chap3-1-forecasting (1)

7/23/2019 chap3-1-forecasting (1)

1/54

Chapter 3.1

ForecastingForecasting


2/54

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


3/54

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.


4/54

'

T"E DEMAND FORECASTING S#STEM$ASED ON

IDEF%&ICOM' DEFINITION


5/54

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


6/54

Forecasting 6rocess

7


7/54

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'


8/54

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

+:


9/54

Common Time Series Patterns


10/54

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


11/54

=* 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.


19/54

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


20/54

Exponential Smoothing orDierent ?al+es o Alpha


21/54

&)' 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'


22/54


)* &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+++=


23/54

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.



24/54

&=' 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



25/54

An Example o a Regression5ine


26/54

&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


27/54

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



28/54

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



29/54

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+=


30/54

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 *


31/54

C5ASS EBAMP5E 7*) PRO$5EM

J)




0a"e forecasts of demand for =ovemer and


32/54

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


33/54

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>


34/54

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'


35/54

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


36/54

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'


37/54

REGRESSION6$ASED MODE5Class Example Pro,lem

&Determining the Nee0e0 Correlation Coecients'


38/54

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% &'(('*


&Ro Re0+ction Matrix Sol+tion or Sim+ltaneo+sE1+ations'


39/54

+) 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


&(sing Matrix Sol+tion Approach rom Scratch'


40/54

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', &eth0

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


&(sing Matrix Sol+tion Approach rom Scratch'


41/54

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 +=+=


42/54

C5ASS EBAMP5E 7*) PRO$5EMCONT9D

'





43/54

A Seasonal Deman0 Series


44/54

SEASONA5 FORECASTING

). 2ompute the sample mean of all the data

.


45/54

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


46/54

Seasonal Series ithIncreasing Tren0


47/54

%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


48/54

'N

TRIP5E EBPONENTIA5 SMOOT"INGJ


49/54

Initiali!ationor


50/54

n a !a onor


51/54

n a !a onor


52/54

B

n a !a onor


53/54

INITIA5ILATION OF T"E


54/54

Alternati.e Initiali!ationProce0+re or

chap3-1-forecasting (1)

Documents

Transcript of chap3-1-forecasting (1)