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Chapter 3
Forecasting
McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
You should be able to:1. List the elements of a good forecast2. Outline the steps in the forecasting process3. Describe at least three qualitative forecasting techniques and the
advantages and disadvantages of each4. Compare and contrast qualitative and quantitative approaches
to forecasting5. Describe averaging techniques, trend and seasonal techniques,
and regression analysis, and solve typical problems6. Explain three measures of forecast accuracy7. Compare two ways of evaluating and controlling forecasts8. Assess the major factors and trade-offs to consider when
choosing a forecasting technique
Chapter 3: Learning Objectives
3-2Student Slides
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
3-3Student Slides
Forecast Accuracy Metrics
n
100
Actual
ForecastActual
MAPE t
tt
n
tt ForecastActualMAD
2
tt
1
ForecastActualMSE
n
MAD weights all errors evenly
MSE weights errors according to their squared values
MAPE weights errors according to relative error
3-4Student Slides
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
3-5Student Slides
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
1. Moving average2. Weighted moving average3. Exponential smoothing
3-6Student Slides
Moving Average
• 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
1
n
tA
n
tF
n
AF
t
n
t
n
iit
nt
3-7Student Slides
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
etc. ,1 periodfor valueactual the , periodfor valueactual the
etc. ,1 periodfor weight , periodfor weight
where
)(...)()(
1
1
11
tAtA
twtw
AwAwAwF
tt
tt
ntntttttt
3-8Student Slides
Exponential Smoothing
• A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error
period previous thefrom salesor demand Actual
constant Smoothing=
period previous for theForecast
periodfor Forecast
where
)(
1
1
111
t
t
t
tttt
A
F
tF
FAFF
3-9Student Slides
Linear Trend
• A simple data plot can reveal the existence and nature of a trend
• Linear trend equation
Ft a btwhere
Ft Forecast for period t
aValue of Ft at t 0
bSlope of the line
t Specified number of time periods from t 0
3-10Student Slides
Estimating slope and intercept
• Slope and intercept can be estimated from historical data
bn ty t yn t 2 t
2
ay b tn
or y bt
where
n Number of periods
y Value of the time series
3-11Student Slides
Trend-Adjusted Exponential Smoothing
• The trend adjusted forecast consists of two components– Smoothed error– Trend factor
TAFt+1 St Ttwhere
St Previous forecast plus smoothed error
Tt Current trend estimate
3-12Student Slides
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 + At TAFt Tt Tt 1 TAFt TAFt 1 Tt 1
3-13Student Slides
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)
3-14Student Slides
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
3-15Student Slides