Transcript Slide 1

LSS Black Belt Training
Forecasting
Forecasting Models
Forecasting
Techniques
Qualitative
Models
Time Series
Methods
Delphi
Method
Jury of Executive
Opinion
Sales Force
Composite
Consumer Market
Survey
Naive
Moving
Average
Weighted
Moving Average
Exponential
Smoothing
Trend Analysis
Causal
Methods
Simple
Regression
Analysis
Multiple
Regression
Analysis
Seasonality
Analysis
Multiplicative
Decomposition
Model Differences

Qualitative – incorporates judgmental &
subjective factors into forecast.

Time-Series – attempts to predict the future by
using historical data.

Causal – incorporates factors that may influence
the quantity being forecasted into the model
Qualitative Forecasting Models
Delphi method

Iterative group process allows experts to make
forecasts

Participants:



decision makers: 5 -10 experts who make the forecast
staff personnel: assist by preparing, distributing, collecting,
and summarizing a series of questionnaires and survey
results
respondents: group with valued judgments who provide
input to decision makers
Qualitative Forecasting Models (cont)

Jury of executive opinion



Sales force composite




Opinions of a small group of high level managers, often in
combination with statistical models.
Result is a group estimate.
Each salesperson estimates sales in his region.
Forecasts are reviewed to ensure realistic.
Combined at higher levels to reach an overall forecast.
Consumer market survey.


Solicits input from customers and potential customers
regarding future purchases.
Used for forecasts and product design & planning
Forecast Error






Bias - The arithmetic sum
of the errors
Mean Square Error Similar to simple sample
variance
Variance - Sample variance
(adjusted for degrees of
freedom)
Standard Error - Standard
deviation of the sampling
distribution
MAD - Mean Absolute
Deviation
MAPE – Mean Absolute
Percentage Error
Forecast Error  At  Ft
T
MSE   | forecast error | 2 /T
t 1
T
  (At  Ft ) 2 / T
t 1
T
MAPE  100 [|At  Ft | / At ] / T
t 1
T
T
t 1
t 1
MAD   | forecast error | /T   |At  Ft | / T
Quantitative Forecasting Models
Time Series Method

Naïve




Whatever happened
recently will happen
again this time
(same time period)
The model is simple
and flexible
Provides a baseline
to measure other
models
Attempts to capture
seasonal factors at
the expense of
ignoring trend
Ft  Yt 1
Ft  Yt 4 : Quarterly data
Ft  Yt 12 : Monthly data
Naïve Forecast
Wallace Garden Supply
Forecasting
Period
January
February
March
April
May
June
July
August
September
October
November
December
Storage Shed Sales
Actual
Naïve
Value
Forecast
10
N/A
12
10
16
12
13
16
17
13
19
17
15
19
20
15
22
20
19
22
21
19
19
21
Error
2
4
-3
4
2
-4
5
2
-3
2
-2
0.818
BIAS
Absolute
Error
2
4
3
4
2
4
5
2
3
2
2
3
MAD
Percent
Error
16.67%
25.00%
23.08%
23.53%
10.53%
26.67%
25.00%
9.09%
15.79%
9.52%
10.53%
17.76%
MAPE
Standard Error (Square Root of MSE) =
Squared
Error
4.0
16.0
9.0
16.0
4.0
16.0
25.0
4.0
9.0
4.0
4.0
10.091
MSE
3.176619
Naïve Forecast Graph
Wallace Garden - Naive Forecast
25
20
Sheds
15
Actual Value
Naïve Forecast
10
5
0
February
March
April
May
June
July
Period
August
September
October
November
December
Quantitative Forecasting Models
Time Series Method

Moving Averages


Assumes item forecasted
will stay steady over time.
Technique will smooth out
short-term irregularities in
the time series.
k
k - period moving average   (Actual value in previous k periods) /k
k 1
Moving Averages
Wallace Garden Supply
Forecasting
Storage Shed Sales
Period
January
February
March
April
May
June
July
August
September
October
November
December
Actual
Value
10
12
16
13
17
19
15
20
22
19
21
19
Three-Month Moving Averages
10
12
16
13
17
19
15
20
22
+
+
+
+
+
+
+
+
+
12
16
13
17
19
15
20
22
19
+
+
+
+
+
+
+
+
+
16
13
17
19
15
20
22
19
21
/
/
/
/
/
/
/
/
/
3
3
3
3
3
3
3
3
3
=
=
=
=
=
=
=
=
=
12.67
13.67
15.33
16.33
17.00
18.00
19.00
20.33
20.67
Moving Averages Forecast
Wallace Garden Supply
Forecasting
3 period moving average
Input Data
Period
Month 1
Month 2
Month 3
Month 4
Month 5
Month 6
Month 7
Month 8
Month 9
Month 10
Month 11
Month 12
Next period
Actual Value - Forecast
Forecast Error Analysis
Actual Value
10
12
16
13
17
19
15
20
22
19
21
19
19.667
Forecast
12.667
13.667
15.333
16.333
17.000
18.000
19.000
20.333
20.667
Average
Error
0.333
3.333
3.667
-1.333
3.000
4.000
0.000
0.667
-1.667
12.000
BIAS
Absolute
error
0.333
3.333
3.667
1.333
3.000
4.000
0.000
0.667
1.667
2.000
MAD
Squared
error
0.111
11.111
13.444
1.778
9.000
16.000
0.000
0.444
2.778
6.074
MSE
Absolute
% error
2.56%
19.61%
19.30%
8.89%
15.00%
18.18%
0.00%
3.17%
8.77%
10.61%
MAPE
Moving Averages Graph
Three Period Moving Average
25
20
Value
15
Actual Value
Forecast
10
5
0
1
2
3
4
5
6
7
Time
8
9
10
11
12
Quantitative Forecasting Models
Time Series Method

Weighted Moving Averages


Assumes data from some periods are more
important than data from other periods (e.g. earlier
periods).
Use weights to place more emphasis on some
periods and less on others.
k - period weighted moving average 
k
k
i 1
i 1
 (Weight for each period i)(Actual value in previous k periods) /  (weights)
Weighted Moving Average
Wallace Garden Supply
Forecasting
Storage Shed Sales
Period
January
February
March
April
May
June
July
August
September
October
November
December
Next period
Actual
Value
Weights
10
0.222
12
0.593
16
0.185
13
17
19
15
20
22
19
21
19
20.185
Sum of weights =
1.000
Three-Month Weighted Moving Averages
2.2
2.7
3.5
2.9
3.8
4.2
3.3
4.4
4.9
+
+
+
+
+
+
+
+
+
7.1
9.5
7.7
10
11
8.9
12
13
11
+
+
+
+
+
+
+
+
+
3
2.4
3.2
3.5
2.8
3.7
4.1
3.5
3.9
/
/
/
/
/
/
/
/
/
1
1
1
1
1
1
1
1
1
=
=
=
=
=
=
=
=
=
12.298
14.556
14.407
16.484
17.814
16.815
19.262
21.000
20.036
Weighted Moving Average
Wallace Garden Supply
Forecasting
3 period weighted moving average
Input Data
Period
Month 1
Month 2
Month 3
Month 4
Month 5
Month 6
Month 7
Month 8
Month 9
Month 10
Month 11
Month 12
Forecast Error Analysis
Actual value
10
12
16
13
17
19
15
20
22
19
21
19
Next period
Sum of weights =
Weights
0.222
0.593
0.185
Forecast
12.298
14.556
14.407
16.484
17.814
16.815
19.262
21.000
20.036
Average
20.185
1.000
Error
0.702
2.444
4.593
-1.484
2.186
5.185
-0.262
0.000
-1.036
1.988
BIAS
Absolute
error
0.702
2.444
4.593
1.484
2.186
5.185
0.262
0.000
1.036
6.952
MAD
Squared
error
0.492
5.971
21.093
2.202
4.776
26.889
0.069
0.000
1.074
6.952
MSE
Absolute
% error
5.40%
14.37%
24.17%
9.89%
10.93%
23.57%
1.38%
0.00%
5.45%
10.57%
MAPE
Quantitative Forecasting Models
Time Series Method

Exponential Smoothing


Moving average technique that requires little record
keeping of past data.
Uses a smoothing constant α with a value between 0 and
1. (Usual range 0.1 to 0.3)
Forecast for period t 
forecast for period t - 1   (actual value in period t - 1 - forecast for period t - 1)
Exponential Smoothing Data
Wallace Garden Supply
Forecasting
Storage Shed Sales
Exponential Smoothing
Period
January
February
March
April
May
June
July
August
September
October
November
December
Actual
Value
10
12
16
13
17
19
15
20
22
19
21
19
Ft
10
10
10
10
11
11
12
12
13
13
14
15
+
+
+
+
+
+
+
+
+
+
+
α
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
At
*(
*(
*(
*(
*(
*(
*(
*(
*(
*(
*(
10
12
16
13
17
19
15
20
22
19
21
Ft
-
10
10
10
11
11
12
12
13
13
14
15
Ft+1
)
)
)
)
)
)
)
)
)
)
)
=
=
=
=
=
=
=
=
=
=
=
10.000
10.200
10.780
11.002
11.602
12.342
12.607
13.347
14.212
14.691
15.322
Exponential Smoothing
Wallace Garden Supply
Forecasting
Exponential smoothing
Input Data
Forecast Error Analysis
Period
Month 1
Month 2
Month 3
Month 4
Month 5
Month 6
Month 7
Month 8
Month 9
Month 10
Month 11
Month 12
Actual value
10
12
16
13
17
19
15
20
22
19
21
19
Alpha
0.419
Next period
19.573
Forecast
10.000
10.000
10.838
13.000
13.000
14.675
16.487
15.864
17.596
19.441
19.256
19.987
Average
Error
2.000
5.162
0.000
4.000
4.325
-1.487
4.136
4.404
-0.441
1.744
-0.987
Absolute
error
2.000
5.162
0.000
4.000
4.325
1.487
4.136
4.404
0.441
1.744
0.987
2.608
MAD
Squared
error
4.000
26.649
0.000
16.000
18.702
2.211
17.106
19.391
0.194
3.041
0.973
9.842
MSE
Absolute
% error
16.67%
32.26%
0.00%
23.53%
22.76%
9.91%
20.68%
20.02%
2.32%
8.30%
5.19%
14.70%
MAPE
Exponential Smoothing
Exponential Smoothing
25
20
15
Sheds
Actual value
Forecast
10
5
0
January
April
July
October
Trend & Seasonality
Trend analysis

technique that fits a trend equation (or curve) to a
series of historical data points.

projects the curve into the future for medium and long
term forecasts.
Seasonality analysis

adjustment to time series data due to variations at
certain periods.

adjust with seasonal index – ratio of average value of
the item in a season to the overall annual average
value.
 example: demand for coal & fuel oil in winter months.
Linear Trend Analysis
Midwestern Manufacturing Sales
Sales(in units) vs. Time
Scatter Diagram
160
Actual
value (or)
Y
74
79
80
90
105
142
122
140
Period
number
(or) X
1995
1996
1997
1998
1999
2000
2001
120
100
Period number (or) X
80
60
40
20
0
1994
1996
1998
2000
2002
Least Squares for Linear Regression
Midwestern Manufacturing
Values of Dependent Variables
Le ast Square s M e thod
Time
Least Squares Method
_ _
^
Y  a  bX
b=
Where
[ XY - n X Y ]
_

2
2
X
n
X




^
Y
= predicted value of the dependent variable
(demand)
X = value of the independent variable (time)
a = Y-axis intercept
b = slope of the regression line
Linear Trend Data & Error Analysis
Midwestern Manufacturing Company
Forecasting
Linear trend analysis
Input Data
Period
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Intercept
Slope
Next period
Forecast Error Analysis
Actual value Period number
(or) Y
(or) X
74
1
79
2
80
3
90
4
105
5
142
6
122
7
56.714
10.536
141.000
8
Forecast
67.250
77.786
88.321
98.857
109.393
119.929
130.464
Average
Error
6.750
1.214
-8.321
-8.857
-4.393
22.071
-8.464
Absolute
Squared Absolute
error
error
% error
6.750
45.563
9.12%
1.214
1.474
1.54%
8.321
69.246 10.40%
8.857
78.449
9.84%
4.393
19.297
4.18%
22.071 487.148 15.54%
8.464
71.644
6.94%
8.582 110.403
8.22%
MAD
MSE
MAPE
Least Squares Graph
Trend Analysis
160
140
y = 10.536x + 56.714
120
Value
100
80
60
40
20
0
1
2
3
4
5
6
T i me
Actual values
Linear (Actual values)
7
Seasonality Analysis
Eichler Supplies
Year
1
2
Month
January
February
March
April
May
June
July
August
September
October
November
December
January
February
March
April
May
June
July
August
September
October
November
December
Average
Demand Demand
80
94
75
94
80
94
90
94
115
94
110
94
100
94
90
94
85
94
75
94
75
94
80
94
100
94
85
94
90
94
110
94
131
94
120
94
110
94
110
94
95
94
85
94
85
94
80
94
Ratio = demand / average demand
Ratio
0.851
0.798
0.851
0.957
1.223
1.170
1.064
0.957
0.904
0.798
0.798
0.851
1.064
0.904
0.957
1.170
1.394
1.277
1.170
1.170
1.011
0.904
0.904
0.851
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 – ratio of the
average value of the item in a
season to the overall average
annual value.
Example: average of year 1
January ratio to year 2 January
ratio.
(0.851 + 1.064)/2 = 0.957
If Year 3 average monthly demand is
expected to be 100 units.
Forecast demand Year 3 January:
100 X 0.957 = 96 units
Forecast demand Year 3 May:
100 X 1.309 = 131 units
Deseasonalized Data



Going back to the conceptual model, solve for
trend:
 Trend = Y / Season
(96 units/ 0.957 = 100.31)
This eliminates seasonal variation and isolates
the trend
Now use the Least Squares method to
compute the Trend
Forecast
Now that we have the Seasonal Indices and
Trend, we can reseasonalize the data and
generate the forecast.
Y = Trend x Seasonal Index