimum constant workforce = max (71, 76, 66) = 76 (1 point)
b. (4 points) Assume that the inventory holding cost is 14 cents per cookie per month, hiring cost is
$300 per worker, and firing cost is $500 per worker. Evaluate the cost of the plan derived in a.
Number of workers to Hire = 76-60=16. Hiring cost = 16 × 300 = $4,800. (1 point)
To compute holding cost, first compute ending inventory in each period.
Month
1
2
3
Beginning
Inventory
(000 units)
0
59
16
Production
(000 units)
1076=760
760
760
Total
Demand
(000 units)
701
803
452
Inventory holding cost = 399,000(0.14) = $55,860 (1 point)
Total cost = $55,860 + $4,800 = $60,660 (1 point)
8
Ending Inventory
= BI + Production – Requirement
(000 units) (1 point)
= 0 + 760 – 701 = 59
= 59 + 760 – 803 = 16
= 16 + 760 – 452 = 324
399