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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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&imple Moving Average
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.
&imple Moving Average
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
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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
-east *uares '9ample
.he trend line is
y $ 6*0 ! 10) x ;
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: 2011 Pearson ducation 6nc
#u!lis%in' as Prentice ;all
-east *uares '9ample
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
.1
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1
End