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