Last Name _________________________ First Name _________________________ ID _______________________
Operations Management I 73-331 Fall 2004
Odette School of Business
University of Windsor
Midterm Exam I Solution
Thursday, October 14
Ambassador Auditorium
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 11 pages including this cover page.
 Please be sure to put your name and student ID number on each odd-numbered page.
 Show your work.
Grading:
Question
Marks:
1
/10
2
/16
3
/15
4
/14
5
/10
Total:
/65
Last Name _________________________ First Name _________________________ ID _______________________
Question 1: (10 points) Circle the most appropriate answer
1.1 If learning is faster, the rate of learning, L is
a. more and the learning curve is steeper
b. more and learning curve is flatter
c. less and the learning curve is steeper
d. less and learning curve is flatter
1.2 The following is a disadvantage of too frequent capacity addition:
a. Cost of capital tied to build and maintain excess capacity
b. Installation
c. Unused capacity
d. Both b and c
1.3 The exponential smoothing method with   0.25 yields the same distribution of forecast errors
as the simple moving average method with
a. N = 7
b. N  5
c. N  3
d. none of the above
1.4 The demand for lawn mower in spring is more than average quarterly demand. Which of the
following is not a possible multiplicative seasonal factor for demand of lawn mower in spring?
a. 1.75
b. 0.75
c. 4.75
d. Both b and c
1.5 The multiplicative seasonal factor for snow shovels is 2.00 in winter. If the demand forecast for
2005 is 4000 units, which of the following is a demand forecast for winter, 2005?
a. 500
b. 1000
c. 2000
d. 8000
1.6 Which of the following forecasting method yields the smoothest series?
a. Exponential smoothing method with   0.10
b. Exponential smoothing method with   1.00
c. Simple moving average method with N  1
d. Both b and c
1.7 Which of the following is an advantage of level strategy?
a. Less inventory
b. Efficiency of machines an workers
c. High worker morale
d. Both b and c
1.8 An aggregate production plan is developed using
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a. an aggregate unit of production after maser production schedule is developed in terms of
actual units
b. an aggregate unit of production and master production schedule translates the plan in
terms of actual units
c. actual units of production after maser production schedule is developed in terms of an
aggregate unit
d. actual units unit of production and master production schedule translates the plan in terms of
an aggregate unit
1.9 It’s possible to find an optimal aggregate production plan without considering the following:
a. cost of labor
b. cost of material
c. cost of capital assets such as plants and machines
d. Both b and c
1.10
a.
b.
c.
d.
What is F4 , 7
A 4-step ahead forecast for period 7
A 3-step ahead forecast for period 7
A forecast for period 4
A forecast for period 3
Question 2: (16 points)
You’ve recorded production time of a major product and found the processing time for each unit as
follows:
Unit Number, u
Time (Hours), Y(u)
14
10
18
9
24
8
33
7
a. (4 points) Compute logarithms of the numbers in each column (use natural logs).
ln u 
ln Y u 
i
1
2.6391
2.3026
2
2.8904
2.1972
3
3.1781
2.0794
4
3.4965
1.9459
(Continued…)
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b. (6 points) Using linear regression method on ln(u) and ln(Y(u)) values, derive slope and intercept
of the regression line.
i
x
y
xy
x2
1
2.6391
2.3026
6.0768
6.9648
2
2.8904
2.1972
6.3508
8.3544
3
3.1781
2.0794
6.6085
10.1003
4
3.4965
1.9459
6.8038
12.2255
Sum
12.2041
8.5251
25.8399
37.6450
Average
3.0510
2.1313
--------
--------
(2 points)
Slope, m 
n xy   x y
n x 2   x 
2

425.8399   12.20418.5251
437.6450   12.2041
2

 0.6816
 0.4156 (2 points)
1.6399
Intercept, c  y  m x  2.1313   0.4156 3.0510   3.3994 (2 points)
c. (4 points) Estimate the learning curve parameters. What is the time required to produce the first
unit? What is the rate of learning?
Time required by the first unit, a  e c  e 3.3994  29.9461 hours (2 points including 1 for unit)
b  m   0.4156   0.4156
Rate of learning, L  e m ln2   e 0.4156 0.6931  e 0.2881  0.7497  74.97% (2 points including 1 for unit)
d. (2 points) How much time will it be required to produce the 75 th unit?
yu   au b
y 75   29.946175 
0.4156
 29.94610.1662   4.9772 hours (2 points including 1 for unit)
Question 3: (15 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. (2 points) An 80% increase in capacity results in a 60% increase in cost. Is this an example of
economy of scale or diseconomy of scale? Circle the correct answer.
a) Economy of scale
b) Diseconomy of scale
b. (2 points) Continue from Part a. Which of the following is true? Circle the correct answer.
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a) k  1
b) k  1
c) a  1
d) a < 1
c. (3 points) Continue from Parts a and b. Compute parameter a in f ( y)  ky a .
f 1.8 y 
 1.6 (1 point)
f y
k 1.8 y 
or,
 1.6
ky a
a
or, 1.8 a  1.6 (1 point)
So, a 
ln 1.6 0.4700

 0.7996 (1 point)
ln 1.8 0.5878
d. (3 points) Ignore Parts a, b and c. Suppose that the cost function is f ( y )  ky 0.70 . Find the
percentage increase in cost if the capacity increases by 90%.
f 1.9 y  k 1.9 y 

f y
ky 0.70
0.70
 1.9 0.70  1.5672 (2 points)
Hence, cost increases by 56.72% (1 point)
e. (5 points) Continue from Part d. So, the cost function is f ( y )  ky 0.70 . If a capacity is added once
after every x years, find optimal x if the rate of interest, r is 15%.
Figure 1-14
From Figure 1-14, rx  0.675 (2 points)
rx 0.675

 4.5 years
Hence, x 
r
0.15
(2 points, including 1 for unit)
1.00
0.90
Function = a
rx
0.675
 0.675
 0.7001  0.70  a
Check: rx
e 1 e
1
0.80
0.70
0.60
0.50
0.40
0.30
0
1
u = rx
5
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Last Name _________________________ First Name _________________________ ID _______________________
Question 4: (14 points)
Historical demand for a product is:
Month
t
Demand
1
January
41
2
February
45
3
March
46
4
April
51
5
May
52
a. (4 points) Using a simple three-month moving average, find April and May forecast. Compute
MAD.
F4 
D1  D2  D3 41  45  46

 44 (1 point)
3
3
F5 
D2  D3  D4 45  46  51

 47.3333 (1 point)
3
3
E4  F4  D4  44  51  7
MAD 
E 4  E5
2

E5  F5  D5  47.33  52  4.6667
 7   4.6667
2
 5.8334 (2 points)
b. (3 points) Using a single exponential smoothing with   0.20 and a May forecast = 50, find June
forecast
F6  D5  1   F5  0.2052  1  0.2050  50.4
(1 point each for formula, substitution and computation)
c. (4 points) Using a double exponential smoothing method with   0.25,   0.20, S 0  37, and
G0  3 , find S1 and G1 .
S1  D1  1   S 0  G0   0.2541  1  0.2537  3  40.25 (2 points)
G1   S1  S 0   1   G0  0.2040.25  37  1  0.203  3.05 (2 points)
d. (3 points) Using S1 and G1 found in part (c ) , find June forecast made in January.
F1, 6  S1  G1  S1  5G1  40.25  53.05   55.50
(1 point each for formula, substitution and computation)
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Last Name _________________________ First 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 1200, 1300 and 1350, expressed in thousands of cookies. During a 50day period when there were 100 workers, the company produced 2 million cookies. Assume that the
numbers of workdays over the three months are respectively 19, 21 and 22. There are currently 143
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
Number of workers hired at the
Number of workers fired at the
i
beginning of Month i
beginning of Month i
1
15
2
5
3
13
Assume that the inventory holding cost is 10 cents per cookie per month, backorder cost 20 cents
per cookie, hiring cost $300 per worker, and firing cost $500 per worker. Evaluate the cost of the
plan.
a. (2 points) Compute productivity in number of cookies per worker per day
Productivity =
2,000,000
 400 cookies per worker per day
50100 
b. (5 points) Show number of units produced and ending inventory carried in each of the next three
months
Month
Demand
000s
Beginning
Inventory
000s
Number
of
Workers
Hired
Number
of
Workers
Fired
Total
Workers
Number
of Days
of Work
(1 point)
Production
000s
Ending
Inventory
000s
(1 point)
(1 point)
(1 point)
1
1200
0
15
0
158
19
1200.800
0.800
2
1300
0.800
5
0
163
21
1369.200
70.000
3
1350
70.000
0
13
150
22
1320.000
40.000
20
13
Total (1 point)
-------
110.800
c. (3 points) Assume that the inventory holding cost is 10 cents per cookie per month, backorder
cost 20 cents per cookie, hiring cost $300 per worker, and firing cost $500 per worker. Compute
total cost of the plan.
Hiring cost = 20(300)
= $6,000
Firing cost = 13(500)
= $6,500 (1 point)
Inventory holding cost = 110.800(1000)(0.10) =$11,080 (1 point)
Total cost
=$23,580 (1 point)
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