chapter 2;forecasting

8/17/2019 Chapter 2;Forecasting

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Forecasting

Chapter 3

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Forecasting is the art and science of predicting future events

Focus on the forecasting of demand for output from the

operations function (Demand may dier from sales,

forecasting may serve for developing operating planning)

Demand management is coordinating and controlling all

source of demand so the production system can be used

eciently and product be delivered on time

Demand can be: Dependent: demand for a product caused by the demand

for other product (a product linked to demand of other) ndependent: occurs independently of demand from any

other product (can not be derived directly from that of otherproduct)

A Forecasting Framework

!


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Dierence bet"een forecasting and planning

Forecasting: "hat "e think "ill happen

#lanning: "hat "e think should happen

Forecasting is an input to all business planning and

control

$arketing uses for planning product, promotion and pricing

Finance uses for %nancial planning

Forecasting for operation decision

Forecasting application in various decision areas of operations

(capacity planning, inventory management, others)

A Forecasting Framework

&


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Forecasting andoperation system

nformation on most recent

demand and production

Demand forecastfor operations

#lanning the system(design)• #roduct design• #rocess design'uipment investmentand replacement•apacity planning

*cheduling thesystem• +ggregateproduction planning• perationscheduling

ontrolling thesystem•#roduction control•nventory control•

-abor control•ost control

utput of goods

and services

.


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Time series analysis

#lot the demand data on a time scale, study the plotand look for consistent shape or pattern/ 0he timeseries of demand might have the follo"ing pattern

onstant

0rends*easonal(cyclical) pattern

andom variation (cause by chance of event)

*ome combinations of these patterns

Conditions-o" noise: most the points lies around 2very close

to the pattern

3igh noise: many points lies relatively far a"ayfrom the pattern

Characteristics of demandover time

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Techniques

6ualitative and 7udgment method: based on

estimates and opinions

8aive (time series)uantitative2'9trapolative

model: based on data related to past demand can

be used to predict future demand

ausal relationship (uantitative) or '9planatory

model: using linear regression techniues

*imulation

Useful Forecasting Model

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%elphi Technique

t is a panel of group of e9perts "ith dierent levelof e9pertise (variety of kno"ledgeable people) andans"er uestionnaires and summari?ed given backto the entire group "ith ne" set of uestions

Delphi conceals the identity of individualsparticipating in the study

Market &urveys 'research(panel, uestionnaire, market test

)ife*cycles 'historical( Analogy n forecasting ne" products, "here an e9istingproduct or generic product could be used as a model

+nformed ,udgment (group of individuals one9perience, facts)

"#ualitative$ ForecastingMethods

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0ry to predict the future based on the past data

0o select forecasting model: 0ime hori?on, Data availability,+ccuracy reuired, si?e of forecasting budget, uali%edpersonnel

Components of time*series data

0rendAgeneral direction (up or do"n)

*easonalityAshort term recurring cyclesycleAlong term business cycle

'rror (random or irregular component)

B%ecomposition- of time*seriesData are broken into the four components

*imple +verage

=eighted $oving +verages

'9ponential *moothing

egression +nalysis@

Time*&eries Forecasting


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+ssumes no trend, seasonal or cyclical

components/

*imple $oving +verage: combines demand data

from several of the most recent periodsC theiraverage being the forecast for ne9t period/

+s general rule: the longer the averaging period,

the slo"er response to demand change

11

&imple Moving Average


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Forecast Ft is average of n previous observationsor actuals Dt :

8ote that the n past observations are eually"eighted/

ssues "ith moving average forecasts:

+ll n past observations treated euallyC

bservations older than n are not included atallC

euires that n past observations be retainedC

∑−+=

+

−+−+

=

+++=

t

nt i

it

nt t t t

Dn

F

D D Dn

F

1

1

111

1

)(1


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&imple Moving Averagenclude n most recent observations

=eight euallygnore older observations

weight

today

./3000n

.1n

1&


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111.


Period Actual Demand Forecast

1 10

2 18

3 29

4 19

(10+18+29)/3 = 19

Period 5 ill !e (18+29+actual "or #eriod 4)/3

$om#ute t%ree #eriod mo&in' a&era'e (num!er o" #eriods is

t%e decision o" t%e "orecaster)


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=eighted $oving +verage: "ants to use themoving average but does not "ant to have alln periods eually "eighted/ 0his makesresponsive:

2eighted Moving Average

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January 10

February 12

March 13

April 16May 19

June 23

July 26

Actual 3-Month %eighted

Month Shed Sales Moving Average

&3 ' 16" ! 2 ' 13" ! 12"(#6 $ 1)1#3&3 ' 19" ! 2 ' 16" ! 13"(#6 $ 1*

&3 ' 23" ! 2 ' 19" ! 16"(#6 $ 201#2

=eighted $oving +verage

1010

1212

1313

&3 ' 1313" ! 2 ' 1212" ! 1010"(#6 $ 121

#6

%eights Applied +eriod

33 ,ast onth

22 ./o onths ago

11 .hree onths ago

6 Su o /eights

'9ample


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4ponential &moothingConceptnclude all past observations=eight recent observations much more heavily

than very old observations:

weight

today

%ecreasing weight given to older o5servations

0 1<


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0he forecast:

Fforecast of demand (both this period and ne9t)

D actual demand (this period)

t time period

0he value of the smoothing constant (α) is a choice/ t

determines ho" much the calculation smoothes out the

random variations/ ts value can be set bet"een ?ero (E)

and one (1)/ 8ormally it is in the E/1 to E/& range/111@

&imple 4ponential&moothing


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f Ft1 is to be very responsive to recent demand,

choose the large value of α the most recent occurrences are more indicative

of the future than in the more distant past

Facts:

*eptember forecast for sales "as 14*eptember actual sales "ere 1&

+lpha ( G) is E/!

=hat is the forecast for ctoberH

alculationctober Forecast *eptember forecast G(*eptemberactual*eptember forecast)

14E/!(1&14)14E/!(!)14E/.1./5

11!E

4ponential &moothing*calculation


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'9ponential *moothing

'9ample+redicted deand t-1"$ 1)2 Ford Mustangs

Actual deand $ t-1"13

Soothing constant $ 20

e/ orecast t" $ 1)2 ! 213 4 1)2"


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5'ponential Soothing 5'aple

+redicted deand $ 1)2 Ford Mustangs

Actual deand $ 13

Soothing constant $ 20

e/ orecast $ 1)2 ! 213 4 1)2"

$ 1)2 ! 22

$ 1))2 1)) cars


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'rror 'stimation might be used

0o monitor erratic demand observations

and outliers (#erhaps may be re7ected from

data)

0o set safety stock or safety capacity and

ensure against stock out

Forecast rrors

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umulative *um of Forecast 'rror (F')

and $ean Forecast 'rror ($F')

$ean *uare 'rror ($*')

$ean +bsolute Deviation ($+D)Ameasure

of deviation in units/

$ean +bsolute #ercentage 'rror ($+#')

0racking *ignal (0*)Arelative measure ofbias

Forecast error for #eriod t is et

◦ et+ctual demand (Dt) Forecast (Ft)11!.

Forecast rrors


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Forecasting 6erformance

$ean Forecast 'rror ($F' or


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Mean A5solute %eviation'MA%(

$easures absolute error

#ositive and negative errors thus do not

cancel out (as "ith $F')

=ant $+D to be as small as possible

∑=

−=

n

t

t t F Dn

MAD1

1

!5


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Forecast rrors Formulas

11!;

t

n

=1i

e=CFE ∑

ean *uare rror

n

t

n

=1i

e

= MSE

2

∑

n

|e|

= MAD

t

n

=1i

∑ean A!soluteDe&iation

n

| D

e|

= MAPE t

t

n

=1i

100∑ean A!solutePercenta'e rror

MAD

e

=TS

t

n

=1i

∑,rac-in' i'nal

n

t

n

=1i

e

= ME ∑ean rror


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11!>

Tracking &ignal

A trac-in' si'nal monitors an. "orecasts t%at %a&e

!een made in com#arison it% actuals and arns %en

t%ere are une#ected de#artures o" t%e outcomes "rom

t%e "orecasts

Analo'ous to control c%arts in *ualit. control viz i"

t%ere is no !ias its &alues s%ould "luctuate around ero


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!@

#eriod Demand Forecast 'rror+bsolute'rror

& 11 1&/4 !/4 !/4

. @ 1& ./E ./E

4 1E 1E E E/E

5 > @/4 1/4 1/4

; 1. @ 4/E 4/E> 1! 11 1/E 1/E

Example

n = o!ser&ations

F = 2/ = 033

AD = 14/ = 233

7onclusion odel tends to sli'%tl. o&er"orecast it% an a&era'e a!solute error o"

233 units

6deal &alue = 07

F 0 model tends to under"orecast

F 0 model tends to o&er"orecast


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0ime series compares data being forecast overtime, i.e. 0ime is the independent variable or 9

a9is or Ivariable/

ausal models compare data being forecast

against some other data set "hich the forecaster

may think is a cause of the forecasted data,

e.g. population size causes newspaper sales.

11&E

Time &eries vs0 CausalModels


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0he general regression model:(-east*uares $ethod)

0he Jalues of a and b

11&1

Causal Forecasting Models


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-east *uares $ethod

.ie period

8 a l u e s

o 0 9 e p e n d e n t 8 a r i a b l e

Figure ))

eviation1error"

eviation

eviation*

eviation2

eviation6

eviation)

eviation3

Actual observation y-value"

.rend line: y $ a ! bx ;


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-east *uares $ethod

.ie period

8 a l u e s

o 0 9 e p e n d e n t 8 a r i a b l e

Figure ))

eviation1error"

eviation

eviation*

eviation2

eviation6

eviation)

eviation3

Actual observation y-value"

.rend line: y $ a ! bx ;

,east s


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-east *uares '9ample

b $ $ $ 10)> xy - nxy

> x 2 - nx 2

3:063 - *")"9??6"

1)0 - *")2"

a $ y - bx $ 9??6 - 10))" $ 6*0

.ie 5lectrical +o/er@ear +eriod x " eand ega/att" x 2 xy

2006 1 *) 1 *)

200* 2 *9 ) 1?

200? 3 ?0 9 2)0

2009 ) 90 16 3602010 10 2 2

2011 6 1)2 36 ?2

2012 * 122 )9 ?)

> x $ 2? > y $ 692 > x 2 $ 1)0 > xy $ 3:063

x $ ) y $ 9??6


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b $ $ $ 10)> xy - nxy

> x 2 - nx 2

3:063 - *")"9??6"

1)0 - *")2"

a $ y - bx $ 9??6 - 10))" $ 6*0

.ie 5lectrical +o/er@ear +eriod x " eand x 2 xy

2003 1 *) 1 *)

200) 2 *9 ) 1?

200 3 ?0 9 2)0

2006 ) 90 16 360200* 10 2 2

200? 6 1)2 36 ?2

2009 * 122 )9 ?)

> x $ 2? > y $ 692 > x 2 $ 1)0 > xy $ 3:063

x $ ) y $ 9??6


.he trend line is

y $ 6*0 ! 10) x ;


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: 2011 Pearson ducation 6nc

#u!lis%in' as Prentice ;all


2006 200* 200? 2009 2010 2011 2012 2013 201)

160 4

10 4

1)0 4

130 4

120 4 110 4

100 4

90 4

?0 4

*0 4 60 4

0 4

@ear

+ o / e r d e - a n d

.rend line:

y $ 6*0 ! 10) x ;


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11&>

'9ample of 0ime *eries $odel

@t $ a ! bt"

F


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Kser and *ystems *ophistication:#eople reluctant to use "hat they donLt

understand3o" sophisticated are the managers

nside and outside operations=ho is e9pecting to use the forecasting results

0ime and resource available=hen is forecast neededH

=hat is value of forecastH

*electing + Forecasting$ethods

&@


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Kse and decision characteristics◦ +ccuracy reuired, 0ime hori?on

◦ #ricing decision reuire highly accurate shortranged forecasts for large number of item

Data availability and uality

Data pattern aects the type of forecasting◦ f the time series is Mat, + %rst order method can

be used, "here as if the data sho"s trend orseasonal pattern some advance method "ill be

used◦ f the data is unstable over time, a ualitative

method may be selected

DonLt force the data to %t the modelN

*electing + Forecasting$ethods

.E


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0he longer the forecast hori?on, the lessaccurate the forecast

-ong lead times reuire long forecasthori?ons

-ean, responsive companies have the goalof decreasing lead times so they areshorter than the forecast hori?on

Forecast 3ori?ons and Forecast+ccuracy

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chapter 2;forecasting

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