This document discusses various forecasting techniques. It begins by defining a forecast and explaining that forecasts are used to help managers plan systems and use of systems. Common features of all forecasts are discussed, as are elements of a good forecast. The forecasting process involves determining purpose, time horizon, technique, data analysis, making the forecast, and monitoring. Accuracy is important and can be measured using MAD, MSE, and MAPE. Qualitative and quantitative techniques are covered, along with judgmental, time series, and associative models. Specific time series techniques like naive, moving average, exponential smoothing, and trend/seasonal adjustments are explained. The document concludes by discussing using forecast information reactively or proactively.

1. McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Chapter 3
Forecasting

2. 3-2
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

3. 3-3
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
• Degree of Accuracy
– Related to the potential size of forecast error

4. 3-4
Uses for forecasts
1. Help Managers plan the system: involves Long-
range plans such as
• Types of Products & Services to offer
• What facilities and equipment to have
• Where to locate….etc
2. Help Managers plan the use of the system: involves
short and intermediate range plans such as
• Planning inventory
• Workforce levels
• Purchasing and production
• Budgeting
• scheduling

5. 3-5
Features Common to All Forecasts
1. Techniques assume that the same underlying causal
system that existed in the past will continue to exist in
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. 3-6
Elements of a Good Forecast
The forecast
• should be timely: time is needed to respond to the
information in a forecast
• should be accurate: degree of accuracy should be
stated
• should be reliable; it should work consistently
• should be expressed in meaningful units (ex. $ or
units)
• should be in writing
• technique should be simple to understand and use
• should be cost effective

7. 3-7
Steps in the Forecasting Process
1. Determine the purpose of the forecast
2. Establish a time horizon
3. Select a forecasting technique
4. Obtain, clean, and analyze appropriate data
5. Make the forecast
6. Monitor the forecast

8. 3-8
Forecast Accuracy and Control
• Forecasters want to minimize forecast errors
– 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

9. 3-9
Forecast Accuracy and Control (contd.)
• Forecast errors should be monitored
– Error = Actual – Forecast
– If errors fall beyond acceptable bounds, corrective
action may be necessary

10. 3-10
Forecast Accuracy Metrics
n
∑ −
= tt ForecastActual
MAD
( )2
tt
1
ForecastActual
MSE
−
−
=
∑
n
n
∑ ×
−
=
100
Actual
ForecastActual
MAPE t
tt
MAD weights all errors
evenly
MSE weights errors according
to their squared values
MAPE weights errors
according to relative error

11. 3-11
Forecast Error Calculation
Period
Actual
(A)
Forecast
(F)
(A-F)
Error |Error| Error2
[|Error|/Actual]x100
1 107 110 -3 3 9 2.80%
2 125 121 4 4 16 3.20%
3 115 112 3 3 9 2.61%
4 118 120 -2 2 4 1.69%
5 108 109 1 1 1 0.93%
Sum 13 39 11.23%
n = 5 n-1 = 4 n = 5
MAD MSE MAPE
= 2.6 = 9.75 = 2.25%

12. 3-12
Forecasting Approaches
• Qualitative Forecasting
– Qualitative techniques consist mainly of subjective inputs. They permit
the inclusion of soft information such as:
• Human factors
• Personal opinions
– 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

13. 3-13
Forecasting Techniques
1. Judgmental Forecasts
• Forecasts that use subjective inputs such as opinions from
consumer surveys, sales staff, managers, executives, and experts
– Executive opinions: a small group of upper-level managers
may meet and collectively develop a forecast
– Sales force opinions: members of sale staff or customer
service staff are often good sources of information because of
their direct contact with customers
– Consumer surveys: Soliciting inputs from customers through
surveys
– Delphi method: an iterative (repetitive) process in which
managers and staff complete a series of questionnaires, each
developed from the previous one to achieve a consensus
forecast

14. 3-14
2. Time-Series Forecasts
• Time Series Forecasts attempt to project past
experience into the future
– Time-series - a time-ordered sequence of observations taken at
regular time intervals (hourly, daily, weekly, annually)
• Assume that future values of the time-series can be
estimated from past values of the time-series
3. Associative models use equations that consist of one
or more explanatory variables that can be used to
predict demand. For ex. Demand for paint might be
related to variables such as price, amount spent on
advertising, specific characteristics of the paint such as
its drying time or ease of cleanup

15. 3-15
Time-Series Behaviors
• Trend: a long term upward or downward movement in
data. Ex: changing incomes, populations shift
• Seasonality: short-term regular variations related to the
calendar or time of day. Ex:Resturants
• Cycles: wavelike variations lasting more than 1 year.
Ex. Economic, political, and agricultural conditions
• Irregular variations: Caused by unusual
circumstances, not reflective of typical behavior such as
severe weather conditions
• Random variation: residual variations after all other
behaviors are accounted for

16. 3-16
Time-Series Forecasting - Naïve Forecast
• 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 when
• The time series is stable
• There is a trend
• There is seasonality

17. 3-17
Time-Series Forecasting - Averaging
• 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
• Moving average
• Weighted moving average
• Exponential smoothing

18. 3-18
Moving Average
• Technique that averages a number of the most
recent actual values in generating a forecast
averagemovingin theperiodsofNumber
1periodinvalueActual
averagemovingperiodMA
periodfor timeForecast
where
MA
1
1
t
=
−=
=
=
==
−
=
−∑
n
tA
n
tF
n
A
F
t
t
t
n
i
it
t

19. 3-19
Moving Average
• As new data become available, the forecast is
updated by adding the newest value and
dropping the oldest and then recomputing the
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

20. 3-20
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
Ft =wnAt−n +wn−1At−(n−1) +...+w1At−1
where
wt =weightforperiodt, wt−1 =weightforperiodt−1, etc.
At =theactualvalueforperiodt, At−1 =theactualvalueforperiodt−1, etc.

21. 3-21
Exponential Smoothing
• A weighted averaging method that is based on
the previous forecast plus a percentage of the
forecast error
periodpreviousthefromsalesordemandActual
constantSmoothing=
periodpreviousfor theForecast
periodforForecast
where
)(
1
1
111
=
=
=
−+=
−
−
−−−
t
t
t
tttt
A
F
tF
FAFF
α
α

22. 3-22
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

23. 3-23
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

24. 3-24
Techniques for Trend
• Linear trend equation
• Non-linear trends
– Parabolic trend equation
– Exponential trend equation
– Growth curve trend equation

25. 3-25
Linear Trend
• A simple data plot can reveal the existence and
nature of a trend
• Linear trend equation
Ft =a+bt
where
Ft =Forecast for periodt
a=Value ofFt at t =0
b=Slope of the line
t =Specifiednumber of time periods fromt =0

26. 3-26
Estimating slope and intercept
• 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

27. 3-27
Trend-Adjusted Exponential Smoothing
• The trend adjusted forecast consists of two
components
– Smoothed error
– Trend factor
TAFt+1 =St +Tt
where
St =Previousforecastplussmoothederror
Tt =Currenttrendestimate

28. 3-28
Trend-Adjusted Exponential Smoothing
• Alpha and beta are smoothing constants
• Trend-adjusted exponential smoothing has the
ability to respond to changes in trend
TAFt+1 =St +Tt
St =TAFt +α At −TAFt( )
Tt =Tt−1+β TAFt −TAFt−1−Tt−1( )

29. 3-29
Techniques for Seasonality
• Seasonality is 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 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

30. 3-30
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
components of the data series
• Divide each data point by its seasonal relative
– To incorporate seasonality in a forecast
• Obtain trend estimates for desired periods using a trend
equation
• Add seasonality by multiplying these trend estimates by the
corresponding seasonal relative

31. 3-31
Techniques for Cycles
• 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, it can develop an equation that describes the
relationship, enabling forecasts to be made

32. 3-32
Associative Forecasting Techniques
– Home values may be related to such factors as home
and property size, location, number of bedrooms, and
number of bathrooms
• 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

33. 3-33
Simple Linear Regression
• 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)

34. 3-34
Least Squares Line
yc = a+ bx
where
yc = Predicted (dependent) variable
x = Predicted (independent) variable
b =Slope of the line
a = Value of yc when x = 0 (i.e., the height of the line at the y intercept)
and
b =
n xy − x y∑∑∑
n x2
− x∑( )∑
2
a =
y −b x∑∑
n
or y −bx
where
n = Number of paired observations

35. 3-35
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
Se =
y − yc( )
2
∑
n−2
where
Se =standard error of estimate
y =the value of each data point
n =number of data points

36. 3-36
Correlation Coefficient
• Correlation
– 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
r2
=
n xy∑( )− x∑( ) y∑( )
n x2
∑( )− x∑( )
2
n y2
∑( )− y∑( )
2











37. 3-37
Simple Linear Regression Assumptions
1. Variations around the line are random
2. Devaiations around the average value (the
line) should be normally distributed
3. Predictions are made only within the range of
observed values

38. 3-38
Issues to consider:
• Always plot the line to verify that a linear
relationships 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

39. 3-39
Using Forecast Information
• 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 and explanatory model or a subjective
assessment of the influence on demand