2. #profevad2015
You should be able to:
1. List the elements of a good forecast
2. Outline the steps in the forecasting process
3. Describe at least three qualitative forecasting techniques and the
advantages and disadvantages of each
4. Compare and contrast qualitative and quantitative approaches to
forecasting
5. Describe averaging techniques, trend and seasonal techniques,
and regression analysis, and solve typical problems
6. Explain three measures of forecast accuracy
7. Compare two ways of evaluating and controlling forecasts
8. Assess the major factors and trade-offs to consider when
choosing a forecasting technique
Chapter 3: Learning Objectives
2
3. Forecast
Forecast – a statement about the future value of a
variable of interest
We make forecasts about such things as weather,
demand, and resource availability
Forecasts are an important element in making informed
decisions
#profevad2015
3
4. Forecasts affect decisions and activities throughout an
organization
Accounting Cost/profit estimates
Finance Cash flow and funding
Human Resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
MIS IT/IS systems, services
Operations Schedules, MRP, workloads
Product/service design New products and services
5. Two Important Aspects of
Forecasts
Expected level of demand
The level of demand may be a function of some
structural variation such as trend or seasonal variation
Accuracy
Related to the potential size of forecast error
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5
6. Features Common to All Forecasts
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1. Techniques assume some underlying causal system that
existed in the past will persist into the future
2. Forecasts are not perfect
3. Forecasts for groups of items are more accurate than
those for individual items
4. Forecast accuracy decreases as the forecasting horizon
increases
6
7. Elements of a Good Forecast
#profevad2015
The forecast
should be timely
should be accurate
should be reliable
should be expressed in meaningful units
should be in writing
technique should be simple to understand and use
should be cost effective
7
8. Steps in the Forecasting Process
#profevad2015
1. Determine the purpose of the forecast
2. Establish a time horizon
3. Obtain, clean, and analyze appropriate data
4. Select a forecasting technique
5. Make the forecast
6. Monitor the forecast
8
9. Forecasting Approaches
Qualitative Forecasting
Qualitative techniques permit the inclusion of soft information such as:
Human factors
Personal opinions
Hunches
These factors are difficult, or impossible, to quantify
Quantitative Forecasting
Quantitative techniques involve either the projection of historical data or
the development of associative methods that attempt to use causal
variables to make a forecast
These techniques rely on hard data
9
#profevad2015
10. Judgmental Forecasts
Forecasts that use subjective inputs such as opinions
from consumer surveys, sales staff, managers,
executives, and experts
Executive opinions
Salesforce opinions
Consumer surveys
Delphi method
10
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11. Time-Series Forecasts
Forecasts that project patterns identified in recent
time-series observations
Time-series - a time-ordered sequence of observations
taken at regular time intervals
Assume that future values of the time-series can be
estimated from past values of the time-series
#profevad2015 3-11
11
13. Trends and Seasonality
Trend
A long-term upward or downward movement in data
Population shifts
Changing income
Seasonality
Short-term, fairly regular variations related to the calendar or time
of day
Restaurants, service call centers, and theaters all experience
seasonal demand
13
#profevad2015
14. Cycles and Variations
Cycle
Wavelike variations lasting more than one year
These are often related to a variety of economic, political, or even
agricultural conditions
Random Variation
Residual variation that remains after all other behaviors have been
accounted for
Irregular variation
Due to unusual circumstances that do not reflect typical behavior
Labor strike
Weather event
14
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16. Time-Series Forecasting - Naïve Forecast
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Naïve Forecast
Uses a single previous value of a time series as the basis
for a forecast
The forecast for a time period is equal to the previous
time period’s value
Can be used with
a stable time series
seasonal variations
trend
16
17. Naïve Forecasts
Forecast for any period = previous period’s actual
value
Ft = At-1
F: forecast A: Actual t: time period
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18. Naïve Forecast Example
Week Sales (actual) Sales (forecast) Error
t A F A - F
1 20 -
2 25 20 5
3 15 25 -10
4 30 15 15
5 27 30 -3
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19. Naïve Forecasts
Simple to use
Virtually no cost
Quick and easy to prepare
Data analysis is nonexistent
Easily understandable
Cannot provide high accuracy
Can be a standard for accuracy
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21. Time-Series Forecasting - Averaging
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These Techniques work best when a series tends to
vary about an average
Averaging techniques smooth variations in the data
They can handle step changes or gradual changes in the
level of a series
Techniques
1. Moving average
2. Weighted moving average
3. Exponential smoothing
21
22. Moving Average
Technique that averages a number of the most recent
actual values in generating a forecast
#profevad2015
average
moving
in the
periods
of
Number
1
period
in
value
Actual
average
moving
period
MA
period
for time
Forecast
where
MA
1
1
n
t
A
n
t
F
n
A
F
t
n
t
n
i
i
t
n
t
22
23. Moving Average
#profevad2015
As new data become available, the forecast is updated
by adding the newest value and dropping the oldest
and then re-computing the average
The number of data points included in the average
determines the model’s sensitivity
Fewer data points used-- more responsive
More data points used-- less responsive
23
24. Week Sales (actual) Sales (forecast) Error
t A F = MA3 A - F
1
20
-
2 25 -
3 15 -
4 30 20 10
5 27 23.3333 3.66667
6 24
Moving Average Example
24
#profevad2015
25. Simple Moving Average
Figure 3-4 Revised
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual
Forecast
(MA3)
Forecast
(MA5)
Questions:
• Why is MA3 longer than MA5?
• Which curve fluctuate the most?
• Which curve is the smoothest?
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26. Simple Moving Average
Figure 3-4 Revised
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual
Forecast
(MA3)
Forecast
(MA5)
Responsiveness vs. Stability
• Smaller m, responsiveness , stability
• Larger m, responsiveness , stability
• Must maintain stability when fluctuations are high.
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27. Weighted Moving Average
The most recent values in a time series are given more
weight in computing a forecast
The choice of weights, w, is somewhat arbitrary and
involves some trial and error
#profevad2015
etc.
,
1
period
for
value
actual
the
,
period
for
value
actual
the
etc.
,
1
period
for
weight
,
period
for
weight
where
)
(
...
)
(
)
(
1
1
1
1
t
A
t
A
t
w
t
w
A
w
A
w
A
w
F
t
t
t
t
n
t
n
t
t
t
t
t
t
27
28. Weighted Moving Average Example
Week Sales (actual) Sales (forecast) Error
t A F = MA3 A - F
1 20 -
2 25 -
3 15 -
4 30 19 11
5 27 24.5 2.5
6 25.5
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29. Exponential Smoothing
A weighted averaging method that is based on the
previous forecast plus a percentage of the forecast
error
#profevad2015
period
previous
the
from
sales
or
demand
Actual
constant
Smoothing
=
period
previous
for the
Forecast
period
for
Forecast
where
)
(
1
1
1
1
1
t
t
t
t
t
t
t
A
F
t
F
F
A
F
F
3-29
29
30. Exponential Smoothing
Weighted averaging method based on previous forecast
plus a percentage of the forecast error
A-F is the error term, is the % feedback
Ft = Ft-1 + (At-1 - Ft-1)
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32. Picking a Smoothing Constant
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12
Period
Demand
.1
.4
Actu
al
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33. Other Forecasting Methods - Focus
Focus Forecasting
Some companies use forecasts based on a “best current
performance” basis
Apply several forecasting methods to the last several periods
of historical data
The method with the highest accuracy is used to make the
forecast for the following period
This process is repeated each month
33
#profevad2015
34. Other Forecasting Methods - Diffusion
Diffusion Models
Historical data on which to base a forecast are not
available for new products
Predictions are based on rates of product adoption and usage
spread from other established products
Take into account facts such as
Market potential
Attention from mass media
Word-of-mouth
34
#profevad2015
36. Linear Trend
A simple data plot can reveal the existence and nature
of a trend
Linear trend equation
#profevad2015
Ft a bt
where
Ft Forecast for period t
a Value of Ft at t 0
b Slope of the line
t Specified number of time periods from t 0
36
37. Linear Trend Equation
Ft = Forecast for period t
t = Specified number of time periods
a = Value of Ft at t = 0
b = Slope of the line
Ft = a + bt
0 1 2 3 4 5
t
Ft
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39. Linear Trend Equation
Easy to use: a built-in function
in spreadsheet software
Based on Least Squares method
used in linear regression, which
Minimizes the sum of the
squares of the deviations
Uses equal weight for all time
periods
Both a and b must be
recalculated on regular basis to
include new data.
Deviation
Yt
At
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40. Estimating slope and intercept
#profevad2015
Slope and intercept can be estimated from historical
data
b
n ty t y
n t2
t
2
a
y b t
n
or y bt
where
n Number of periods
y Value of the time series
3-40
40
41. Linear Trend Equation Example
Period (t) Sales (Yt) t*Yt t^2
1 67 67 1
2 74 148 4
3 102 305 9
4 87 346 16
5 106 530 25
6 86 516 36
7 117 817 49
8 113 904 64
9 130 1168 81
10 116 1156 100
55 996 5958 385
t t
Y
t
2
t
t
Y
79
.
5
55
385
10
996
55
5958
10
2
2
2
t
t
n
Y
t
tY
n
b t
t
78
.
67
10
55
79
.
5
996
n
t
b
Y
a t
Exercise: Calculate b and a by using
the sums on the left.
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42. Linear Trend Equation Example
t y
Week t2
Sales ty
1 1 150 150
2 4 157 314
3 9 162 486
4 16 166 664
5 25 177 885
t = 15 t2
= 55 y = 812 ty = 2499
(t)2
= 225
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43. Linear Trend Calculation
y = 143.5 + 6.3t
a =
812 - 6.3(15)
5
=
b =
5 (2499) - 15(812)
5(55) - 225
=
12495 -12180
275 -225
= 6.3
143.5
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44. Techniques for Seasonality
#profevad2015
Seasonality – regularly repeating movements in series
values that can be tied to recurring events
Expressed in terms of the amount that actual values deviate
from the average value of a series
Models of seasonality
Additive
Seasonality is expressed as a quantity that gets added to or
subtracted from the time-series average in order to incorporate
seasonality
Multiplicative
Seasonality is expressed as a percentage of the average (or trend)
amount which is then used to multiply the value of a series in order
to incorporate seasonality
44
48. Seasonal Relatives
Seasonal relatives
The seasonal percentage used in the multiplicative seasonally
adjusted forecasting model
Using seasonal relatives
To deseasonalize data
Done in order to get a clearer picture of the nonseasonal (e.g.,
trend) components of the data series
Divide each data point by its seasonal relative
To incorporate seasonality in a forecast
1. Obtain trend estimates for desired periods using a trend
equation
2. Add seasonality by multiplying these trend estimates by the
corresponding seasonal relative
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49. Techniques for Cycles
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Cycles are similar to seasonal variations but are of longer
duration
Explanatory approach
Search for another variable that relates to, and leads, the variable
of interest
Housing starts precede demand for products and services
directly related to construction of new homes
If a high correlation can be established with a leading variable,
an equation can be developed that describes the relationship,
enabling forecasts to be made
49
50. Associative Forecasting Techniques
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Associative techniques are based on the
development of an equation that summarizes
the effects of predictor variables
Predictor variables - variables that can be used to
predict values of the variable of interest
Home values may be related to such factors as home and
property size, location, number of bedrooms, and number of
bathrooms
50
51. Simple Linear Regression
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Regression - a technique for fitting a line to a set of
data points
Simple linear regression - the simplest form of
regression that involves a linear relationship between
two variables
The object of simple linear regression is to obtain an
equation of a straight line that minimizes the sum of squared
vertical deviations from the line (i.e., the least squares
criterion)
51
52. Least Squares Line
#profevad2015
ns
observatio
paired
of
Number
where
or
and
intercept)
at the
line
the
of
height
the
(i.e.,
0
when
of
Value
line
the
of
Slope
variable
nt)
(independe
Predictor
variable
)
(dependent
Predicted
where
2
2
n
x
b
y
n
x
b
y
a
x
x
n
y
x
xy
n
b
y
x
y
a
b
x
y
bx
a
y
c
c
c
52
53. Standard Error
Standard error of estimate
A measure of the scatter of points around a regression
line
If the standard error is relatively small, the predictions
using the linear equation will tend to be more accurate
than if the standard error is larger
#profevad2015
points
data
of
number
point
data
each
of
value
estimate
of
error
standard
where
2
2
n
y
y
S
n
y
y
S
e
c
e
53
54. Correlation Coefficient
Correlation, r
A measure of the strength and direction of relationship between
two variables
Ranges between -1.00 and +1.00
r2, square of the correlation coefficient
A measure of the percentage of variability in the values of y that is
“explained” by the independent variable
Ranges between 0 and 1.00
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2
2
2
2
y
y
n
x
x
n
y
x
xy
n
r
54
55. Simple Linear Regression Assumptions
1. Variations around the line are random
2. Deviations around the average value (the line)
should be normally distributed
3. Predictions are made only within the range of
observed values
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55
56. Forecast Accuracy and Control
Forecasters want to minimize forecast errors
It is nearly impossible to correctly forecast real-world
variable values on a regular basis
So, it is important to provide an indication of the extent
to which the forecast might deviate from the value of the
variable that actually occurs
Forecast accuracy should be an important forecasting
technique selection criterion
Error = Actual – Forecast
If errors fall beyond acceptable bounds, corrective
action may be necessary
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56
57. Forecast Accuracy Metrics
n
100
Actual
Forecast
Actual
MAPE t
t
t
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n
t
t Forecast
Actual
MAD
2
t
t
1
Forecast
Actual
MSE
n
MAD weights all errors
evenly
MSE weights errors according
to their squared values
MAPE weights errors
according to relative error
57
59. Issues to consider:
#profevad2015
Always plot the line to verify that a linear
relationship is appropriate
The data may be time-dependent.
If they are
use analysis of time series
use time as an independent variable in a multiple
regression analysis
A small correlation may indicate that other
variables are important
59
60. Monitoring the Forecast
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Tracking forecast errors and analyzing them can provide useful
insight into whether forecasts are performing satisfactorily
Sources of forecast errors
The model may be inadequate
Irregular variations may have occurred
The forecasting technique has been incorrectly applied
Random variation
Control charts are useful for identifying the presence of non-
random error in forecasts
Tracking signals can be used to detect forecast bias
60
61. Choosing a Forecasting Technique
Factors to consider
Cost
Accuracy
Availability of historical data
Availability of forecasting software
Time needed to gather and analyze data and prepare a
forecast
Forecast horizon
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61
62. Using Forecast Information
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Reactive approach
View forecasts as probable future demand
React to meet that demand
Proactive approach
Seeks to actively influence demand
Advertising
Pricing
Product/service modifications
Generally requires either an explanatory model or a subjective
assessment of the influence on demand
62
63. Operations Strategy
The better forecasts are, the more able organizations will
be to take advantage of future opportunities and reduce
potential risks
A worthwhile strategy is to work to improve short-term forecasts
Accurate up-to-date information can have a significant effect on
forecast accuracy:
Prices
Demand
Other important variables
Reduce the time horizon forecasts have to cover
Sharing forecasts or demand data through the
supply chain can improve forecast quality
#profevad2015 63
