indo heizer 04

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2008 Prentice Hall, Inc. 4 1

Operat ionsManagementChap ter 4 Peramalan

PowerPoint p resentat ion to acco mp anyHeizer/RenderPrinciples o f Op erat ions Management , 7eOperation s Managem ent, 9e


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Learn ing Ob ject iv es

K etika A nd a m eny elesaikan bab ini ,A nd a harus d apat :

Mem aham i t iga cakraw ala w aktu d anyang m od el ber laku un tuk se tiappenggunaan

Je lask an kapan mengg un akan m as ing - m asin g d ar i em pat mo del kuali tat i fTerapk an n aif , m ov ing average,exp on ent ial sm oo th ing , dan m etodetrend


3/103


Learn ing Ob ject iv es

K etika A nd a m eny elesaikan bab ini ,A nd a harus d apat :

Hitung t ig a uk uran akurasi perkiraanMengembangkan indeks m us im an

Melaku kan anal is is regres i d an k orelas i

Gun akan s inyal pelacakan


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Wh at is Fo rec as t ing ?

Pros es m em prediks iper is t iwa m asadepan

Yang m endasarisemu a keputusanb isn i s?

Product ion

Inventory

Personnel

Facili t ies

? ?


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Short-rang e forecastSam pai dengan 1 tahun, umu m ny a ku rang dari 3bulan

Penjadw alan p emb elian, pekerjaan, t ingk at tenagakerja, tugas pekerjaan, t ingk at produ ksi

Mediu m -range forecast3 bulan samp ai 3 tahu n

Perencanaan p rodu ks i dan p enjualan, pengangg aran

Lo ng -range forecast

3 + t ahunPerenc anaan pro du k baru , lok asi fasil i tas, penelit iandan pengembangan

For ecast in g Tim e Hor izon s


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Dist in gu ish ing Differen ces

Medium /long rang e peram alan b eruru sandengan i su-i su y ang leb ih k om prehens i fdan kepu tusan m anajem en du kun gan

m eng enai perenc anaan dan pro du k,tanaman d an p roses

Short- term peram alan biasany am em peker jakan m etodo logi y ang berbeda

dar i peram alan jang ka panjangShort- term perkiraan cenderung lebihakurat dar ipada perkiraan jang ka p anjang


7/103 2008 Prentice Hall, Inc. 4 7

In f luenc e of Pro d uc t L ife

Cycle

In t rodu ct ion and gro wth m em butuhkan l eb ihlam a dar i perkiraan jatuh tem po danpenurunan

Sebagai pro du k m elewat i s ik lu s hid up ,

prak i raan berguna da lam m em proy eks ikant ingkat s taf

t ing kat persediaan

kapasi tas pabrik

In t roduct ion Grow th Matur i ty Decline



Pro d u ct L ife Cyc le

Periode terbaikuntukmeningkatkanpangs a pasar

R&D engineer ing iscrit ical

Berguna untukmengub ah hargaatau kualitasgambar

Strengthen niche

Waktu yang bu rukuntuk m engub ah c i tra ,harg a, atau kualitas

Biaya yang kom pet i t i f

menjadi kr i t i s

Per tahankan po sis ipasar

Pengendalianbiaya krit is

Introd uct io n Growth Maturi ty Decl ine

C o m p a n y

S t r

a t e

g y /

I s s u e s

Figure 2.5

Internet search engin es

Sales

Xbox 360

Drive- throughrestaurants

CD-ROMs

3 1/2Floppydisks

LCD & plasm a TVsAnalog TVs

iPods



Pro d u ct L ife Cyc le

Desain danpengembanganproduk kr i t is

Produk dan d esainproses perubahanFrequent

Produksi ber ja lansingkat

Biaya produ ksiyang t inggi

mo del terbatas

Perhatian terhadapkualitas

Introd uct io n Growth Maturi ty Decl ine

O M

S t r

a t e

g y

/ I s s u

e s

peramalan kr i t i s

P roduk dan p rosesreliabil i tas

Perbaikan prod uk yangkom pet i t i f dan pi l ihan

men ingka tkankapasi tas

Bergeser ke arah fokusp r o d u k

meningka tkandis t r ibusi

Standardisas i

Perubahan p rodu kkurang cepat -perubahan yang lebihkeci l

kapasi tas opt imu m

Meningkatkanstabi l i tas pro ses

Produks i ber ja lan lama

Perbaikan produ k danpemotongan b iaya

Diferensiasip roduk kec i l

minim isas i b iaya

Kelebihankapasi tas d iindus t r i

Memangkas u n tukmengh i l angkanbarang t idakmember ikanmarg in yang ba ik

mengurang ikapasi tas

Figure 2.5



Typ es o f Fo rec as ts

Econo m ic forecas tsSiklus alamat bisn is - t ing kat inf lasi , jum lahuang beredar, perum ahan, dl l .

Tech no logic al forecastsMem prediks i t ing kat kem ajuan teknolog i

Damp ak pengem bangan produk baru

Dem and forecas tsMem prediks i p enjualan prod uk dan jasayang ada



Pen ting n ya Strateg i

PeramalanSum ber Daya Manu sia -Mem pek erjakan, pelat ihan, pem utu san

hu bun gan ker jaKapasi tas Kekurang an kapasi tasdapat m engakibatkan peng ir iman t idakdip ercaya, keh ilang an pelang gan,kehi lang an p ang sa pasar

Supp ly Chain Managem ent - hu bu ng anpemasok y ang b aik dan keuntun ganharga



Tuju h Lang kah d alam Forecas t ing

Menentu kan p eng gu naan p erkiraan

Pil ih b arang yang akan d iperkirakan

Menentukan hor iso n w aktuperkiraan

Pil ih m od el p eram alan

Meng um pu lkan dataMem bu at p erkiraan

Mem validasi dan m enerapk an hasi l



The Realities!

Prakiraan jarang sem pu rna

K ebanyakan teknik m eng ang gapstabi l itas y ang m end asar i dalamsis tem

Prakiraan pro du k k eluarga danagregat leb ih aku rat daripadaperkiraan pro du k individu al



Forecas t ing A pp roaches

Digun akan k et ika s i tuasi t idak

jelas d an ada s ed ik it dataNew produc t s

New techn olog y

Melibatkan in tuis i , p en galam an m isalny a, peram alan penjualan diInternet

Quali tat ive Meth o ds



Forecas t ing A pp roaches

Digun akan bi lam ana s i tuasi adalah

's tabil ' dan d ata h isto ris adaprod uk yang ada

tekn olog i saat in i

Melibatkan tekn ik m atem atikam isalny a, peram alan pen jualantelevis i berw arna

Quanti tat ive Meth od s



Sek ilas Meto d e K u ali tat if

Opin i Ju r i eks eku t i f

Pend apat kelom po k ahl i t ingk att ing gi , kadang-kadang m enam bahdengan m od el s tat i s t ik

Delphi m ethodPanel ahli , b ertany a secara i teratif



Sek ilas Meto d e K u ali tat if

Gab un g an Tenaga Pen jualan

Est im ates f rom indiv idualsalesp erso ns are reviewed fo rreaso nableness , th en aggr egated

Perkiraan dar i penjualan ind ividuterakh ir yang w ajar, kem ud iand ikumpulkan

Survei K on su m en Pasar

B ertany a pada pelangg an



Melibatkan s ekelom po k k eci l ahl i danm anajer t ingk at t ingg i

Grup m eng es t im as i p erm intaan denganbekerja sam a

Meng gabu ng kan p eng alam an m anajer ialdengan m od el s tat i s t ik

Relatif c epat'Ke lompok- berpikir

kelemahan

Opini Ju r i eks eku t i f


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Gab u n gan Tenag a Pen jualan

Set iap p enju al m em pro yeksikanpenjualannya

Gabu ng an di t ing kat nasion al dankabupaten

Penju alan reps tahu keingin an

pelangganCend erun g ter lalu op t im is


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Delph i Metho d

Proseske lompokberulang-ulang,

terus sam paitercapaikonsensus

3 jenis p esertaDecis io n m akers

Staff

Respondents

Staff(penyelenggar

a sur vei)

Decis ion Makers(Mengevaluasitang gapan dan

membuat

keputusan)

Respondents(Orang yang b isa

membuatpenilaian

berharga)


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Su rvei K on su m en Pasar

Tanyakan k ep ada pelang gantentang renc ana p em bel ian

Opini Ko ns um en, dan apa yangm ereka benar-b en ar m elakuk anser ing berbeda

K adang-kadang s ul i t un tukmenjawab


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Sek ilas Meto d e Ku an ti tat i f

1. Pendekatan na if

2. Moving average3. Pem u l u s an

Eksponensia l

4. Proyeks i tr end5. Regres i lin ier

Time-SeriesModels

Assoc ia t iveModel


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Set data nu m erik m erata sp asiDiperoleh dengan m engam ativar iabel resp on pada per iod e waktuyang tera tur

Prakiraan h any a did asarkan p adan ilai-n ilai m asa lalu , t id ak adavariab el lain yang

Meng asu m sikan bahw a faktor y angm em pengaruhi m asa lalu dansekarang akan terus berpeng aruh dim asa depan

Tim e Series Fo recas t ing


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Com po nents o f Dem and

D e m a n

d f o

r p r o

d u c

t o r s e r v

i c e

| | | |1 2 3 4

Year

Average

demand overfour years

Seaso nal peaks

Trendcomponent

Actualdemand

Randomvariat ion

Figure 4.1


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Persis tent , keseluru h an p ola keatas atau ke b aw ah

Peru b ahan k arena po p ulasi ,tekno log i , us ia, b ud aya, d l l

Durasi B iasany a b eb erapatahun

Trend Com po nent


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Pola yang teratur f luktu asi dar iatas d an ke bawah

K aren a cuaca, kebiasaan , d llTerjadi d alam s atu tahu n

Seaso nal Com po nent

Numb er ofPeriod Length Seasons

Week Day 7Month Week 4-4.5 Month Day 28-31 Year Quarter 4 Year Month 12

Year Week 52


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Tidak m enentu , t idak sis tem atis ,' s isa' f luk tuasi

K arena v ariasi acak atau kejadiantak terdu ga

Durasi pend ek dan

Tidak b erulang

Rand om Com pon en t

M T W T F


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MA adalah s erang kaian aritm atikaDigu nakan j ika sed iki t atau t id akada trend

Ser ing d igun akan untu kmenghaluskan

Meny ediakan k esan k eseluruh an

data dar i waktu k e w aktu

Mov ing A verage Metho d

Movin g average = permin taan di per iode n sebelum ny a

n


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January 10 February 12 March 13 Apr i l 16May 19

June 23Ju ly 26

Actual 3-MonthMont h Shed Sales Movin g Av erage

(12 + 13 + 16)/3 = 13 2 /3

(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1 /3

Mov ing A verage Exam p le

10

12 13

(10 + 12 + 13 )/3 = 11 2 /3


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Grap h o f Mo vin g A verag e

| | | | | | | | | | | |

J F M A M J J A S O N D

S h

e d S

a l e

s

30 28 26 24 22 20 18 16

14 12 10

ActualSales

MovingAverageForecast


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Digun akan k et ika t rendData yang lebih lam a biasany a

kurang pent ingB ob ot berdasarkan pengalam andan in tu is i

Weigh ted Mov ing A verage

Weightedm ov ing average =

(w eigh t for per iod n ) x (demand in per iod n )

w eigh ts


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January 10 February 12 March 13

Apr i l 16May 19June 23Ju ly 26

A ctu al 3-Month Weigh ted

Month Shed Sales Movin g Av erage

[(3 x 16) + (2 x 13) + (12)]/6 = 14 1 /3 [(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 20 1 /2

Weigh ted Mov ing A verage

10 12 13

[(3 x 13 ) + (2 x 12 ) + (10 )]/6 = 121

/6

Weights Ap pl ied Per iod

3 Las t mo nth2 Two mo nths ago1 Three m on ths ago

6 Sum of weights


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Mening katkan n m eng halusk anperkiraan te tapi m em bu at ku rangsensi t i f terhadap perub ahan

Tidak m em perkirakan t ren denganbaik

Mem erlukan d ata his tor is yangluas

Potens i Masalah Den g an

Mov ing A verage


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Moving A verage An dWeigh ted Mo vin g A verage

30

25

20

15

10

5

S a

l e s

d e m a n

d

| | | | | | | | | | | |

J F M A M J J A S O N D

Actualsales

Movingaverage

Weightedmo v ingaverage

Figure 4.2


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B entu k berg erak rata-rata ter t im bangPenu runan secara ekspon ensia l ter t imb ang

Data terbaru p aling ter t im bang

Mem bu tuhk an kon s tanta ( ) pemulusan B erkis ar dari 0 ke 1

Dipil ih secara su by ektif

Melibatkan s ediki t penc atatan data m asalalu

Exp on ent ial Sm oo th ing


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New fo recast = Perk iraan m asa lalu+ (Perm intaan aktu al period e lalu

Perkiraan m asa lalu )

F t = F t 1 + (A t 1 - F t 1)

where F t = new fo recas tF t 1 = previous fo recas t

= sm ooth ing (or weight ing)cons tan t (0 1)


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ExamplePrediks i perm intaan = 142 Ford Mus tang sPerm intaan aktu al = 153Sm ooth ing co ns tan t = .20


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ExamplePrediks i perm intaan = 142 Ford Mus tang sPerm intaan aktu al = 153Sm ooth ing co ns tan t = .20

New forecast = 142 + .2(153 142)

= 142 + 2.2= 144.2 144 cars


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Effec t o f

Sm oo thing Con s tan ts

Weight Ass igned to

Most 2nd Most 3rd Most 4th Most 5th MostRecent Recent Recent Recent RecentSmoo thing Period Period Period Period PeriodConstant ( ) (1 - ) (1 - )2 (1 - )3 (1 - )4

= .1 .1 .09 .081 .073 .066

= .5 .5 .25 .125 .063 .031


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Im p act o f Differen t

225

200

175

150 | | | | | | | | |1 2 3 4 5 6 7 8 9

Quarter

D e m a n d

= .1

Actualdemand

= .5


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Im p act o f Differen t

225

200

175

150 | | | | | | | | |1 2 3 4 5 6 7 8 9

Quarter

D e m a n d

= .1

Actualdemand

= .5Mem ilih n i lai-ni lai yangt inggi ket ika m endasar ira ta-ra ta kemu ng kinanperubahan

Pil ih ni lai-ni lai rend ah ket ika m endasari rata- rata s tabi l


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Choos ing

Tuju ann ya adalah un tukm end apatkan p erkiraan y ang pal ingaku rat apapu n teknikn ya

K am i biasanya m elakuk an hal in i denganm em ilih m odel yang m em ber i k i takesalahan perkiraan ( forecast error) terendahForecast error = Ac tual demand - Forecast value

= A t - F t


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Com m on Measu res o f Error

Mean A bs olu te Deviation (MA D )

MAD = |Ac tu al - Forecast |n

Mean Sq uared Error (MSE )

MSE = (Forecast Errors )2

n


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Com m on Measu res o f Error

Mean A bs olu te Percent Error (MAPE )

MA PE =100 |Actual i - Forec ast i | /Actual i

n

n

i = 1


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Com par ison of Forecas tError

Rounded Absolu te Rounded Absolu teAc tual Forecast Deviation Forecast Deviation

Tonn age with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.3082.45 98.62

MAD = |deviat ion s |n

= 82.45/8 = 10.31

For = .10

= 98.62/8 = 12.33For = .50


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1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.3082.45 98.62

MAD 10.31 12.33

= 1,526.54/8 = 190.82

For = .10

= 1,561.91/8 = 195.24For = .50

MSE = (forecast errors )2 n


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1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.3082.45 98.62

MAD 10.31 12.33MSE 190.82 195.24

= 44.75/8 = 5.59%

For = .10

= 54.05/8 = 6.76%For = .50

MA PE = 100 |deviat ion i | /actual i n

n

i = 1


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Exp on ent ial Sm oo th ing w i th

Trend A djus tm entWhen a t rend is p resent , exp on ent ialsm ooth ing m us t be m odi f ied

Forecastinc lud ing (FIT t ) =t rend

Exponent ia l ly Exponent ia l lysmoothed (F t ) + (T t ) sm oo thedforecas t t rend


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Exp on ent ial Sm oo th ing w i th

Trend A djus tm ent

F t = (A t - 1) + (1 - )(F t - 1 + T t - 1)

T t = b(F t - F t - 1) + (1 - b)T t - 1

Step 1: Com pu te F t

S tep 2: Com pu te T t

Step 3: Calcu late th e forec ast FIT t = F t + T t


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Exp on ent ial Sm oo th ing w ithTrend A djus tm ent Exam ple

ForecastAc tual Smooth ed Smooth ed Inc luding

Month (t ) Demand (A t ) Forecast, F t Trend, T t Trend , FIT t 1 12 11 2 13.002 173 204 195 246 21

7 318 289 36

10

Table 4.1


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Month (t ) Demand (A t ) Forecast, F t Trend, T t Trend , FIT t 1 12 11 2 13.002 17 12.803 204 195 246 21

7 318 289 36

10

Table 4.1

T 2 = b(F 2 - F 1) + (1 - b )T 1 T 2 = (.4)(12.8 - 11) + (1 - .4)(2)

= .72 + 1.2 = 1.92 units

Step 2: Trend fo r Mon th 2


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Month (t ) Demand (A t ) Forecast, F t Trend, T t Trend , FIT t 1 12 11 2 13.002 17 12.80 1.923 204 195 246 21

7 318 289 36

10

Table 4.1

FIT 2 = F 2 + T 1 FIT 2 = 12.8 + 1.92= 14.72 units

Step 3: Calcu late FIT for Mo nt h 2


60/103




Month (t ) Demand (A t ) Forecast, F t Trend, T t Trend , FIT t 1 12 11 2 13.002 17 12.80 1.92 14.723 204 195 246 21

7 318 289 36

10

Table 4.1

15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.89

24.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16


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Figure 4.3

| | | | | | | | |

1 2 3 4 5 6 7 8 9

Time (m on th)

P r o

d u c

t d

e m a n

d

35

30

25

20

15

10

5

0

Actu al demand (A t )

Forecast includ ing t rend (FIT t )

with = .2 and b = .4


62/103


Tren d Projec t ion s

Fit t ing a t rend l ine to h is tor ic al data po intsto pro jec t in to th e medium to long -rang e

Lin ear t rend s can be foun d u sing the leas tsq uares tech nique

y = a + b x^

w here y = com pu ted value of the var iable tobe p redicted (depend ent v ariable)

a = y-axis int erceptb = s lop e of the regress ion l inex = the ind epend ent variable

^


63/103


L eas t Sq u ares Metho d

Time p eriod

V a

l u e s o

f D e p e n

d e n

t V a r i a

b l e

Figure 4.4

Deviation 1

(error)

Deviation 5

Deviation 7

Deviation 2

Deviation 6

Deviation 4

Deviation 3

Ac tual observat ion(y v alue)

Trend line, y = a + bx^


64/103



Time p eriod

V a

l u e s o

f D e p e n

d e n

t V a r i a

b l e

Figure 4.4

Deviation 1

Deviation 5

Deviation 7

Deviation 2

Deviation 6

Deviation 4

Deviation 3

Ac tual observat ion(y v alue)

Trend line, y = a + bx^

Least sq uares m etho dm inim izes the sum of the

sq uared error s (deviat ions )


65/103



Equat ions to c alcu late the regress ion var iables

b =Sxy - nxy

Sx 2 - n x 2

y = a + b x^

a = y - bx


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L eas t Sq u ares Exam p le

b = = = 10.54 xy - nxyx 2 - nx 2

3,063 - (7)(4)(98.86)140 - (7)(4 2)

a = y - b x = 98.86 - 10.54(4) = 56.70

Time Electrical Pow erYear Period (x) Dem and x 2 xy

2001 1 74 1 742002 2 79 4 1582003 3 80 9 2402004 4 90 16 3602005 5 105 25 5252005 6 142 36 8522007 7 122 49 854

x = 28 y = 692 x 2 = 140 xy = 3,063x = 4 y = 98.86


67/103



b = = = 10.54 Sxy - nxy

Sx 2 - nx 2

3,063 - (7)(4)(98.86)140 - (7)(4 2)

a = y - b x = 98.86 - 10.54(4) = 56.70

Time Electrical Pow erYear Period (x) Dem and x 2 xy

1999 1 74 1 742000 2 79 4 1582001 3 80 9 2402002 4 90 16 3602003 5 105 25 5252004 6 142 36 8522005 7 122 49 854

Sx = 28 Sy = 692 Sx 2 = 140 Sxy = 3,063x = 4 y = 98.86

The trend l ine is

y = 56.70 + 10.54x ^


68/103



| | | | | | | | |2001 2002 2003 2004 2005 2006 2007 2008 2009

160 150 140 130

120 110 100

90 80

70 60 50

Year

P o w e r

d e m

a n

d

Trend line,y = 56.70 + 10.54x ^


69/103


Seaso nal Variation s In Data

The m ult ip l icat iveseaso nal m od elcan adju st t rendd ata for s eason alvar iat ions indemand


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Seaso n al In d ex Exam p le

Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94

Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Ju l 100 102 113 105 94A u g 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94

Demand Av erage Av erage SeasonalMon th 2005 2006 2007 2005-2007 Mon th ly Index


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Jan 80 85 105 90 94 0.957 Feb 70 85 85 80 94 0.851 Mar 80 93 82 85 94 0.904

Apr 90 95 115 100 94 1.064 May 113 125 131 123 94 1.309 J un 110 115 120 115 94 1.223 Ju l 100 102 113 105 94 1.117 A u g 88 102 110 100 94 1.064 Sept 85 90 95 90 94 0.957 Oct 77 78 85 80 94 0.851 Nov 75 72 83 80 94 0.851 Dec 82 78 80 80 94 0.851

Demand Av erage Av erage SeasonalMon th 2005 2006 2007 2005-2007 Mon th ly Index

Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,20012

Forecas t fo r 2008


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140

130

120

110

100

90

80 70

| | | | | | | | | | | |J F M A M J J A S O N D

Time

D e m a n d

2008 For ecast

2007 Demand

2006 Demand

2005 Demand


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San Dieg o Hos p ital

10,200

10,000

9,800

9,600

9,400

9,200

9,000 | | | | | | | | | | | |Jan Feb Mar Ap r May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

I n p a

t i e n

t D a y s

9530

9551

9573

9594

9616

9637

9659

9680

97029724

97459766

Figure 4.6

Trend Data

l


77/103


San Dieg o Hos p ital

1.06

1.04

1.02

1.00

0.98

0.96

0.94 0.92 | | | | | | | | | | | |

Jan Feb Mar Ap r May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

I n

d e x

f o r

I n p a t i e n

t D

a y s

1.04

1.021.01

0.99

1.031.04

1.00

0.98

0.97

0.99

0.970.96

Figure 4.7

Season al Ind ices


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A ss o ciat ive For ecast in g

Used w hen changes in one or m oreind epend ent var iables can be used to predic t

the ch ang es in the dependent v ar iable

Most com m on techn ique is l inearregress ion analysis

We app ly th is techniqu e jus t as w e d idin th e t im e ser ies exam ple


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A ss o ciat ive For ecast in g

Forecas t ing an o utco m e based onpredicto r var iables us ing the leas t squ arestechnique

y = a + b x^

w here y = com pu ted value of the var iable tobe p redicted (depend ent v ariable)

a = y-axis int erceptb = s lop e of the regress ion l inex = the independent var iable thou gh to

predic t the value of the dependentvariable

^


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A ss o ciat ive Forecas t ingExample

Sales Lo cal Payroll($ m ill ion s), y ($ bil l io ns ), x

2.0 13.0 3

2.5 42.0 22.0 13.5 7

4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

S a

l e s

Area payroll

A i i i


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Sales, y Payroll , x x 2 xy

2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5

y = 15.0 x = 18 x 2 = 80 xy = 51.5

x = x /6 = 18/6 = 3

y = y /6 = 15/6 = 2.5

b = = = .25xy - nxyx 2 - nx 2

51.5 - (6)(3)(2.5)80 - (6)(3 2)

a = y - b x = 2.5 - (.25)(3) = 1.75

A i i F i


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4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

S a

l e s

Area payroll

y = 1.75 + .25 x^ Sales = 1.75 + .25( payrol l )

If p ayrol l n ext y earis est im ated to b e$6 bi l l ion , then:

Sales = 1.75 + .25(6)Sales = $3,250,000

3.25


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Stand ard Erro r o f th e

EstimateA forecast i s jus t a po int es t im ate of afutu re value

This p oin t i sactu ally them ean o f aprobabi l i tyd is t r ibut ion

Figure 4.9

4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

S a

l e s

Area payroll

3.25


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Estimate

w here y = y-value of each data po int

y c = com pu ted value of the dependentvariable, f rom the regress ionequat ion

n = num ber of data poin ts

S y,x =(y - y c )2

n - 2


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EstimateCom pu tat ional ly, th is equ at ion isco ns iderably eas ier to u se

We us e the s tandard error to se t uppredict ion intervals arou nd th e

po int es t im ate

S y,x =y 2 - a y - b x y

n - 2


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Estimate

4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

S a

l e s

Area payroll

3.25

S y,x = =y 2 - a y - b xy

n - 239.5 - 1.75(15) - .25(51.5)

6 - 2

S y,x = .306

The stand ard errorof th e est im ate is$306,000 in s ales

C l i


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How s t ron g is the l inearrelat ion sh ip between thevariables?

Correlat ion do es n ot n ecessar ilyim ply c aus al i ty!

Coefficient of co rrelat ion , r,

m easu res d egree of asso ciat ionValues range f rom -1 to +1

Correlat ion


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Cor relat ion Coefficien t

r =n Sx y - Sx Sy

[n Sx 2 - (Sx )2][n Sy 2 - (Sy )2]


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Cor relat ion Coefficien t

r =n Sx y - Sx Sy

[n Sx 2 - (Sx )2][n Sy 2 - (Sy )2]

y

x(a) Perfect po siti vecorrelat ion:

r = +1

y

x(b) Pos itiv ecorrelat ion:

0 < r < 1

y

x(c) No cor relation :r = 0

y

x(d) Perfect negativ ecorrelat ion:r = -1

C l i


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Coefficient of Determ ination , r 2,m easu res th e percent o f ch ang e iny p redic ted b y th e ch ang e in x

Values range f rom 0 to 1 Easy to in terpret

Correlat ion

For th e Nod el Con stru ct ion exam ple:

r = .901r 2 = .81


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Multiple Reg ress ion

Analys isIf m ore than o ne ind epend ent var iable is to be

us ed in the m od el , l inear regress ion can b eextended to m ul t ip le regress ion to

acc om m od ate several ind epend ent v ar iables

y = a + b 1x 1 + b 2x 2 ^

Com pu tat ional ly, th is i s q ui tecom plex and g eneral ly d one on the

compute r


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Multiple Reg ress ion

Analys is

y = 1.80 + .30 x 1 - 5.0 x 2 ^

In th e Nod el exam ple, inc lud ing interest rates inthe mo del g ives the new equat ion:

An imp roved co rrelat ion c oeff ic ient of r = .96 m eans th is m od el does a bet ter job o f predic t ingthe chang e in con st ruc t ion sa les

Sales = 1.80 + .30(6) - 5.0(.12) = 3.00Sales = $3,000,000


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Measu res ho w w ell the forecast i spredic t ing actu al values

Rat io of running sum of forecas t er rors(RSFE) to m ean abso lute d eviat ion (MAD)

Good t racking s ign al has low valuesIf forecas ts are cont inu ally h igh or low , theforecast h as a bias error

Moni tor ing and Con t ro ll ing

ForecastsTrackin g Sign al

d ll


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Moni tor ing and Con t ro ll ing

ForecastsTracking

signalRSFEMAD=

Trackingsignal =

(Ac tual dem and inperiod i -

Forecast demandin p eriod i)

|A c tu al - Forec ast | /n )


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Track ing Sign al

Tracking s ignal

+

0 MADs

Upper cont ro l l imi t

Low er cont ro l l imi t

Time

Signal exc eeding l imit

Acceptablerange


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Track ing Sign al Ex am p leCumulat ive

Absolu te Absolu teActu al Forecast Forecast Forecast

Qtr Demand Demand Error RSFE Error Error MAD

1 90 100 -10 -10 10 10 10.0

2 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2


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Cumulat iveAbsolu te Absolu te

Actu al Forecast Forecast ForecastQtr Demand Demand Error RSFE Error Error MAD

1 90 100 -10 -10 10 10 10.0

2 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2

Track ing Sign al Ex am p leTracking

Signal(RSFE/MAD)

-10/10 = -1

-15/7.5 = -20/10 = 0-10/10 = -1

+5/11 = +0.5+35/14.2 = +2.5

The variat ion o f the t rack ing s ign albetween -2.0 and +2.5 i s w i th in acceptablel imi t s


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A d ap t ive Fo recast ing

Its possible to use the computer tocon t inual ly m on i tor forecas t er ror andadju st th e values of the and b co effic ients us ed in expo nent ialsm ooth ing to co nt inual ly m in im izeforecast error

This techn iqu e is c al led adaptiv esmoo th ing


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Foc u s Forecas t in g

Develop ed at A m erican Hard w are Sup ply,focu s forecas t ing i s based on two pr inc ip les :

1. Sophis t ica ted forecas t ing m odels are no t

always bet ter than s imp le ones2. There i s no s ing le techniqu e that should

be used for al l produc ts or s ervices

This approach uses h is tor ica l data to tes tm ul t ip le forecas t ing m od els for individ ual i tem s

The forecas t ing m od el wi th th e low est er ror i sthen used to fo recas t the next dem and

F ti i th S i


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Fo recas t ing in th e Serv iceSector

Presents u nu su al ch al leng esSpecial need for s hor t term reco rds

Needs di ffer great ly as fun ct ion ofindus t ry and p roduc t

Hol idays and o ther calend ar events

Unus ual events


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F d E C llC F


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Fed Ex Call Cen ter Fo recast

12%

10%

8%

6%

4%

2%

0% 2 4 6 8 10 12 2 4 6 8 10 12

indo heizer 04

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