Chapter TwoForecastingForecasting

Planning Forecast

Customer

ProductionProcess

FinishedGoods

Inputs

Forecasting

Marketing: forecasts sales for new and

existing products.

Production: uses sales forecasts to plan

production and operations; sometimes

involved in generating sales forecasts.

Characteristics of Forecasts

They are usually wrong A good forecast is usually more than a

single number Aggregate forecast are more accurate The longer the forecasting horizon, the

less accurate the forecasts will be Forecasts should not be used to the

exclusion of known information

Forecasting Horizon

Short term(inventory management, production plans..)

Intermediate term(sales patterns for product families..)

Long term(long term planning of capacity needs)

Forecasting Techniques

JudgmentalModels

Time SeriesMethods Causal Methods

ForecastingTechnique

DelphiMethod

MovingAverage

ExponentialSmoothing

RegressionAnalysis

SeasonalityModels

Types of forecasting Methods

Subjective methodsSales force compositesCustomer surveyJury of executive opinionThe Delphi method

Objective methodsCausal methods

Time series methods

Qualitative Methods

Don’t have data Don’t have time to develop a forecast Often used in practice “Close enough” Depend on expert opinions Market surveys More appropriate for long term forecasts

Delphi Technique

A method to obtain a consensus forecast by using opinions from a group of “experts” expert opinionconsulting salespersonsconsulting consumers

Causal Methods Causal methods use data from sources other than the

series being predicted.

If Y is the phenomenon to be forecast and X1 , X2 , . .., Xn

are the n variables we believe to be related to Y, then a causal model is one in which the forecast for Y is some function of these variables:

Y = f (X1 , X2 , . .., Xn )

Econometric models are causal models in which the relationship between Y and (X1 , X2 , . .., Xn ) is linear.

That is Y = ao + a1 X1 + a2 X2 + … an Xn

for some constants a1 , a2 , . . . , an

Forecasting Steps for Quantitative Methods

Collect data Reduce/clean data Build and evaluate model(s) Forecast (model extrapolation) Track the forecast

Identify the correct pattern

• Collect data. Look for possible cause/effect relationships

• Determine which form can be used to generate the pattern

• Determine specific values of the parameters

0

200

400

600

800

1000

1200

1400

1600

Jan

Apr Jul

Oct Ja

nApr Ju

lO

ct Jan

Apr Jul

Oct

Period

Sal

es i

n t

ho

usa

nd

s o

f ca

ses

Building Models

Plot data over time. (remove outliers & get right scale).

Using part of the data, estimate model parameters. Forecast the rest of the data with the model. Evaluate accuracy of the model. Use judgment to modify. Keep track of model accuracy over time (redo, if

needed).

Forecasting Stationary Series

Time series Analysis

Patterns that arise most often

Trend Seasonality Cycles Randomness

Time Series PatternsFig. 2-2

Notation

: Observed value of the demand during period t

time series we would like to predict

forecast made for period t in period t-1 forecast made at the end of t-1 after having observed , , …

1−tD

:

:}1,{

t

t

t

F

tD

D

≥

2−tD

Time Series Forecast

For some set of weights

,...., 10

0

aa

DaFn

ntnt ∑∞

=−=

Evaluating forecasts

Forecast error in period t

For multiple-step-ahead

ttt DFe −=

ttt DFe −= −τ

Evaluating Forecasts Mean Absolute Deviation

Mean Square Errorn

eMAD

n

ii∑

== 1

||

n

eMSE

n

ii∑

== 1

2

Forecast Errors Over TimeFig. 2-3

TIME SERIES METHODSStationary Series

A stationary time series is represented by a

constant plus a random fluctuation:

Dt = µ+ εt

where µ is an unknown constant corresponding to the mean of the series and εt is a random error with mean 0 and variance σ2 .

The methods described for stationary series are: Moving Averages Exponential Smoothing

Methods of Forecasting Stationary Series Moving Averages

Exponential SmoothingN

DDD

N

DF Nttt

t

Ntii

t−−−

−

−= +++==∑ ...21

1

11 )1( −− −+= ttt FDF αα

Moving Average

N

DDDF Nttt

t−−− +++= ...21

90Oct

110Sep

130Aug

75Jul

50Jun

110May

75Apr

100Mar

90Feb

120Jan

DeliveriesMonth

0

20

40

60

80

100

120

140

Jan Feb Mar Apr May Jun Jul Aug Sep Oct

Mo n t h

94110

92

90

83

91

MA(6)

105

85

78

78

95

88

103

MA(3)

90Oct

110Sep

130Aug

75Jul

50Jun

110May

75Apr

100Mar

90Feb

120Jan

DeliveriesMonth

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 10 11

17202412

1922

15182211

13 162010

11 14189

9 12168

7 10147

8126

6105

484

63

42

21

MA(6)MA(3)DeliveriesMonth

Moving-Average Forecasts Lag Behind a Trend

Fig. 2-4

EXPONENTIAL SMOOTHING

Current forecast is a weighted average of the last forecast and the current value of demand

New forecast = α (current observation of demand)

+ (1- α ) (last forecast)

Exponential Smoothing

11

111

11

)(

)1(

−−

−−−

−−

−=−−=

−+=

ttt

tttt

ttt

eFF

DFFF

FDF

αα

αα

Ft = Ft-1 – (fraction of the observed forecast error in t-1)

If we forecast high in period t-1 error is positive adjustment to decrease current forecast

If we forecast low in period t-1 error is negative adjustment to increase current forecast

( ) 1

22

21

221

11

1

)1()1(

)1(

)1(

−−

∞

=

−−−

−−−

−−

∑ −=

−+−+=

−+=−+=

itoi

it

tttt

ttt

ttt

DF

FDDF

FDF

FDF

αα

αααα

αααα

Example

2201908

2113057

2032856

2012255

2021864

2051753

2002502

200 2001

ForecastFailuresQuarter

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7 8

Weights in Exponential Smoothing

Fig. 2-5

Exponential Smoothing for Different Values of Alpha

Fig. 2-6

Smaller values of α produce more stable forecasts,whereas larger values of α will produce forecasts which react more quickly to changes in the demand pattern.

Comparison

2

1)1()...321(

1 +=+=++++ N

N

NNN

N

( )α

αα 11 1

1

=− −∞

=∑ i

i

i

2

11 += N

α

Similarities & Differences

Stationary series Single parameter Lag behind a trend When α=2/(N+1)

Same distribution of forecast error

ES weighted average of all past data

MA only last N periods

MA : save past N data ES : only last forecast

Multiple-Step-Ahead Forecasts

Same as one-step-ahead-forecast

Trend Based Methods

Regression Analysis

Double Exponential Smoothing

btaFt +=

tttt GSF ττ +=+,

Double Exponential Smoothing

Intercept at time t

and slope at time t

))(1( 11 −− +−+= tttt GSDS αα

11 )1()( −− −+−= tttt GSSG ββ

tttt GSF ττ +=+,