Chapter 12
Forecasting
Lecture Outline
• Strategic Role of Forecasting in Supply Chain
Management
• Components of Forecasting Demand
• Time Series Methods
• Forecast Accuracy
• Time Series Forecasting Using Excel
• Regression Methods
Copyright 2011 John Wiley & Sons, Inc.
12-2
Forecasting
• Predicting the future
• Qualitative forecast methods
• subjective
• Quantitative forecast methods
• based on mathematical formulas
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12-3
Supply Chain Management
• Accurate forecasting determines inventory levels
in the supply chain
• Continuous replenishment
•
•
•
•
supplier & customer share continuously updated data
typically managed by the supplier
reduces inventory for the company
speeds customer delivery
• Variations of continuous replenishment
•
•
•
•
quick response
JIT (just-in-time)
VMI (vendor-managed inventory)
stockless inventory
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12-4
The Effect of Inaccurate Forecasting
Copyright 2011 John Wiley & Sons, Inc.
12-5
Forecasting
• Quality Management
• Accurately forecasting customer demand is a key to
providing good quality service
• Strategic Planning
• Successful strategic planning requires accurate
forecasts of future products and markets
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12-6
Types of Forecasting Methods
• Depend on
• time frame
• demand behavior
• causes of behavior
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12-7
Time Frame
• Indicates how far into the future is forecast
• Short- to mid-range forecast
• typically encompasses the immediate future
• daily up to two years
• Long-range forecast
• usually encompasses a period of time longer than
two years
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12-8
Demand Behavior
• Trend
• a gradual, long-term up or down movement of
demand
• Random variations
• movements in demand that do not follow a pattern
• Cycle
• an up-and-down repetitive movement in demand
• Seasonal pattern
• an up-and-down repetitive movement in demand
occurring periodically
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12-9
Demand
Demand
Forms of Forecast Movement
Random
movement
Time
(b) Cycle
Demand
Demand
Time
(a) Trend
Time
(c) Seasonal pattern
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Time
(d) Trend with seasonal pattern
12-10
Forecasting Methods
• Time series
• statistical techniques that use historical demand data
to predict future demand
• Regression methods
• attempt to develop a mathematical relationship
between demand and factors that cause its behavior
• Qualitative
• use management judgment, expertise, and opinion to
predict future demand
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12-11
Qualitative Methods
• Management, marketing, purchasing, and
engineering are sources for internal qualitative
forecasts
• Delphi method
• involves soliciting forecasts about technological
advances from experts
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12-12
Forecasting Process
1. Identify the
purpose of forecast
2. Collect historical
data
3. Plot data and identify
patterns
6. Check forecast
accuracy with one or
more measures
5. Develop/compute
forecast for period of
historical data
4. Select a forecast
model that seems
appropriate for data
7.
Is accuracy of
forecast
acceptable?
No
8b. Select new
forecast model or
adjust parameters of
existing model
Yes
8a. Forecast over
planning horizon
Copyright 2011 John Wiley & Sons, Inc.
9. Adjust forecast based
on additional qualitative
information and insight
10. Monitor results
and measure forecast
accuracy
12-13
Time Series
• Assume that what has occurred in the past will
continue to occur in the future
• Relate the forecast to only one factor - time
• Include
• moving average
• exponential smoothing
• linear trend line
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12-14
Moving Average
• Naive forecast
• demand in current period is used as next period’s
forecast
• Simple moving average
• uses average demand for a fixed sequence of periods
• stable demand with no pronounced behavioral
patterns
• Weighted moving average
• weights are assigned to most recent data
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12-15
Moving Average: Naïve Approach
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
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ORDERS
PER MONTH
120
90
100
75
110
50
75
130
110
90
-
FORECAST
120
90
100
75
110
50
75
130
110
90
12-16
Simple Moving Average
n
Di

i=1
MAn =
n
where
n = number of periods in
the moving average
Di = demand in period i
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12-17
3-month Simple Moving Average
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
ORDERS
PER MONTH
120
90
100
75
110
50
75
130
110
90
-
Copyright 2011 John Wiley & Sons, Inc.
MOVING
AVERAGE
–
–
–
103.3
88.3
95.0
78.3
78.3
85.0
105.0
110.0
3
Di

i=1
MA3 =
=
3
90 + 110 + 130
3
= 110 orders for Nov
12-18
5-month Simple Moving Average
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
ORDERS
PER MONTH
120
90
100
75
110
50
75
130
110
90
-
Copyright 2011 John Wiley & Sons, Inc.
MOVING
AVERAGE
–
–
–
–
–
99.0
85.0
82.0
88.0
95.0
91.0
5
Di

i=1
MA5 =
=
5
90 + 110 + 130+75+50
5
= 91 orders for Nov
12-19
Smoothing Effects
150 –
5-month
125 –
Orders
100 –
75 –
50 –
3-month
Actual
25 –
0–
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
|
June July
|
|
Aug Sept
|
Oct
|
Nov
Month
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12-20
Weighted Moving Average
• Adjusts moving average method to more closely
reflect data fluctuations
n
WMAn =
 Wi Di
i=1
where
Wi = the weight for period i,
between 0 and 100
percent
 Wi = 1.00
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12-21
Weighted Moving Average Example
MONTH
August
September
October
WEIGHT
DATA
17%
33%
50%
130
110
90
3
November Forecast
WMA3 =
Wi Di

i=1
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= 103.4 orders
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12-22
Exponential Smoothing
•
•
•
•
Averaging method
Weights most recent data more strongly
Reacts more to recent changes
Widely used, accurate method
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12-23
Exponential Smoothing
Ft +1 = Dt + (1 - )Ft
where:
Ft +1 = forecast for next period
Dt = actual demand for present period
Ft = previously determined forecast for
present period
=
weighting factor, smoothing constant
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12-24
Effect of Smoothing Constant
0.0  1.0
If = 0.20, then Ft +1 = 0.20 Dt + 0.80 Ft
If = 0, then Ft +1 = 0 Dt + 1 Ft = Ft
Forecast does not reflect recent data
If = 1, then Ft +1 = 1 Dt + 0 Ft = Dt
Forecast based only on most recent data
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12-25
Exponential Smoothing (α=0.30)
PERIOD
1
2
3
4
5
6
7
8
9
10
11
12
MONTH
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
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DEMAND
37
40
41
37
45
50
43
47
56
52
55
54
F2 = D1 + (1 - )F1
= (0.30)(37) + (0.70)(37)
= 37
F3 = D2 + (1 - )F2
= (0.30)(40) + (0.70)(37)
= 37.9
F13 = D12 + (1 - )F12
= (0.30)(54) + (0.70)(50.84)
= 51.79
12-26
Exponential Smoothing
PERIOD
MONTH
DEMAND
1
2
3
4
5
6
7
8
9
10
11
12
13
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
37
40
41
37
45
50
43
47
56
52
55
54
–
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FORECAST, Ft + 1
( = 0.3)
( = 0.5)
–
37.00
37.90
38.83
38.28
40.29
43.20
43.14
44.30
47.81
49.06
50.84
51.79
–
37.00
38.50
39.75
38.37
41.68
45.84
44.42
45.71
50.85
51.42
53.21
53.61
12-27
Exponential Smoothing
70 –
60 –
 = 0.50
Actual
Orders
50 –
40 –
 = 0.30
30 –
20 –
10 –
0–
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
Month
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12-28
Adjusted Exponential Smoothing
AFt +1 = Ft +1 + Tt +1
where
T = an exponentially smoothed trend factor
Tt +1 = (Ft +1 - Ft) + (1 - ) Tt
where
Tt = the last period trend factor
= a smoothing constant for trend
0 ≤  ≤ 1
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12-29
Adjusted Exponential Smoothing (β=0.30)
PERIOD
MONTH
DEMAND
1
2
3
4
5
6
7
8
9
10
11
12
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
37
40
41
37
45
50
43
47
56
52
55
54
Copyright 2011 John Wiley & Sons, Inc.
T3
= (F3 - F2) + (1 - ) T2
= (0.30)(38.5 - 37.0) + (0.70)(0)
= 0.45
AF3 = F3 + T3 = 38.5 + 0.45
= 38.95
T13 = (F13 - F12) + (1 - ) T12
= (0.30)(53.61 - 53.21) + (0.70)(1.77)
= 1.36
AF13 = F13 + T13 = 53.61 + 1.36 = 54.97
12-30
Adjusted Exponential Smoothing
PERIOD
MONTH
DEMAND
FORECAST
Ft +1
1
2
3
4
5
6
7
8
9
10
11
12
13
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
37
40
41
37
45
50
43
47
56
52
55
54
–
37.00
37.00
38.50
39.75
38.37
38.37
45.84
44.42
45.71
50.85
51.42
53.21
53.61
Copyright 2011 John Wiley & Sons, Inc.
TREND
Tt +1
ADJUSTED
FORECAST AFt +1
–
0.00
0.45
0.69
0.07
0.07
1.97
0.95
1.05
2.28
1.76
1.77
1.36
–
37.00
38.95
40.44
38.44
38.44
47.82
45.37
46.76
58.13
53.19
54.98
54.96
12-31
Adjusted Exponential Smoothing
Forecasts
70 –
Adjusted forecast ( = 0.30)
60 –
Actual
Demand
50 –
40 –
Forecast ( = 0.50)
30 –
20 –
10 –
0–
|
1
|
2
|
3
Copyright 2011 John Wiley & Sons, Inc.
|
4
|
5
|
|
6
7
Period
|
8
|
9
|
10
|
11
|
12
|
13
12-32
Linear Trend Line
y = a + bx
where
a = intercept
b = slope of the line
x = time period
y = forecast for
demand for period x
Copyright 2011 John Wiley & Sons, Inc.
xy - nxy
b =
x2 - nx2
a = y-bx
where
n = number of periods
x
x =
= mean of the x values
n
y
y = n = mean of the y values
12-33
Least Squares Example
x(PERIOD)
y(DEMAND)
xy
x2
1
2
3
4
5
6
7
8
9
10
11
12
73
40
41
37
45
50
43
47
56
52
55
54
37
80
123
148
225
300
301
376
504
520
605
648
1
4
9
16
25
36
49
64
81
100
121
144
78
557
3867
650
Copyright 2011 John Wiley & Sons, Inc.
12-34
Least Squares Example
x = 78 = 6.5
12
y = 557 = 46.42
12
b = xy - nxy =
x2 - nx2
3867 - (12)(6.5)(46.42) =1.72
650 - 12(6.5)2
a = y - bx
= 46.42 - (1.72)(6.5) = 35.2
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12-35
Linear trend line y = 35.2 + 1.72x
Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units
70 –
60 –
Actual
Demand
50 –
40 –
Linear trend line
30 –
20 –
10 –
|
1
|
2
|
3
Copyright 2011 John Wiley & Sons, Inc.
|
4
|
5
|
|
6
7
Period
|
8
|
9
|
10
|
11
|
12
|
13
12-36
Seasonal Adjustments
 Repetitive increase/ decrease in demand
 Use seasonal factor to adjust forecast
Seasonal factor = Si =
Copyright 2011 John Wiley & Sons, Inc.
Di
D
12-37
Seasonal Adjustment
YEAR
2002
2003
2004
Total
DEMAND (1000’S PER QUARTER)
1
2
3
4
Total
12.6
14.1
15.3
42.0
8.6
10.3
10.6
29.5
6.3
7.5
8.1
21.9
17.5
18.2
19.6
55.3
45.0
50.1
53.6
148.7
D1
42.0
S1 =
=
= 0.28
D 148.7
D3
21.9
S3 =
=
= 0.15
D 148.7
D2
29.5
S2 =
=
= 0.20
D 148.7
D4
55.3
S4 =
=
= 0.37
D 148.7
Copyright 2011 John Wiley & Sons, Inc.
12-38
Seasonal Adjustment
For 2005
y = 40.97 + 4.30x = 40.97 + 4.30(4) = 58.17
SF1 = (S1) (F5) = (0.28)(58.17) = 16.28
SF2 = (S2) (F5) = (0.20)(58.17) = 11.63
SF3 = (S3) (F5) = (0.15)(58.17) = 8.73
SF4 = (S4) (F5) = (0.37)(58.17) = 21.53
Copyright 2011 John Wiley & Sons, Inc.
12-39
Forecast Accuracy
• Forecast error
• difference between forecast and actual demand
• MAD
• mean absolute deviation
• MAPD
• mean absolute percent deviation
• Cumulative error
• Average error or bias
Copyright 2011 John Wiley & Sons, Inc.
12-40
Mean Absolute Deviation (MAD)
 Dt - Ft 
MAD =
n
where
t = period number
Dt = demand in period t
Ft = forecast for period t
n = total number of periods
 = absolute value
Copyright 2011 John Wiley & Sons, Inc.
12-41
MAD Example
PERIOD
1
2
3
4
5
6
7
8
9
10
11
12
DEMAND, Dt
Ft ( =0.3)
(Dt - Ft)
|Dt - Ft|
37
40
41
37
45
50
43
47
56
52
55
54
37.00
37.00
37.90
38.83
38.28
40.29
43.20
43.14
44.30
47.81
49.06
50.84
–
3.00
3.10
-1.83
6.72
9.69
-0.20
3.86
11.70
4.19
5.94
3.15
–
3.00
3.10
1.83
6.72
9.69
0.20
3.86
11.70
4.19
5.94
3.15
49.31
53.39
557
Copyright 2011 John Wiley & Sons, Inc.
12-42
MAD Calculation
 Dt - Ft 
MAD =
n
53.39
=
11
= 4.85
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12-43
Other Accuracy Measures
Mean absolute percent deviation (MAPD)
|Dt - Ft|
MAPD =
Dt
Cumulative error
E = et
Average error
et
E= n
Copyright 2011 John Wiley & Sons, Inc.
12-44
Comparison of Forecasts
FORECAST
MAD
MAPD
E
(E)
Exponential smoothing (= 0.30)
Exponential smoothing (= 0.50)
Adjusted exponential smoothing
(= 0.50, = 0.30)
Linear trend line
4.85
4.04
3.81
9.6%
8.5%
7.5%
49.31
33.21
21.14
4.48
3.02
1.92
2.29
4.9%
–
–
Copyright 2011 John Wiley & Sons, Inc.
12-45
Forecast Control
• Tracking signal
• monitors the forecast to see if it is biased high or low
• 1 MAD ≈ 0.8 б
• Control limits of 2 to 5 MADs are used most frequently
Tracking signal =
Copyright 2011 John Wiley & Sons, Inc.
(Dt - Ft)
E
=
MAD
MAD
12-46
Tracking Signal Values
PERIOD
DEMAND
Dt
FORECAST,
Ft
1
2
3
4
5
6
7
8
9
10
11
12
37
40
41
37
45
50
43
47
56
52
55
54
37.00
37.00
37.90
38.83
38.28
40.29
43.20
43.14
44.30
47.81
49.06
50.84
TS3 =
Copyright 2011 John Wiley & Sons, Inc.
ERROR
Dt - Ft
–
3.00
3.10
-1.83
6.72
9.69
-0.20
3.86
11.70
4.19
5.94
3.15
E =
(Dt - Ft)
MAD
–
3.00
6.10
4.27
10.99
20.68
20.48
24.34
36.04
40.23
46.17
49.32
–
3.00
3.05
2.64
3.66
4.87
4.09
4.06
5.01
4.92
5.02
4.85
TRACKING
SIGNAL
–
1.00
2.00
1.62
3.00
4.25
5.01
6.00
7.19
8.18
9.20
10.17
6.10
= 2.00
3.05
12-47
Tracking Signal Plot
Tracking signal (MAD)
3 –
2 –
Exponential smoothing ( = 0.30)
1 –
0 –
-1 –
-2 –
Linear trend line
-3 –
|
0
|
1
|
2
|
3
Copyright 2011 John Wiley & Sons, Inc.
|
4
|
5
|
6
Period
|
7
|
8
|
9
|
10
|
11
|
12
12-48
Statistical Control Charts
=
(Dt - Ft)2
n-1
 Using  we can calculate statistical
control limits for the forecast error
 Control limits are typically set at  3
Copyright 2011 John Wiley & Sons, Inc.
12-49
Statistical Control Charts
18.39 –
UCL = +3
12.24 –
Errors
6.12 –
0–
-6.12 –
-12.24 –
-18.39 –
|
0
LCL = -3
|
1
|
2
|
3
Copyright 2011 John Wiley & Sons, Inc.
|
4
|
5
|
6
Period
|
7
|
8
|
9
|
10
|
11
|
12
12-50
Time Series Forecasting Using Excel
• Excel can be used to develop forecasts:
•
•
•
•
Moving average
Exponential smoothing
Adjusted exponential smoothing
Linear trend line
Copyright 2011 John Wiley & Sons, Inc.
12-51
Exponentially Smoothed and Adjusted
Exponentially Smoothed Forecasts
=B5*(C11-C10)+
(1-B5)*D10
=C10+D10
=ABS(B10-E10)
=SUM(F10:F20)
=G22/11
Copyright 2011 John Wiley & Sons, Inc.
12-52
Demand and Exponentially Smoothed
Forecast
Click on “Insert” then “Line”
Copyright 2011 John Wiley & Sons, Inc.
12-53
Data Analysis Option
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12-54
Forecasting With Seasonal Adjustment
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12-55
Forecasting With OM Tools
Copyright 2011 John Wiley & Sons, Inc.
12-56
Regression Methods
• Linear regression
• mathematical technique that relates a dependent
variable to an independent variable in the form of a
linear equation
• Correlation
• a measure of the strength of the relationship between
independent and dependent variables
Copyright 2011 John Wiley & Sons, Inc.
12-57
Linear Regression
y = a + bx
a = y-bx
xy - nxy
b =
x2 - nx2
where
a = intercept
b = slope of the line
x
x =
= mean of the x data
n
y
y = n = mean of the y data
Copyright 2011 John Wiley & Sons, Inc.
12-58
Linear Regression Example
x
(WINS)
y
(ATTENDANCE)
xy
x2
4
6
6
8
6
7
5
7
36.3
40.1
41.2
53.0
44.0
45.6
39.0
47.5
145.2
240.6
247.2
424.0
264.0
319.2
195.0
332.5
16
36
36
64
36
49
25
49
49
346.7
2167.7
311
Copyright 2011 John Wiley & Sons, Inc.
12-59
Linear Regression Example
49
= 6.125
8
346.9
y=
= 43.36
8
x=
xy - nxy2
b=
x2 - nx2
(2,167.7) - (8)(6.125)(43.36)
=
(311) - (8)(6.125)2
= 4.06
a = y - bx
= 43.36 - (4.06)(6.125)
= 18.46
Copyright 2011 John Wiley & Sons, Inc.
12-60
Linear Regression Example
60,000 –
Attendance, y
50,000 –
40,000 –
30,000 –
Linear regression line, y
= 18.46 + 4.06x
20,000 –
Attendance forecast for 7 wins
y = 18.46 + 4.06(7)
= 46.88, or 46,880
10,000 –
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Wins, x
Copyright 2011 John Wiley & Sons, Inc.
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Correlation and Coefficient of
Determination
• Correlation, r
• Measure of strength of relationship
• Varies between -1.00 and +1.00
• Coefficient of determination, r2
• Percentage of variation in dependent variable
resulting from changes in the independent variable
Copyright 2011 John Wiley & Sons, Inc.
12-62
Computing Correlation
r=
n xy -  x y
[n x2 - ( x)2] [n y2 - ( y)2]
(8)(2,167.7) - (49)(346.9)
r=
[(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2]
r = 0.947
Coefficient of determination
r2 = (0.947)2 = 0.897
Copyright 2011 John Wiley & Sons, Inc.
12-63
Regression Analysis With Excel
=INTERCEPT(B5:B12,A5:A12)
=SUM(B5:B12)
Copyright 2011 John Wiley & Sons, Inc.
=CORREL(B5:B12,A5:A12)
12-64
Regression Analysis with Excel
Copyright 2011 John Wiley & Sons, Inc.
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Regression Analysis With Excel
Copyright 2011 John Wiley & Sons, Inc.
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Multiple Regression
Study the relationship of demand to two or more
independent variables
y = 0 + 1x1 + 2x2 … + kxk
where
0 = the intercept
1, … , k = parameters for the
independent variables
x1, … , xk = independent variables
Copyright 2011 John Wiley & Sons, Inc.
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Multiple Regression With Excel
r2, the coefficient
of determination
Copyright 2011 John Wiley & Sons, Inc.
Regression equation
coefficients for x1 and x2
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Multiple Regression Example
y = 19,094.42 + 3560.99 x1 + .0368 x2
y = 19,094.42 + 3560.99 (7) + .0368 (60,000)
= 46,229.35
Copyright 2011 John Wiley & Sons, Inc.
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Copyright 2011 John Wiley & Sons, Inc.
All rights reserved. Reproduction or translation of this
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by the use of these programs or from the use of the
information herein.
Copyright 2011 John Wiley & Sons, Inc.
12-70