chap3-1-forecasting (1)
TRANSCRIPT
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Chapter 3.1
ForecastingForecasting
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FORECASTING
Defnition Forecasting is the process of estimating future demand in terms of the
quantity, timing, quality, and location for desired products and services.
Goals
The importance of forecasting as an activity.
The forecasting system within an organization.
The various forecasting methods for dierent applications.
Characteristics
Forecasting involves error - forecasts are usually wrong .
A good forecast is more than a single numer
Aggregate forecasts are more accurate than item forecasts
The longer the forecast horizon, the less accurate the forecast will e
Forecasts should not e used to the e!clusion of "nown information
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IMPORTANCE OF FORECASTING
#everal factors aect the future success of a $rm. %hat are some of thesefactors that require planning decisions&
Forecasting is responsile for the most valuale input to planning decisions. Types of organization decisions may e aected y dierent forecasts
ased on the planning period of interest.
Examples o Organi!ation Decisions
Future Planning Period Organization Decisions
Long-Term (months/years) Types of products or services to offer.
Types and sizes of markets to serve.
Processes and technologies to employ.
Plant location and plant sizes.
ntermediate-term(!eeks/months)
"ize of !ork force to employ.#inds and amount of inventories to maintain.
$mount of desired su%contracting !hen needed.
$mount of desired overtime.
"hort & Term (days/!eeks) $ssignment of orders to specific facilities and personnel.
'ispatching to meet delivery times.
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'
T"E DEMAND FORECASTING S#STEM$ASED ON
IDEF%&ICOM' DEFINITION
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T"E DEMAND FORECASTING S#STEM
As a system, demand forecasting consists of si! components(inputs, outputs, constraints, decisions, performance, criteria
and forecasting methods.
CONSTRAINTS
FORECATING MET"ODS
).#u*ective +ualitative./*ective +uantitative a. 0oving Averages . 1!ponential #moothing
c. 2ausal Forecasting d. 3rowth Analysis - 4olt5s 0ethod e. #easonal Forecasting - %inter5s 0ethods
O(TP(TS
INP(TS
FORECASTER+6erformance 2riteria
DECISIONS
. 'ata . Time
*. +,pertise . unds
. "election of data & ho! far to go0
. "election of method
.nternal
1istorical
"u%2ective
"urvey
. +nvironmental 'ata
+conomic
"ocial
Technological
+,pected 'emand
orecast error
CONSTRAINTS
The time availa%le to prepare a forecastThe lack of relevant data from internal and e,ternal sourcesThe 3uality of availa%le data
The e,pertise !ithin the organizationThe availa%le computing facilities
. $ccuracy
. "implicity of computation
*. le,i%ility to ad2ust the rate of response. o%2ectivity
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Forecasting 6rocess
7
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FORECASTING MET"ODS
)* S+,-ecti.e &/+alitati.e' Forecasting
8nvolves techniques that rely on the e!perience andopinions of people +e!perts for such reasons as
9ittle time or no past relevant data.
Availale data may not e enough to cover possile
developments in the more distant future.
#uch methods include(
The Delphi Metho0
Nominal Gro+p Techni1+e &NGT'
Mar2et Research &Cons+mer S+r.e3'
Management Decision &4+r3 o Exec+ti.e Opinion'
Sales Force Composites
"istorical Analogies
5ie C3cle C+r.es &S6C+r.es'
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7*O,-ecti.e &/+antitati.e' Forecasting
:ased on time series data Time series data transfer refer to a set of values osome .aria,les o
interest meas+re0 at e1+all3 space0 time inter.als &e*g* ho+rl38
0ail38wee"ly, monthly, yearly, etc.'
Techni1+es
Stationar3 Mo0els
+A 0oving Averages
+) #imple 0oving Average
+ %eighted 0oving Average
+: #imple 1!ponential #moothing +/ne-step-ahead forecast
Tren0 Mo0els
+A ;egression-:ased Forecasting
Trend refers to the long term growth or decline in the average level of demand.
Two typical cases are(
+) Intrinsic mo0els +growth analysis
+ Extrinsic mo0els +causal forecasting
+:
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Common Time Series Patterns
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MEAS(REMENT : CONTRO5 OF FORECAST ERRORS&FORECAST ERROR ANA5#SIS'
)* Forecast error ; e&t'
+t ? actual value
? forecast value
7* R+nning s+m o the orecast errors ; &RSFE'
A measure of ias or lac" of ias
implies lac" of ias +an ideal forecasting
model
)(4)()( tYtYte =
)(4 tY
)5(4)(6
tYtYRSFE
N
t
==
=7)(te
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=* Commonl3 (se0 Meas+res o Acc+rac3>
&a' Mean A,sol+te De.iation &MAD'
+#um of asolute errors@+=umer of periods
%hen forecast errors are normally distriuted, as is generally
assumed, an estimate of the standard deviation of the forecast
error, e, is given y ).BC0A periods of data.
n order to use moving averages= one must save all > past
data points. n order to use e,ponential smoothing= one need only save thelast forecast. This is the most significant advantage of thee,ponential smoothing method and one reason for its popularityin practice.
or e,ponential smoothing the parameter is ? & the smoothingconstant.
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E/(I?A5ENT COMPARISON OF MO?ING A?ERAGE ANDEBPONENTIA5 SMOOT"ING TEC"NI/(ES DEPENDS ON T"E
RE5ATIONS"IP OF N :
The average age of data in mA@;egression model as a function
of = is given y +=-)@.
#imilarly, the average age of data in an e!ponentially
smoothed average as a function of is given y
Therefore,
=
N
+=N
=
N
9B
9B
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Exponential Smoothing orDierent ?al+es o Alpha
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&)' Intrinsic Mo0els &Groth Anal3sis'
A time series analysis that de$nes how a certain production
indicator varies only with time.
3eneral growth e!pression include
2onstant
9inear
uadratic
1!ponential
6olynomial nn
tb
tztwtctbatY
eatY
tctbatY
tbatY
atY
44..........444)(4
4)(4444)(4
44)(4
4)(4
4
+++++=
=++=
+=
=
TIMES SERIES FORECASTING MET"ODS&Regression6$ase0 Metho0s'
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TIMES SERIES FORECASTING MET"ODS&Regression6$ase0 Metho0s'
)* &7' Extrinsic Mo0els &Cas+al Forecasting' Times-series models ased on the e!istence of a cause-and-eect
relationship etween independent predictor variale+s and the
dependent forecast variale.
3eneral e!pressions for one predictor variale include
2onstant(
9inear(
uadratic(
1!ponential
A general for more than one predictor variale
)(4
4)(4
)(4)(44)(4
)(44)(4
4)(4
tXbeatY
tXctXbatY
tXbatY
atY
=
++=
+=
=
)(4..........)(4)(44)(4 tXztXctXbatY n+++=
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1!amples of some products and their relevant economicindicators
Product Economic indicators useful in forecasting
AhildrenCs Alothing >um%er of %irth certificates issued in past several years.
Aonsumer purchasing po!er.
Primary school enrollments.
1ome $ppliances Personal income in e,cess of %asic e,penditures.
>um%er of ne! homes sold.
nterest rate on credit sales.
Price inde, of home furnishings
:a,imum credit availa%le to individuals.
Aonstruction materials Aonstruction contracts a!arded
Planned high!ay construction
>um%er of construction permits issued
:achine tools ederal ;eserve nde, of ndustrial Production.
+,isting and planned productive capacity of metal fa%ricatingindustries.
Prices of metal products.
$verage la%or cost.
TIMES SERIES FORECASTING MET"ODS&Regression6$ase0 Metho0s'
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&=' Determination o the Regression Pre0iction E1+ation
;egression equation is determined y the method of least squares
which aims at $tting a line to a set of n points in such a way that
the parameters or coecients minimize the sum of the squared
error deviations
The methodology is applicale to oth +) intrinsic models and +
e!trinsic models.
))5(4)(6(
=
n
t
tYtY
TIMES SERIES FORECASTING MET"ODS&Regression6$ase0 Metho0s'
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An Example o a Regression5ine
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&i'Constant Mo0el>
+ii 5inear Mo0el>
REGRESSION6$ASED MET"OD&$3 Dierential Calc+l+s'
YN
tYa
N
t == = )(4
544)(6)( tbatYteN
t
N
t
==
=
=
= ==N
t
N
t tbatYda
ted
7544)(6
)(6
=
= ==N
t
N
tatY
da
ted
754)(6
)(6
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HHHHH.
+)
HHHHHH.+
From +)
INTERCEPT
#ustituting a in +, we have
==
+=N
t
N
t
tbaNtY
44)(
=
= ==N
t
N
t tbatYdb
ted
7544)(6
)(6
== +=N
t
N
t
tbtattY
)(
N
tbtYa
=4)(
+
= )(
)( tbtN
tbtYttY
+=
)()()( tbNtbtYttYN
REGRESSION6$ASED MET"OD&$3 Dierential Calc+l+s'
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S5OPE
1quations +) and + are called =/;0A9 1IAT8/=# a set of simultaneous
linear equations. Alternatively,
= )()(5)(6
tYttYNttNb t
=
)(
)()(
ttN
ttYttYNb
)(
-D
))((
)(
EE
)(
+=
++
=
+=
+
=
==
nba
nn
nninxy
xx
xy
D
nnnS
DDS
S
Sb
xx
n
i i
n
i i
REGRESSION6$ASED MET"OD&$3 Dierential Calc+l+s'
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REGRESSION6$ASED MET"OD&Acc+rac3 o Regression 5ine'
8ndicates a relatively strong or wea" relation etween two
variales ! and y.
3iven that the prediction of y depends on one independent
variale +!, the correlation coecient +ry! is calculated as
follows(
3iven that the prediction depends on two independent
variales +! and z, the coecient of multiple correlation +;y!z
is calculated as follows(
5)(56)(6
=
YYXXn
yxxynryx
xz
zxyzyxyzyx
yxzr
rrrrrR+=
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C5ASS EBAMP5E 7*) PRO$5EM
JK
'emand during the first 7 months of the year !as as follo!sF
:onth (t) Gan e% :ar $pr :ay Gun Gul $ug "ep Hct
'emand -I(t) J K J * M *K *
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C5ASS EBAMP5E 7*) PRO$5EM
J)
'emand during the first 7 months of the year !as as follo!sF
:onth (t) Gan e% :ar $pr :ay Gun Gul $ug "ep Hct
'emand -I(t) J K J * M *K *
0a"e forecasts of demand for =ovemer and
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SO5(TION TO EBAMP5E7*)
Month #&t' t t7 t#&t'
LA= B ) ) B
F1: )M ' JN
0A; )N J M B'
A6; )B ' )7 7K
0A> J) B B )BB
LI= 7 J7 )J
LI9 O O 'M )NM
AI3 JM N 7' J)
#16 JN M N) J'
/2T '' )K )KK ''K
S(M @ 7 = )H7H
J
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Alternatively, using the matri! approach when the prediction
of y depends on two or more variales, the coecient of
determination is calculated as follows(
%here the coecient of correlation P is simply the square
root of the coecient of determination, and
SSTO
SSE
SSTO
SSR
R ==
YYn
YYSSTO
YXbYYSSE
YYn
YXbSSR
=
=
=
REGRESSION6$ASED MET"OD&$3 Matrix Approach'
? +Q5Q-)+Q5>
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The relationship etween y and a set of independent variales!), !, !J, H..etc. is e!pressed through the following matri!relationships(
> ? Q and ? +Q5Q-)+Q5>
where
=
ny
y
y
Y
=nmn
m
m
xx
xx
xx
X
=
mb
b
b
b
7
REGRESSION6$ASED MET"OD&$3 Matrix Approach'
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REGRESSION6$ASED MODE5&Class Example 7*7 Pro,lem ; Ca+sal Forecasting'
Pro,lem Statement>
The demand for new furniture is suspected to have a relationshipwith either or oth of two factors, the numer of marriagelicenses issued in the previous year and the numer of uildingpermits issued for houses in the previous year. The data for thesefactors are given in the following tale (
Iear 'emand of ne! furniture
(millions of dollars)
:illions of marriagelicenses in previousyear
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Ising spreadsheet +1!cel, answer the following questions(
/+estions >
+a there are three alternatives for forecasting, using the numer of
marriage licenses, the numer of uilding permits or oth.
+ :ased on your result in +a, forecast the demand for year )) if it is
"nown that the numer of marriage licenses issued was '.K million
and uilding permits were issued for ),KKK,KKK housing units in year
)K.
+c Assuming that the two economic indicators +numer of marriage
licenses and uilding permits together have strong correlation with
the demand of new furniture, derive the necessary normal equations
for the prediction parameters +either y intuitive approach or the
dierential calculus approach and solve the simultaneous linear
equation y the row reduction technique to otain the prediction
parameters.
+d ;epeat +c using purely the matri! approach from scratch +with uilt-
in regression tools in 1!cel
REGRESSION6$ASED MODE5&Class Example Pro,lem ; Ca+sal Forecasting'
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REGRESSION6$ASED MODE5Class Example Pro,lem
&Determining the Nee0e0 Correlation Coecients'
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b) EQUATIONS y(x1,x2) = a + bx1 + cx2
SUM(y) = na + bSUM(x1) + cSUM(x2)
SUM(x1y) = aSUM(x1) + bSUM(x1^2) + cSUM(x1x2)
SUM(x2y) = aSUM(x2) + bSUM(x1x2) + cSUM(x2^2)
MATRIX SOLUTION FOR SIMULTANEOUS EQUATIONSa c t a c t
10 35.5 109 1437 1 0 7.82808 60.84BAS! 35.5 134.75 394.5 5305 4 0 1 0.86533 23.34
109 394.5 1289 16903 0 0 94.3668 1063
1 3.55 10.9 143.7 1 0 7.82808 60.84
1 35.5 134.75 394.5 5305 5 0 1 0.86533 23.34
109 394.5 1289 16903 0 0 1 11.27
1 3.55 10.9 143.7 1 0 0 -27.38
2 0 8.725 7.55 203.65 6 0 1 0 13.!
0 7.55 100.9 1239.7 0 0 1 11.27
1 3.55 10.9 143.7
3 0 1 0.86533 23.340974
0 7.55 100.9 1239.7
FORECAST "#R$% 11
MARRA '!#!#S "
"#RMS 1#
FORECAST 13!.$7% &'(('*
REGRESSION6$ASED MODE5Class Example Pro,lem
&Ro Re0+ction Matrix Sol+tion or Sim+ltaneo+sE1+ations'
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+) EQUATIONS
b =(x*x)^1 (x*y) R=SSR SS$
, 1 2.50 9 112 1 1
1 3.50 12 145 1
1 3.50 10 105 1
1 5.00 13 180 1
1 4.00 5 95 1
1 3.00 6 80 1
1 4.00 15 200 1
1 5.00 14 210 1
1 2.00 13 150 1
1 3.00 12 160 1
1 2 3 4 5 6 7 8 9 10
, 1 1 1 1 1 1 1 1 1 12.5 3.5 3.5 5 4 3 4 5 2 3
9 12 10 13 5 6 15 14 13 12
112 145 105 180 95 80 200 210 150 160
1 1 1 1 1 1 1 1 1 1 1
REGRESSION6$ASED MODE5Class Example Pro,lem
&(sing Matrix Sol+tion Approach rom Scratch'
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1 ,, 10.00 35.50 109.00 1 '*/ 2.19 0.34 0.08
2 35.50 134.75 394.50 2 0.34 0.12 0.01
3 109.00 394.50 1289.00 3 0.08 0.01 0.01
1 , 1437
2 5305
3 16903
1 b -27.38 +&pare0 t a 27.38 r& &atr', ð0
2 13.! b 13.59 (/'*4 *r&a( e56at'*
3 11.27 + 11.27
SSR=b*x*y(1n)y*-1-1* y SSTO= y*y (1n)y*-1-1*-y
R= SSRSS$
b 27.38 13.59 11.27
b, 223235 1 1437 1 1437 224619
SSR 16738 SSTO 18122
R 0.9236
REGRESSION6$ASED MODE5Class Example Pro,lem
&(sing Matrix Sol+tion Approach rom Scratch'
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DO($5E EBPONENTIA5 SMOOT"ING&"olt9s Metho0'
). 4olt5s method is a type of 0o+,le exponential
smoothing designed to trac" time series with linear
trend.
. The method requires the speci$cation of two
smoothing constants, R and S and uses two
smoothing equations
/ne for the value of the series the intercept
/ne for the trend the slope
J. The -step-ahead forecast made in period t, is given
y the following(
))(( ++= tttt GSDS
)()( += tttt GSSG
tttt GSF +=+=
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C5ASS EBAMP5E 7*) PRO$5EMCONT9D
'
'emand during the first 7 months of the year !as as follo!sF
:onth (t) Gan e% :ar $pr :ay Gun Gul $ug "ep Hct
'emand -I(t) J K J * M *K *
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A Seasonal Deman0 Series
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SEASONA5 FORECASTING
). 2ompute the sample mean of all the data
.
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Class Example 7*= Pro,lemStationar3 Seasonal Data
The quarterly sales of tires during the last 7 years are givenelow(
Ise the simple moving-average to determine the forecast foreach quarter of ne!t year +i.e. year O.
'B
#ear
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Seasonal Series ithIncreasing Tren0
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%inter5s method is a type of triple e!ponentialsmoothing.
8t has the important advantage of eing easy
to update as new data ecomes availale. The method assumes the following model(
Ass+mptions>
The length of the season is e!actly =periods
The seasonal factors +indices are the sameeach season and the property
'O
tttt cGY ++= )(
TRIP5E EBPONENTIA5 SMOOT"INGJ
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'N
TRIP5E EBPONENTIA5 SMOOT"INGJ
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Initiali!ationor
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n a !a onor
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n a !a onor
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B
n a !a onor
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INITIA5ILATION OF T"E
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Alternati.e Initiali!ationProce0+re or