Name (print, please) _______________________________________________ ID ___________________________
Production Management 73-604 Fall 2006
Odette School of Business
University of Windsor
Midterm Exam 1 Solution
Thursday, October 12, 5:30 – 6:50 pm
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.
Time available: 1 hour 20 min
Instructions:
 This exam has 12 pages.
 Please be sure to put your name and student ID number on odd numbered pages.
 Show your work.
Grading:
Question
Marks:
1
/10
2
/10
3
/15
4
/18
5
/12
Total:
/65
Name:_________________________________________________
ID:_________________________
Question 1: (10 points) Circle the most appropriate answer
1.1 Which of the following is a true statement?
a. We should match functional products with a responsive supply-chain.
b. We should match innovative products with an efficient supply-chain.
c. Functional products include the staples that people buy in a wide range of retail outlets,
such as grocery stores and gas stations.
d. Functional products do not include the staples that people buy in a wide range of retail outlets,
such as grocery stores and gas stations.
1.2 Which of the following is a true statement?
a. The capacity utilization ratio is found by dividing best operating level by capacity used.
b. At some point, the size of a growing plant can become too large and diseconomies of
scale become a capacity-planning problem.
c. The objective of strategic capacity planning is to provide an approach for determining the
overall capacity level of capital-intensive resources (including facilities, equipment, and overall
labor force size) that best supports the company’s short-range competitive strategy.
d. When plotted on a graph, the learning curve can’t be expressed as logarithm.
1.3 An assumption necessary for the learning curve theory is which of the following?
a. Unit time will decrease at a decreasing rate
b. Unit time will hold constant
c. Unit time will increase at an increasing rate
d. Unit time will increase at a decreasing rate
1.4 Which of the following is a true statement?
a. RSFE in forecasting stands for Readable Safety Function for Error detection.
b. When errors that occur in a forecast are normally distributed, the relationship of the MAD to
the standard deviation is 2 to 1, or 2(MAD)= 1 standard deviation.
c. Random errors can be defined as those that cannot be explained by the forecasting
model being used.
d. Random errors in forecasting can occur when the existence of some undetected secular trend
is not included in a forecasting model.
1.5 Which of the following is false?
a. The major restriction in using linear regression as a model for forecasting is that past data and
future projections are assumed to fall about a straight line.
b. Regression can be defined as a functional relationship between two or more correlated
variables, where we use one variable to predict another.
c. Linear regression is useful for long-term forecasting of major occurrences and aggregate
planning.
d. When using linear regression in forecasting, the standard error of the estimate cannot
be used to see how well the line the model generates fits the data.
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Name:_________________________________________________
ID:_________________________
1.6 Which of the following is false?
a. In the simple exponential smoothing forecasting model the data pattern should remain
stationary.
b. Single exponential smoothing has the shortcoming of lagging changes in demand.
c. The weights used in the weighted moving average forecasting model have to add up to
2.
d. When choosing weights for the weighted moving average forecasting model experience and
trial and error are the simplest ways to do it.
1.7 Demand for products or services can be broken down into which of the following components of
demand?
a. Average demand for a period
b. Trend influences
c. Seasonal influences
d. All of the above
1.8 Which of the following is false?
a. Aggregate planning involves translating annual and quarterly business plans into broad labor
and output plans for the intermediate term of 6 to 18 months.
b. The aggregate planning process is very different in every aspect when comparing
service operations with manufacturing operations.
c. The fixed and variable costs incurred in producing a given product type in a given period are
relevant aggregate production planning costs.
d. Master production schedule is not an input into the aggregate production plan.
1.9 The main purpose of aggregate planning is to specify the optimal combination of which of the
following?
a. Production rates
b. Workforce levels
c. Inventory on hand
d. All of the above
1.10 Matching the production rate to the order rate by hiring and laying off employees as the order
rate varies is which of the following production planning strategies?
a. Chase
b. Level
c. Stable workforce, variable work hours
d. All of the above
3
Name:_________________________________________________
ID:_________________________
Question 2 (10 Points)
A builder has located a piece of property that she would like to buy and eventually build on. The land
is currently zoned for four homes per acre, but she is planning to request new zoning. What she
builds depends on the approval of zoning requests and your analysis of this problem to advise her.
With her input and your help, the decision process has been reduced to the following costs,
alternatives, and probabilities:
Cost of land: $3 million.
Probability of rezoning: 0.70.
If the land is rezoned, there will be additional costs for new roads, lighting, and so on, of $2 million.
If the land is rezoned, the contractor must decide whether to build a shopping center or 1,500
apartments that the tentative plan shows would be possible. If she builds a shopping center, there is
a 75 percent chance that she can sell the shopping center to a large department chain for $5 million
over her construction cost, which excludes the land; and there is a 25 percent chance that she can
sell it an insurance company for $6 million over her construction cost (also excluding the land). If,
instead of the shopping center, she decides to build the 1,500 apartments, she places probabilities
on the profits as follows: There is a 55 percent chance that she can sell the apartments to a real
estate investment corporation for 4,000 each over her construction cost; there is a 45% chance that
she get only $3,000 each over her construction cost. (Both exclude the land cost.)
If the land is not rezoned, she will comply with the existing zoning restrictions and simply build 700
homes, on which she expects to make $4,500 over the construction cost on each one (excluding the
cost of land).
a. (4 points) Construct a decision tree.
See the next page.
b. (4 points) Compute the expected value of the payoff for each alternative.
EV(1) = 5(0.75)+6(0.25) = $5.25M
EV(2) = 6(0.55)+4.5(0.45) = $5.325M
EV(3) = Max{5.25, 5.325} = $5.325M
EV(4) = $3.15M
EV(5) = (5.325-2)(0.70)+(3.15)(0.30) = $3.2725M
EV(6) = Max{3.2725-3,0} = $0.2725M
c. (2 points) Which is the best alternative, based on the expected values?
Decision: Buy land. If land is rezoned, build apartment. If land is not rezoned, build home.
4
Name:_________________________________________________
ID:_________________________
Use this page, if necessary to answer Question 2
Rezoned,
cost $2M
0.7
Buy
land
5
0.3
Not
rezoned
6
Do not
buy land
3
Department
$5M
Chain
0.75
Shopping
1
Center
0.25
Insurance Co $6M
Real Estate $6M
0.55
Apartments 2
0.45
Selling
$4.5M
Build
$3.15
4
homes
$0
Question 3 (15 points)
Observations of the demand for a certain part stocked at a part supply depot during the last five
months of 2006 were:
Month
Demand
May
60
June
90
July
140
August
180
September
240
a. (3 points) Using a three-month moving average, determine the forecasts for August and
September 2006.
FAug = (60+90+140)/3 = 96.67, FSep = (90+140+180)/3 = 136.67
b. (3 points) Using exponential smoothing method with   0.1 and a July forecast of 150, determine
the forecasts for August and September 2006.
FAug = 0.10(140)+0.90(150) = 149, FSep = 0.10(180)+0.90(149) = 152.1
c. (5 points) Calculate the exponential smoothing with trend component forecast for August and
September using a July trend forecast (TJuly) of 50 for July, an initial exponential smoothing
forecast (FJuly) of 100, an  of 0.25, and a  of 0.20.
FITJuly  FJuly  TJuly  100+50 = 150
FAug  FITJul    AJul  FITJul   150+0.25(140-150) = 147.5
5
Name:_________________________________________________
ID:_________________________
T Aug  TJul   FAug  FITJul   50+0.20(147.5-150) = 49.5
FIT Aug  FAug  T Aug  147.5+49.5 = 197
FSep  FITAug   AAug  FITAug   197+0.25(180-197) = 192.75
TSep  T Aug   FSep  FIT Aug   49.5+0.20(192.75-197) = 48.65
FITSep  FSep  TSep  192.75+48.65 = 241.4
d. (4 points) For each method in a, b and c, compute MAD and tracking signal. Comment on which
method to use, if any. Assume that an acceptable level of the TS value is ±3.0.
Simple moving average
MADAug=(|180-96.67|)/1=83.33
RSFEAug=(180-96.67)=83.33
TSAug=83.33/83.33 =1.0
MADSep=(83.33+|240-136.67|)/2=93.33
RSFESep=83.33+(240-136.67)=186.67
TSSep=186.67/93.33 =2.0
Exponential smoothing
MADAug=(|180-149|)/1=31.0
RSFEAug=(180-149)=31.0
TSAug=31.0/31.0 =1.0
MADSep=(31.0+|240-152.1|)/2=59.45
RSFESep=31.0+(240-136.67)=118.90
TSSep=118.90/59.45 =2.0
Exponential smoothing with trend
MADAug=(|180-197|)/1=17.0
RSFEAug=(180-197)=-17.0
TSAug=-17.0/17.0=-1.0
MADSep=(17.0+|240-241.4|)/2=9.2
RSFESep=-17.0+(240-241.4)=-18.4
TSSep=-18.4/9.2=-2.0
Question 4 (8 points)
Use regression analysis on deseasonalized demand to forecast demand in summer 2007, given the
following historical demand data:
Year
Season
2005
Winter
Spring
Summer
Fall
Winter
Spring
Summer
Fall
2006
Actual
Demand
24
31
39
29
35
42
46
36
Quarterly average demand = (24+31+39+29+35+42+46+36)/8 = 35.25
Season
Average demand
Winter
(24+35)/2 = 29.5
Spring
(31+42)/2 = 36.5
6
Seasonal Index
29.5/35.25 = 0.8369
36.5/35.25 = 1.0354
Name:_________________________________________________
Summer
Fall
(39+46)/2 = 42.5
(29+36)/2 = 32.5
Period
x
Demand
1
2
3
4
5
6
7
8
 x =36
24
31
39
29
35
42
46
36
Deseasonalized
Demand
y
28.6773
29.9372
32.3464
31.4534
41.8210
40.5601
38.1521
39.0456
 y =281.9930
X =4.5
b
ID:_________________________
42.5/35.25 = 1.2057
32.5/35.25 = 0.9220
4.0000
xy
y2
28.6773
59.8745
97.0391
125.8134
209.1050
243.3607
267.0648
312.3644
 xy =1343.2992
1
4
9
16
25
36
49
64
 y 2 =204
Y =35.25
n xy   x y
n x 2   x 
2

81,343.2988   36281.9930 
8204   36
2

594.6424
 1.7698
336.0
a  Y  b X  35.25  1.7698 4.5  27.2850
FS , 07  y11  a  b11  27.2850  1.7698 11  46.7528
Forecast, summer 2007, reseasonalized = 46.7528(1.2057) = 56.37
Question 5 (12 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 650, 925 and 575, expressed in thousands of cookies. During a 40-day
period when there were 90 workers, the company produced 1.71 million cookies. Assume that the
numbers of workdays in a month is 22. There are currently 60 workers employed, and there is no
starting inventory of cookies.
a. (7 points) What is the minimum constant workforce (level strategy) required to meet demand
(shortages not allowed) over the next three months?
Productivity = 1.71  10 6 /40/90 = 475 cookies/worker/day
Production/month/worker = 475  22 = 10,450 cookies
Month
Demand
(000)
Cumulative
Demand
(000)
Production
Per Worker
(000)
1
650
650
10.450
7
Cumulative
Production
Per Worker
(000)
10.450
# of Workers
Needed
 650 
10.450   63
Name:_________________________________________________
ID:_________________________
2
925
1,575
10.450
20.900
3
575
2,150
10.450
31.350
Maximum
 1,575 
 20.900   76
 2,150 
 31.350   69
76
Minimum constant workforce = 76 workers
b. (5 points) Assume that the inventory holding cost is 25 cents per cookie per month, hiring cost is
$400 per worker, and firing cost is $500 per worker. Evaluate the cost of the plan derived in a.
Production / month = 76  10,450 = 794,200 cookies
Month
1
2
3
Beginning
Inventory
(000)
0
144.200
925
Production
(000)
Demand
(000)
Ending Inventory
(000)
794.200
794.200
794.200
650
925
575
0+794.200-650=144.200
144.200+794.200-925=13.400
13.400+794.200-575=232.600
Total = 390.200
Number of workers hired = 76-60 = 16 workers
Hiring cost = 16(400) = $6,400
Inventory holding cost = 390,200(0.25) = $97,550
Total cost = $97,550+$6,400 = $103,950
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