indo heizer 04
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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
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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 :
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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Exp on ent ial Sm oo th ing
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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Exp on ent ial Sm oo th ing
ExamplePrediks i perm intaan = 142 Ford Mus tang sPerm intaan aktu al = 153Sm ooth ing co ns tan t = .20
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Exp on ent ial Sm oo th ing
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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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 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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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 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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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 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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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 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
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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 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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Exp on ent ial Sm oo th ing w ithTrend A djus tm ent Exam ple
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
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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
^
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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^
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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
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 )
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L eas t Sq u ares Metho d
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
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L eas t Sq u ares Exam p le
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 ^
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L eas t Sq u ares Exam p le
| | | | | | | | |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 ^
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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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Seaso n al In d ex Exam p le
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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Seaso n al In d ex Exam p le
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
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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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A ss o ciat ive Forecas t ingExample
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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A ss o ciat ive Forecas t ingExample
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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Stand ard Erro r o f th e
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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Stand ard Erro r o f th e
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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Stand ard Erro r o f th e
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
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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
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