SCM 05 and 06
Forecasting techniques
Time-Series Forecasting
Decomposition of a Time Series
Naive Approach
Moving Averages
 Exponential Smoothing
 Exponential Smoothing with Trend
Adjustment
 Trend Projections
 Seasonal Variations in Data
 Cyclical Variations in Data
Types of Forecasts
• Economic forecasts
– Address business cycle – inflation rate,
money supply, housing starts, etc.
• Technological forecasts
– Predict rate of technological progress
– Impacts development of new products
• Demand forecasts
– Predict sales of existing products and
services
Seven Steps in Forecasting
• Determine the use of the forecast
• Select the items to be forecasted
• Determine the time horizon of the
forecast
• Select the forecasting model(s)
• Gather the data
• Make the forecast
• Validate and implement results
Overview of Quantitative
Approaches
• Naive approach
• Moving averages
• Exponential smoothing
• Trend projection
Time-Series
Models
• Linear regression
Associative
Model
Time Series Forecasting
•
Set of evenly spaced numerical
data
– Obtained by observing response
variable at regular time periods
• Forecast based only on past values,
no other variables important
– Assumes that factors influencing past
and present will continue influence in
future
Time Series Components
Trend
Cyclical
Seasonal
Random
Demand for product or service
Components of Demand
Trend
component
Seasonal peaks
Actual
demand
Average
demand over
four years
Random
variation
|
1
|
2
|
3
Year
|
4
Trend Component
• Persistent, overall upward or
downward pattern
• Changes due to population,
technology, age, culture, etc.
• Typically several years duration
Seasonal Component
• Regular pattern of up and down
fluctuations
• Due to weather, customs, etc.
• Occurs within a single year
Period
Length
Number of
Seasons
Week
Month
Month
Year
Year
Year
Day
Week
Day
Quarter
Month
Week
7
4-4.5
28-31
4
12
52
Cyclical Component
• Repeating up and down movements
• Affected by business cycle, political,
and economic factors
• Multiple years duration
• Often causal or
associative
relationships
0
5
10
15
20
Random Component
• Erratic, unsystematic, ‘residual’
fluctuations
• Due to random variation or
unforeseen events
• Short duration and
nonrepeating
M
T
W
T
F
Naive Approach
 Assumes demand in next
period is the same as
demand in most recent period
 e.g., If January sales were 68, then
February sales will be 68
 Sometimes cost effective and
efficient
 Can be good starting point
Moving Average Method
•
MA is a series of arithmetic means
• Used if little or no trend
• Used often for smoothing
– Provides overall impression of data
over time
∑ demand in previous n periods
Moving average =
n
Moving Average Example
Month
Actual
Shed Sales
3-Month
Moving Average
January
February
March
April
May
June
July
10
12
13
16
19
23
26
(10 + 12 + 13)/3 = 11 2/3
(12 + 13 + 16)/3 = 13 2/3
(13 + 16 + 19)/3 = 16
(16 + 19 + 23)/3 = 19 1/3
Shed Sales
Graph of Moving Average
30
28
26
24
22
20
18
16
14
12
10
Moving
Average
Forecast
–
–
–
–
–
–
–
–
–
–
–
Actual
Sales
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J
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D
Weighted Moving Average
• Used when trend is present
– Older data usually less important
• Weights based on experience and
intuition
Weighted
moving average =
∑ (weight for period n)
x (demand in period n)
∑ weights
Weights Applied
3
2
1
6
Period
Last month
Two months ago
Three months ago
Sum of weights
Weighted Moving Average
Month
Actual
Shed Sales
January
February
March
April
May
June
July
10
12
13
16
19
23
26
3-Month Weighted
Moving Average
[(3 x 13) + (2 x 12) + (10)]/6 = 121/6
[(3 x 16) + (2 x 13) + (12)]/6 = 141/3
[(3 x 19) + (2 x 16) + (13)]/6 = 17
[(3 x 23) + (2 x 19) + (16)]/6 = 201/2
Potential Problems With
Moving Average
• Increasing n smooths the forecast
but makes it less sensitive to
changes
• Do not forecast trends well
• Require extensive historical data
Moving Average And
Weighted Moving Average
Weighted
moving
average
Sales demand
30 –
25 –
20 –
Actual
sales
15 –
Moving
average
10 –
5 –
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Figure 4.2
J
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D
Exponential Smoothing
• Form of weighted moving average
– Weights decline exponentially
– Most recent data weighted most
• Requires smoothing constant ( )
– Ranges from 0 to 1
– Subjectively chosen
• Involves little record keeping of past
data
Exponential Smoothing
New forecast = Last period’s forecast
+ a (Last period’s actual demand
– Last period’s forecast)
Ft = Ft – 1 + a(At – 1 - Ft – 1)
where
Ft = new forecast
Ft – 1 = previous forecast
a = smoothing (or weighting)
constant (0 ≤ a ≤ 1)
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = 142 + .2(153 – 142)
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = 142 + .2(153 – 142)
= 142 + 2.2
= 144.2 ≈ 144 cars
Effect of
Smoothing Constants
Weight Assigned to
Smoothing
Constant
Most
Recent
Period
(a)
2nd Most 3rd Most 4th Most 5th Most
Recent
Recent
Recent
Recent
Period
Period
Period
Period
2
3
a(1 - a) a(1 - a)
a(1 - a)
a(1 - a)4
a = .1
.1
.09
.081
.073
.066
a = .5
.5
.25
.125
.063
.031
Impact of Different a
Demand
225 –
a = .5
Actual
demand
200 –
175 –
a = .1
150 – |
1
|
2
|
3
|
4
|
5
Quarter
|
6
|
7
|
8
|
9
Impact of Different a
Demand
225 –
Actual

Chose
high values
of
demand
200
–
a = .5
a
when underlying average
is likely to change
175 –

Choose low values of a
when underlying average
is stable|
|
|
|
150 – |
1
2
3
4
5
Quarter
a = .1
|
6
|
7
|
8
|
9
Choosing a
The objective is to obtain the most
accurate forecast no matter the
technique
We generally do this by selecting the
model that gives us the lowest forecast
error
Forecast error = Actual demand - Forecast value
= At - Ft
Common Measures of Error
Mean Absolute Deviation (MAD)
MAD =
∑ |Actual - Forecast|
n
Mean Squared Error (MSE)
MSE =
∑ (Forecast Errors)2
n
Common Measures of Error
Mean Absolute Percent Error (MAPE)
n
∑100|Actuali - Forecasti|/Actuali
MAPE =
i=1
n
Comparison of Forecast
Error
Quarter
Actual
Tonnage
Unloaded
Rounded
Forecast
with
a = .10
Absolute
Deviation
for
a = .10
1
2
3
4
5
6
7
8
180
168
159
175
190
205
180
182
175
175.5
174.75
173.18
173.36
175.02
178.02
178.22
5.00
7.50
15.75
1.82
16.64
29.98
1.98
3.78
82.45
Rounded
Forecast
with
a = .50
175
177.50
172.75
165.88
170.44
180.22
192.61
186.30
Absolute
Deviation
for
a = .50
5.00
9.50
13.75
9.12
19.56
24.78
12.61
4.30
98.62
Comparison of Forecast
Error
∑ |deviations|
MADActual
=
Quarter
Tonnage
Unloaded
Rounded
Forecast
n
with
a = .10
Absolute
Deviation
for
a = .10
For a180
= .10 175
5.00
168 = 82.45/8
175.5 = 10.31
7.50
1
2
3
4 For
5
6
7
8
159
174.75
a175
= .50 173.18
190
173.36
205 = 98.62/8
175.02
180
178.02
182
178.22
=
15.75
1.82
16.64
12.33
29.98
1.98
3.78
82.45
Rounded
Forecast
with
a = .50
175
177.50
172.75
165.88
170.44
180.22
192.61
186.30
Absolute
Deviation
for
a = .50
5.00
9.50
13.75
9.12
19.56
24.78
12.61
4.30
98.62
Comparison of Forecast
Error
∑ (forecast errors)2
MSE = Actual
Quarter
Tonnage
Unloaded
Rounded
Forecast
n
with
a = .10
Absolute
Deviation
for
a = .10
For a180
= .10 175
5.00
168
175.5 = 190.82
7.50
= 1,526.54/8
1
2
3
4 For
5
6
7
8
159
174.75
a175
= .50 173.18
190
173.36
= 1,561.91/8
205
175.02
180
178.02
182
178.22
MAD
=
15.75
1.82
16.64
195.24
29.98
1.98
3.78
82.45
10.31
Rounded
Forecast
with
a = .50
175
177.50
172.75
165.88
170.44
180.22
192.61
186.30
Absolute
Deviation
for
a = .50
5.00
9.50
13.75
9.12
19.56
24.78
12.61
4.30
98.62
12.33
Comparison of Forecast
n
Errori|/actuali
∑100|deviation
i=1
MAPE =
Actual
Quarter
1
2
3
4
5
6
7
8
Tonnage
Unloaded
Rounded
Forecast
with
a = .10
n
Absolute
Deviation
for
a = .10
For 180
a = .10 175
5.00
168
175.5
= 44.75/8
= 7.50
5.59%
159
For 175
a=
190
205
180
182
174.75
15.75
1.82
.50 173.18
173.36
16.64
= 54.05/8
=29.98
6.76%
175.02
178.02
1.98
178.22
3.78
82.45
MAD
10.31
MSE
190.82
Rounded
Forecast
with
a = .50
175
177.50
172.75
165.88
170.44
180.22
192.61
186.30
Absolute
Deviation
for
a = .50
5.00
9.50
13.75
9.12
19.56
24.78
12.61
4.30
98.62
12.33
195.24
Comparison of Forecast
Error
Quarter
Actual
Tonnage
Unloaded
Rounded
Forecast
with
a = .10
1
2
3
4
5
6
7
8
180
168
159
175
190
205
180
182
175
175.5
174.75
173.18
173.36
175.02
178.02
178.22
MAD
MSE
MAPE
Absolute
Deviation
for
a = .10
5.00
7.50
15.75
1.82
16.64
29.98
1.98
3.78
82.45
10.31
190.82
5.59%
Rounded
Forecast
with
a = .50
175
177.50
172.75
165.88
170.44
180.22
192.61
186.30
Absolute
Deviation
for
a = .50
5.00
9.50
13.75
9.12
19.56
24.78
12.61
4.30
98.62
12.33
195.24
6.76%
Exponential Smoothing with
Trend Adjustment
When a trend is present, exponential
smoothing must be modified
Forecast
Exponentially
Exponentially
including (FITt) = smoothed (Ft) + (Tt) smoothed
trend
forecast
trend
Exponential Smoothing with
Trend Adjustment
Ft = a(At - 1) + (1 - a)(Ft - 1 + Tt - 1)
Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1
Step 1: Compute Ft
Step 2: Compute Tt
Step 3: Calculate the forecast FITt = Ft + Tt
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Actual
Demand (At)
12
17
20
19
24
21
31
28
36
Smoothed
Forecast, Ft
11
Smoothed
Trend, Tt
2
Forecast
Including
Trend, FITt
13.00
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Forecast
Including
Trend, FITt
13.00
Actual
Smoothed
Smoothed
Demand (At) Forecast, Ft
Trend, Tt
12
11
2
17
20
19
Step 1: Forecast for Month 2
24
21
F2 = aA1 + (1 - a)(F1 + T1)
31
28
F2 = (.2)(12) + (1 - .2)(11 + 2)
36
= 2.4 + 10.4 = 12.8 units
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Forecast
Including
Trend, FITt
13.00
Actual
Smoothed
Smoothed
Demand (At) Forecast, Ft
Trend, Tt
12
11
2
17
12.80
20
19
Step 2: Trend for Month 2
24
21
T2 = b(F2 - F1) + (1 - b)T1
31
28
T2 = (.4)(12.8 - 11) + (1 - .4)(2)
36
= .72 + 1.2 = 1.92 units
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Forecast
Including
Trend, FITt
13.00
Actual
Smoothed
Smoothed
Demand (At) Forecast, Ft
Trend, Tt
12
11
2
17
12.80
1.92
20
19
Step 3: Calculate FIT for Month 2
24
21
FIT2 = F2 + T1
31
28
FIT2 = 12.8 + 1.92
36
= 14.72 units
Exponential Smoothing with
Trend Adjustment Example
Month(t)
1
2
3
4
5
6
7
8
9
10
Actual
Demand (At)
12
17
20
19
24
21
31
28
36
Smoothed
Forecast, Ft
11
12.80
15.18
17.82
19.91
22.51
24.11
27.14
29.28
32.48
Smoothed
Trend, Tt
2
1.92
2.10
2.32
2.23
2.38
2.07
2.45
2.32
2.68
Forecast
Including
Trend, FITt
13.00
14.72
17.28
20.14
22.14
24.89
26.18
29.59
31.60
35.16
Exponential Smoothing with
Trend Adjustment Example
35 –
Actual demand (At)
Product demand
30 –
25 –
20 –
15 –
Forecast including trend (FITt)
with a = .2 and b = .4
10 –
5 –
0 – |
1
|
2
|
3
|
4
|
5
|
6
Time (month)
|
7
|
8
|
9
Trend Projections
Fitting a trend line to historical data points
to project into the medium to long-range
Linear trends can be found using the least
squares technique
y^ = a + bx
^ = computed value of the variable to
where y
be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable
Values of Dependent Variable
Least Squares Method
Actual observation
(y value)
Deviation7
Deviation5
Deviation6
Deviation3
Deviation4
Deviation1
(error)
Deviation2
Trend line, y^ = a + bx
Time period
Values of Dependent Variable
Least Squares Method
Actual observation
(y value)
Deviation7
Deviation5
Deviation3
Deviation6
Least squares method
minimizes the sum of the
Deviation
squared
errors (deviations)
4
Deviation1
Deviation2
Trend line, y^ = a + bx
Time period
Least Squares Method
Equations to calculate the regression variables
y^ = a + bx
b=
Sxy - nxy
Sx2 - nx2
a = y - bx
Least Squares Example
Year
2001
2002
2003
2004
2005
2005
2007
Time
Period (x)
1
2
3
4
5
6
7
∑x = 28
x=4
Electrical Power
Demand
74
79
80
90
105
142
122
∑y = 692
y = 98.86
x2
xy
1
4
9
16
25
36
49
∑x2 = 140
74
158
240
360
525
852
854
∑xy = 3,063
3,063 - (7)(4)(98.86)
∑xy - nxy
b=
=
= 10.54
2)
2
2
140
(7)(4
∑x - nx
a = y - bx = 98.86 - 10.54(4) = 56.70
Least Squares Example
Time
Period (x)
Electrical Power
Demand
x2
xy
1999
1
74
1
2000
2
79
4
line is 80
2001The trend
3
9
2002
4
90
16
2003
105
25
y^ 5= 56.70 + 10.54x
2004
6
142
36
2005
7
122
49
Sx = 28
Sy = 692
Sx2 = 140
x=4
y = 98.86
74
158
240
360
525
852
854
Sxy = 3,063
Year
3,063 - (7)(4)(98.86)
Sxy - nxy
b=
=
= 10.54
2)
2
2
140
(7)(4
Sx - nx
a = y - bx = 98.86 - 10.54(4) = 56.70
Power demand
Least Squares Example
160
150
140
130
120
110
100
90
80
70
60
50
Trend line,
y^ = 56.70 + 10.54x
–
–
–
–
–
–
–
–
–
–
–
–
|
2001
|
2002
|
2003
|
2004
|
2005
Year
|
2006
|
2007
|
2008
|
2009
Seasonal Variations In Data
The multiplicative
seasonal model
can adjust trend
data for seasonal
variations in
demand
Seasonal Variations In Data
Steps in the process:
1. Find average historical demand for each
season
2. Compute the average demand over all
seasons
3. Compute a seasonal index for each season
4. Estimate next year’s total demand
5. Divide this estimate of total demand by the
number of seasons, then multiply it by the
seasonal index for that season
Seasonal Index Example
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Demand
2005 2006 2007
80
70
80
90
113
110
100
88
85
77
75
82
85
85
93
95
125
115
102
102
90
78
72
78
105
85
82
115
131
120
113
110
95
85
83
80
Average
2005-2007
Average
Monthly
90
80
85
100
123
115
105
100
90
80
80
80
94
94
94
94
94
94
94
94
94
94
94
94
Seasonal
Index
Seasonal Index Example
Month
Demand
2005 2006 2007
Average
2005-2007
Average
Monthly
Jan
80
85 105
90
94
Feb
70
85
85
80
94
Mar
80
93 average
82
85 monthly demand
94
2005-2007
Seasonal90index95= 115
Apr
100
94
average monthly
demand
May
113 125 131
123
94
= 90/94 = .957
Jun
110 115 120
115
94
Jul
100 102 113
105
94
Aug
88 102 110
100
94
Sept
85
90
95
90
94
Oct
77
78
85
80
94
Nov
75
72
83
80
94
Dec
82
78
80
80
94
Seasonal
Index
0.957
Seasonal Index Example
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Demand
2005 2006 2007
80
70
80
90
113
110
100
88
85
77
75
82
85
85
93
95
125
115
102
102
90
78
72
78
105
85
82
115
131
120
113
110
95
85
83
80
Average
2005-2007
Average
Monthly
Seasonal
Index
90
80
85
100
123
115
105
100
90
80
80
80
94
94
94
94
94
94
94
94
94
94
94
94
0.957
0.851
0.904
1.064
1.309
1.223
1.117
1.064
0.957
0.851
0.851
0.851
Seasonal Index Example
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sept
Oct
Nov
Dec
Demand
2005 2006 2007
Average
2005-2007
Average
Monthly
80
85 105
90
94
for802008
70
85 Forecast
85
94
80
93
82
85
94
annual demand
= 1,200
90Expected
95 115
100
94
113 125 131
123
94
110 115 120 1,200 115
94
Jan 113
x
.957 = 96 94
100 102
105
12
88 102 110
100
94
1,200
85
90
95
Feb
x90
.851 = 85 94
77
78
85 12
80
94
75
72
83
80
94
82
78
80
80
94
Seasonal
Index
0.957
0.851
0.904
1.064
1.309
1.223
1.117
1.064
0.957
0.851
0.851
0.851
Seasonal Index Example
2008 Forecast
2007 Demand
2006 Demand
2005 Demand
140 –
130 –
Demand
120 –
110 –
100 –
90 –
80 –
70 –
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Associative Forecasting
Used when changes in one or more
independent variables can be used to predict
the changes in the dependent variable
Most common technique is linear
regression analysis
We apply this technique just as we did
in the time series example
Associative Forecasting
Forecasting an outcome based on
predictor variables using the least squares
technique
y^ = a + bx
^ = computed value of the variable to
where y
be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable though to
predict the value of the dependent
variable
Associative Forecasting
Example
Local Payroll
($ billions), x
1
3
4
4.0 –
2
1
3.0 –
7
Sales
Sales
($ millions), y
2.0
3.0
2.5
2.0
2.0
3.5
2.0 –
1.0 –
0
|
1
|
2
|
|
|
|
3 4
5 6
Area payroll
|
7
Associative Forecasting
Example
Sales, y
2.0
3.0
2.5
2.0
2.0
3.5
∑y = 15.0
Payroll, x
1
3
4
2
1
7
∑x = 18
x = ∑x/6 = 18/6 = 3
y = ∑y/6 = 15/6 = 2.5
x2
1
9
16
4
1
49
∑x2 = 80
xy
2.0
9.0
10.0
4.0
2.0
24.5
∑xy = 51.5
51.5 - (6)(3)(2.5)
∑xy - nxy
b=
= 80 - (6)(32) = .25
∑x2 - nx2
a = y - bx = 2.5 - (.25)(3) = 1.75
Associative Forecasting
Example
If payroll next year
is estimated to be
$6 billion, then:
Sales = 1.75 + .25(6)
Sales = $3,250,000
Sales = 1.75 + .25(payroll)
4.0 –
3.25
3.0 –
Sales
y^ = 1.75 + .25x
2.0 –
1.0 –
0
|
1
|
2
|
|
|
|
3 4
5 6
Area payroll
|
7
Standard Error of the
Estimate
 A forecast is just a point estimate of a
future value
4.0 –
3.25
3.0 –
Sales
 This point is
actually the
mean of a
probability
distribution
2.0 –
1.0 –
0
|
1
|
2
|
|
|
|
3 4
5 6
Area payroll
|
7
Standard Error of the
Estimate
Sy,x =
∑(y - yc)2
n-2
where y = y-value of each data point
yc = computed value of the dependent
variable, from the regression
equation
n = number of data points
Standard Error of the
Estimate
Computationally, this equation is
considerably easier to use
Sy,x =
∑y2 - a∑y - b∑xy
n-2
We use the standard error to set up
prediction intervals around the
point estimate
Standard Error of the
Estimate
Sy,x =
∑y2 - a∑y - b∑xy
=
n-2
Sy,x = .306
39.5 - 1.75(15) - .25(51.5)
6-2
4.0 –
The standard error
of the estimate is
$306,000 in sales
Sales
3.25
3.0 –
2.0 –
1.0 –
0
|
1
|
2
|
|
|
|
3 4
5 6
Area payroll
|
7
Correlation
• How strong is the linear relationship
between the variables?
• Correlation does not necessarily
imply causality!
• Coefficient of correlation, r,
measures degree of association
– Values range from -1 to +1
Correlation Coefficient
r=
nSxy - SxSy
[nSx2 - (Sx)2][nSy2 - (Sy)2]
y
y
Correlation Coefficient
nSxy - SxSy
r=
2 - (Sx)2][nSy2 - (Sy)2]
[nSx
(a) Perfect positive x
(b) Positive
correlation:
0<r<1
correlation:
r = +1
y
y
(c) No correlation:
r=0
x
(d) Perfect negative x
correlation:
r = -1
x
Correlation
• Coefficient of Determination, r2,
measures the percent of change in y
predicted by the change in x
– Values range from 0 to 1
– Easy to interpret
For the Nodel Construction example:
r = .901
r2 = .81
Multiple Regression
Analysis
If more than one independent variable is to be
used in the model, linear regression can be
extended to multiple regression to
accommodate several independent variables
y^ = a + b1x1 + b2x2 …
Computationally, this is quite
complex and generally done on the
computer
Multiple Regression
Analysis
In the Nodel example, including interest rates in
the model gives the new equation:
y^ = 1.80 + .30x1 - 5.0x2
An improved correlation coefficient of r = .96
means this model does a better job of predicting
the change in construction sales
Sales = 1.80 + .30(6) - 5.0(.12) = 3.00
Sales = $3,000,000
Monitoring and Controlling
Forecasts
•Tracking
Measures
how
well
the
forecast
is
Signal
predicting actual values
• Ratio of running sum of forecast
errors (RSFE) to mean absolute
deviation (MAD)
– Good tracking signal has low values
– If forecasts are continually high or low,
the forecast has a bias error
Monitoring and Controlling
Forecasts
RSFE
Tracking
=
signal
MAD
∑(Actual demand in
period i Forecast demand
in period i)
Tracking
signal = (∑|Actual - Forecast|/n)
Tracking Signal
Signal exceeding limit
Tracking signal
+
Upper control limit
Acceptable
range
0 MADs
–
Lower control limit
Time
Tracking Signal Example
Qtr
Actual
Demand
Forecast
Demand
Error
RSFE
Absolute
Forecast
Error
1
2
3
4
5
6
90
95
115
100
125
140
100
100
100
110
110
110
-10
-5
+15
-10
+15
+30
-10
-15
0
-10
+5
+35
10
5
15
10
15
30
Cumulative
Absolute
Forecast
Error
MAD
10
15
30
40
55
85
10.0
7.5
10.0
10.0
11.0
14.2
Tracking Signal Example
Qtr
1
2
3
4
5
6
Tracking
Actual Signal
Forecast
(RSFE/MAD)
Demand
Demand
Error
RSFE
Absolute
Forecast
Error
90-10/10
100= -1 -10
95
-15/7.5
100= -2 -5
115 0/10
100
= 0 +15
100-10/10
110= -1 -10
125
+5/11110
= +0.5+15
140
+35/14.2
110= +2.5
+30
-10
-15
0
-10
+5
+35
10
5
15
10
15
30
Cumulative
Absolute
Forecast
Error
MAD
10
15
30
40
55
85
The variation of the tracking signal
between -2.0 and +2.5 is within acceptable
limits
10.0
7.5
10.0
10.0
11.0
14.2
Adaptive Forecasting
It’s possible to use the computer to
continually monitor forecast error and
adjust the values of the a and b
coefficients used in exponential
smoothing to continually minimize
forecast error
This technique is called adaptive
smoothing
Focus Forecasting
Developed at American Hardware Supply,
focus forecasting is based on two principles:
1. Sophisticated forecasting models are not
always better than simple ones
2. There is no single technique that should
be used for all products or services
This approach uses historical data to test
multiple forecasting models for individual items
The forecasting model with the lowest error is
then used to forecast the next demand