Name (print, please) _______________________________________________ ID ___________________________
Production Management 73-604 Winter 2002
Odette School of Business
University of Windsor
Midterm Exam 1 Solution
Tuesday, February 5, 7:00 – 9:00 pm
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.
Time available: 2 hours
Instructions:
 This exam has 11 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
/5
3
/8
4
/10
5
/10
6
/12
7
/10
Total:
/65
Name:_________________________________________________
ID:_________________________
Question 1: (1 points each  10 = 10 points)
Multiple Choice Questions
1.1 Companies that have either a functional product with an efficient supply chain or an innovative
product with a responsive supply chain tend to be the ones with problems.
a. True
b. False
1.2 The Travel EZ Corporation believes that a learning curve accurately describes the evolution of its
production costs for a new line of handbags. Suppose that the first unit costs $200, and the
second unit $150. What is the rate of learning?
a. 160%
b. 125%
c. 80%
d. 75%
e. None of the above
1.3 Which of the following statements about bottlenecks is best?
a. Bottlenecks are most likely to occur in a plant that produces functional products.
b. Increasing bottleneck capacity does not increase plant capacity.
c. When capacities are perfectly balance, it can be said that every operation is a
bottleneck.
d. Bottlenecks are created by uniform demand.
1.4 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
1.5 Which of the following uses less memory?
a. Moving average
b. Exponential smoothing
1.6 Exponential smoothing is designed for
a. stationary series
b. series with trend
c. series with auto-correlation
1.7 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
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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: (5 points)
A manager is trying to decide whether to buy one machine or two. If only one machine is purchased
and demand proves to be excessive, the second machine can be purchased later. Some sales would
be lost, however, because the lead time for delivery of this type of machine is six months. In addition,
the cost per machine will be lower if both machines are purchased at the same time. The probability
of low demand is estimated to be 0.30 and that of high demand, 0.70. The after-tax net present value
of benefits (NPV) from purchasing two machines together is $90,000 if demand is low and $170,000
if demand is high. If one machine is purchased and demand is low, the NPV is $120,000. If the
demand is high, the manager has three options. Doing nothing, which has an NPV of $120,000;
subcontracting, with an NPV of $140,000; and buying the second machine, with an NPV of $130,000.
a. (3 points) Draw a decision tree for this problem.
b. (2 points) What is the best decision and what is expected payoff?
EV(node 4) = Max{120,000, 140,000, 130,000} = $140,000 (subcontract)
EV(node 3) = 0.390,000+0.7170,000 = $146,000
EV(node 2) = 0.3120,000+0.7140,000 = $134,000
EV(node 1) = Max{134,000, 146,000} = $146,000 (2 machines, node 3)
Hence, the best option is to buy 2 machines.
The expected payoff is $146,000.
Marking scheme: 1 point for each of the following
 decision nodes (squares)
 chance nodes (circles)
 payoffs and labels
 decision and
 expected payoff
4
Name:_________________________________________________
ID:_________________________
Question 3: (8 points)
Alpha Computer Products competed for and won a contract to produce two prototype units of a new
type of computer that is based on laser optics rather than on electronic binary bits. The first unit
produced by Alpha took 5,000 hours to produce and required $300,000 worth of materials,
equipment usage, and supplies. The second unit took 4,000 hours and used $255,000 worth of
materials, equipment usage, and supplies. Labor is $25 per hour. Alpha was asked to present a bid
for 4 additional units as soon as the second unit was completed. Production would start immediately.
What would this bid be? The following table reproduces some parts of Exhibits 2.5 and 2.6.
Unit
1
2
3
4
5
6
7
8
Unit Improvement Factor
80%
85%
90%
95%
1.0000 1.0000 1.0000 1.0000
0.8000 0.8500 0.9000 0.9500
0.7021 0.7729 0.8462 0.9219
0.6400 0.7225 0.8100 0.9025
0.5956 0.6857 0.7830 0.8877
0.5617 0.6570 0.7616 0.8758
0.5345 0.6337 0.7439 0.8659
0.5120 0.6141 0.7290 0.8574
Rate of learning for labor hour =
Cumulative Improvement Factor
80%
85%
90%
95%
1.0000 1.0000 1.0000 1.0000
1.8000 1.8500 1.9000 1.9500
2.5021 2.6229 2.7462 2.8719
3.1421 3.3454 3.5562 3.7744
3.7377 4.0311 4.3392 4.6621
4.2994 4.6881 5.1008 5.5380
4.8339 5.3217 5.8447 6.4039
5.3459 5.9358 6.5737 7.2612
4,000
 80% (1 point)
5,000
Rate of learning for materials, equipment usage and supplies =
Unit
(1 point)
3
4
5
6
Total
(1 point)
Labour hour
(1 point)
3,510.519
5,000  0.7021 =
3,200.000
5,000  0.6400 =
2,978.187
5,000  0.5956 =
2,808.415
5,000  0.5617 =
12,497.120
255,000
 85% (1 point)
300,000
Materials, equipment usage and
supplies (1 point)
$231,874.5
300,000  0.7729 =
216,750.0
300,000  0.7225 =
205,701.3
300,000  0.6857 =
197,093.3
300,000  0.6570 =
851,419.1
The total labor cost = 12,497.12025 =
$312,425.0 (1 point)
Materials, equipment usage and supplies are 851,491.1
Hence, the total cost =
$1,163,855.1(1 point)
Alternate solution
Labour hour = 5,000(4.2994-1.8000) = 12,497
Materials, equipment usage and supplies = 300,000(4.6881-1.8500) = $851,430.
5
Name:_________________________________________________
ID:_________________________
Question 4: (10 points)
Observed weekly sales of ball peen hammers at the town hardware store over a six-week period
have been 15, 10, 30, 25, 35, 15.
a. (3 points) Suppose that three-week moving averages are used to forecast sales. Determine the
one-step-ahead forecasts for weeks 4 through 6.
15  10  30
 18.33 (1 point)
3
10  30  25
F5 
 21.67 (1 point)
3
30  25  35
F6 
 30 (1 point)
3
F4 
b. (3 points) Suppose that exponential smoothing is used to with a smoothing constant of   0.20.
Find the exponential smoothing forecasts for weeks 4 through 6. (To get the method started, use
the same forecast for week 4 as you used in part a.)
F4  18.33
F5  18.33  0.2025  18.33  19.66 (2 points)
F6  19.66  0.2035  19.66  22.73 (1 point)
c. (4 points) Based on the MAD, which method did better?
Computing MAD over three periods (1 point)
25  18.33  35  21.67  15  30
MAD MA 
 11.67 (1 point)
3
25  18.33  35  19.66  15  22.73
MAD ES 
 9.91 (1 point)
3
Hence, exponential smoothing is better. (1 point)
Computing MAD over two periods
35  21.67  15  30
MAD MA 
 14.15
2
35  19.66  15  22.73
MAD ES 
 11.53
2
Hence, exponential smoothing is better.
6
Name:_________________________________________________
ID:_________________________
Question 5: (10 points)
Lakeroad, a manufacturer of hard disks for personal computers, was founded in 1998 and has sold
the following number of disks:
Year
Numbers Sold (in 000s)
1998
12
1999
23
2000
32
2001
41
a. (8 points) Calculate the exponential smoothing with trend component forecast for Years 19992001 using an initial trend forecast (T1) of 10, an initial exponential smoothing forecast (F1) of 2,
an  of 0.25, and a  of 0.25.
Year
t
1
Actual
At
12
Ft
Tt
FITt
2
10
2
23
12 + 0.25(12-12) = 12 (2 points)
10+0.25(12-12) = 10 (2 points)
3
32
22 + 0.25(23-22) = 22.25
10+0.25(22.25-22) = 10.06
4
41
32.31 + 0.25(32-32.31) = 32.23
10.06+0.25(32.23-32.31) = 10.04
2+10
= 12.00
12+10
= 22.00
(2 points)
22.25+10.06
= 32.31
(1 point)
32.23+10.04
= 240.27
(1 point)
b. (1 point) What is the sales forecast for the year 2002 made at the end of 2001?
F5  42.27  0.2541  42.27   41.96
T5  10.04  0.2541.96  42.27   9.96
FIT5  41.96  9.96  51.896
c. (1 point) What is the sales forecast for the year 2003 made at the end of 2001?
FIT6  F5  2T5  41.96  29.96  61.88
7
Name:_________________________________________________
ID:_________________________
Question 6: (12 points)
Use regression analysis on deseasonalized demand to forecast demand in Fall 2002, given the
following historical demand data:
Year
Season
2000
Winter
Spring
Summer
Fall
Winter
Spring
Summer
Fall
2001
Actual
Demand
55
70
75
60
60
65
80
70
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Name:_________________________________________________
ID:_________________________
Question 7 (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 four months is 900, 1300, 500, and 1000, expressed in thousands of cookies. During a
50-day period when there were 125 workers, the company produced 2.5 million cookies. Assume that
the numbers of workdays over the four months are respectively 24, 22, 20, and 16. There are
currently 75 workers employed, and there is no starting inventory of cookies.
a. (5 points) What is the minimum constant workforce required to meet demand over the next four
months?
2,500,000
 400 cookies per worker per day (1 point)
Number of units produced 
50  125
Since the maximum in the last column is 120 for Month 2, 120 workers are needed to avoid
shortage in Month 2 and if 120 workers are employed, demand of the other months can be met.
Thus, the minimum constant number of workers needed is 120. (1 point)
b. (5 points) Assume that the inventory holding cost is 10 cents per cookie per month, hiring cost is
$100 per worker, and firing cost is $200 per worker. Evaluate the cost of the plan derived in a.
Number of workers hired = 120-75 = 45
Hiring cost = 45  100 = 4,500 (1 point)
Hence, total holding and hiring cost = $96,400 + $4,500 = $100,900 (1 point)
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