3-1forecasting chapter 3 forecasting homework problems: # 2,3,4,8(a),22,23,25,27 on pp. 121-128
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3-1 Forecasting
CHAPTER3
Forecasting
Homework Problems: # 2,3,4,8(a),22,23,25,27 on pp. 121-128.
3-2 Forecasting
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
ForecastForecast
3-3 Forecasting
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
Uses of ForecastsUses of Forecasts
3-4 ForecastingTwo Important Aspects of Two Important Aspects of
ForecastsForecasts
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
3-5 Forecasting
I see that you willget an A this semester.
Features Common to All ForecastsFeatures Common to All Forecasts
1. Techniques assume some underlying causal system that existed in the past will persist into the future
2. Forecasts are not perfect3. Forecasts for groups of items are more accurate
than those for individual items4. Forecast accuracy decreases as the forecasting
horizon increases
3-6 Forecasting
Elements of a Good ForecastElements of a Good Forecast
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
3-7 Forecasting
Steps in the Forecasting ProcessSteps 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
3-8 Forecasting
Types of ForecastsTypes of Forecasts
Judgmental - uses subjective inputs
Time series - uses historical data assuming the future will be like the past
Associative models - uses explanatory variables to predict the future
3-9 Forecasting
Forecast Accuracy and ControlForecast 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
3-10 Forecasting
Forecast Accuracy and Control (contd.)Forecast Accuracy and Control (contd.)
Forecast errors should be monitored Error = Actual – Forecast If errors fall beyond acceptable bounds,
corrective action may be necessary
3-11 Forecasting
Forecast Accuracy MetricsForecast Accuracy Metrics
n
tt ForecastActualMAD
2
tt
1
ForecastActualMSE
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
3-12 Forecasting
Forecast Error CalculationForecast Error CalculationPeriod
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%
3-13 Forecasting
Forecasting ApproachesForecasting 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
3-14 Forecasting
Judgmental ForecastsJudgmental Forecasts
Forecasts that use subjective inputs such as opinions from consumer surveys, sales staff, managers, executives, and experts Executive opinions Sales force opinions Consumer surveys Delphi method
3-15 Forecasting
Time Series ForecastsTime 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
3-16 Forecasting
Time Series ForecastsTime Series Forecasts
Trend - long-term movement in data Seasonality - short-term regular variations in
data Cycle – wavelike variations of more than one
year’s duration Irregular variations - caused by unusual
circumstances Random variations - caused by chance
3-17 Forecasting
Forecast VariationsForecast Variations
Trend
Irregularvariation
Seasonal variations
908988
Figure 3.1
Cycles
3-18 Forecasting
Naive ForecastsNaive Forecasts
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
3-19 Forecasting
Time-Series Forecasting-- AveragingTime-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
3-20 Forecasting
Moving AveragesMoving Averages
Technique that averages a number of the most recent actual values in generating a forecast
average moving in the periods ofNumber
1 periodin valueActual
average moving period MA
period for timeForecast
where
MA
1
1t
n
tA
n
tF
n
AF
t
t
t
n
iit
t
3-21 Forecasting
Moving AveragesMoving Averages
As new data become available, the forecast is updated by adding the newest value and dropping the oldest and then recomputing 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
3-22 Forecasting
Weighted Moving AveragesWeighted Moving Averages
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 wn At n wn 1At (n 1) ... w1At 1
where
wt weight for period t, wt 1 weight for period t 1, etc.
At the actual value for period t, At 1 the actual value for period t 1, etc.
3-23 Forecasting
Moving Averages ExampleMoving Averages Example
Given the following data: Period # of complaints
1 60
2 65
3 55
4 58
5 64
A). Prepare the forecasts for period 6 using a 3-period, 5-period moving average.
B). Prepare a weighted moving average forecast for period 6 using weights of 0.3, 0.2, and 0.1.
3-24 Forecasting
Simple Moving AverageSimple Moving Average
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual
MA3
MA5
Q. What n to use? Large or small?
3-25 Forecasting
Exponential SmoothingExponential Smoothing
• Premise--The most recent observations might have the highest predictive value.
Therefore, we should give more weight to the more recent time periods when forecasting.
Ft = Ft-1 + (At-1 - Ft-1)
3-26 Forecasting
Exponential SmoothingExponential 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)
3-27 Forecasting
Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87
10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92
Example - Exponential SmoothingExample - Exponential Smoothing
3-28 Forecasting
Picking a Smoothing ConstantPicking a Smoothing Constant
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12
Period
Dem
and .1
.4
Actual
3-29 Forecasting
Other Forecasting Methods - Other Forecasting Methods - FocusFocus
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
3-30 Forecasting
Other Forecasting Methods - DiffusionOther 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
3-31 Forecasting
Technique for TrendTechnique for Trend
Linear trend equation Non-linear trends
Parabolic trend equation Exponential trend equation Growth curve trend equation
3-32 Forecasting
Linear Trend EquationLinear Trend Equation
A simple data plot can reveal the existence and nature of a trend
Linear trend equation
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
3-33 Forecasting
Estimating slope and interceptEstimating slope and intercept
Slope and intercept can be estimated from historical data
b n ty t yn t 2 t
2
a y b t
n or y bt
where
n Number of periods
y Value of the time series
3-34 Forecasting
Linear Trend Equation ExampleLinear Trend Equation Example
t yW e e k t 2 S a l e s t y
1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5
t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5
3-35 Forecasting
Linear Trend CalculationLinear 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
3-36 Forecasting
Associative ForecastingAssociative Forecasting
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
3-37 Forecasting
Simple Linear RegressionSimple 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)
3-38 Forecasting
Least Squares LineLeast 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 yn x 2 x
2
a y b x
n or y bx
where
n Number of paired observations
Predictor
3-39 Forecasting
Standard ErrorStandard 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
points data ofnumber
point dataeach of valuethe
estimate oferror standard
where2
2
n
y
S
n
yyS
e
ce
3-40 Forecasting
Linear Model Seems ReasonableLinear Model Seems Reasonable
A straight line is fitted to a set of sample points.
0
10
20
30
40
50
0 5 10 15 20 25
X Y7 152 106 134 15
14 2515 2716 2412 2014 2720 4415 347 17
Computedrelationship
3-41 Forecasting
Correlation CoefficientCorrelation 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 x 2 x 2n y 2 y 2
3-42 Forecasting
Regression and Correlation ExampleRegression and Correlation Example Given the following values of X and Y, (a) obtain a linear regression line for the
data, and (2) what percentage of the variation is explained by the regression line? x y xy x2 y2 15.00 74.00 1110.0 225.0 5476.0 25.00 80.00 2000.0 625.0 6400.0 40.00 84.00 3360.0 1600.0 7056.0 32.00 81.00 2592.0 1024.0 6561.0 51.00 96.00 4896.0 2601.0 9216.0 47.00 95.00 4465.0 2209.0 9025.0 30.00 83.00 2490.0 900.0 6889.0 18.00 78.00 1404.0 324.0 6084.0 14.00 70.00 980.0 196.0 4900.0 15.00 72.00 1080.0 225.0 5184.0 22.00 85.00 1870.0 484.0 7225.0 24.00 88.00 2112.0 576.0 7744.0 33.00 90.00 2970.0 1089.0 8100.0
3-43 Forecasting
Simple Linear Regression Simple Linear Regression AssumptionsAssumptions
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
3-44 Forecasting
Issues to considerIssues 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
3-45 Forecasting
Controlling the ForecastControlling the Forecast
Control chart A visual tool for monitoring forecast errors Used to detect non-randomness in errors
Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are
present
3-46 Forecasting
Sources of Forecast errorsSources of Forecast errors
Model may be inadequate Irregular variations Incorrect use of forecasting technique
3-47 Forecasting
Choosing a Forecasting TechniqueChoosing a Forecasting Technique
No single technique works in every situation Two most important factors
Cost Accuracy
Other factors include the availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon
3-48 Forecasting
Using Forecast InformationUsing 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
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