Perencanaan dan Pengendalian Produksi IE 2353

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Peramalan Permintaan

Perencanaan dan Pengendalian Produksi IE 2353

Pratya Poeri S

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Series1 Series2 Series3 Series4

1

Forecasting

• The process of predicting the values of a

certain quantity, Q, over a certain time

horizon, T, based on past trends and/or a

number of relevant factors.

• An estimate of future demand & provides

the basis for planning decisions

• Goal is to minimize forecast error

• Forecast

error:

difference

between

forecast and actual demand

Demand

•

Observed demand (O)=Systematic component

(S) + Random component (R)

 Systematic component: Expected value of demand

 Random component: The part of the forecast that deviate

from the systematic component

•

Demand forecasting is based on:

 extrapolating to the future past trends observed in the company sales;

 understanding the impact of various factors on the company future sales:

– market data

– strategic plans of the company

– technology trends

– social/economic/political factors

– environmental factors

Sistem Peramalan

Data Historis

Tujuan model

Forecast (Prediction)

Feedback on forecast accuracy Data checked for

accuracy and reasonableness

Update sesuai kebutuhan

Knowledge of changed condition

Pembandingan dengan kondisi

(2)

Characteristics of Forecast

•

They are almost always going to be wrong

•

A good forecast also gives some measure of error

•

Forecasting aggregate units is generally easier

than forecasting individual units

•

Forecasts made future out into the future are less

accurate

•

A forecasting technique should not be used to the

exclusion of know information

4 5

Forecasting Techniques

•

Qualitative forecasting is based on opinion & intuition.

•

Quantitative forecasting uses mathematical models & historical data to make forecasts.

 Time series models are the most frequently used

among all the quantitative forecasting models.

Forecasting Techniques

(Cont.)

Qualitative Forecasting Methods

Used when data are limited, unavailable, or not

currently relevant. Incorporate factors like the

forecaster’s intuition, emotions, personal experience, and value system.

Four qualitative models used are:

1. Jury of executive opinion 2. Delphi method

3. Sales force composite 4. Consumer survey

Forecasting Techniques

(Cont.)

Quantitative Methods

• Time series forecasting-based on the assumption that the

future is an extension of the past. Historical data is used to predict future demand.

• Cause & Effect forecasting-assumes that one or more

factors (independent variables) predict future demand.

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8

Forecasting Techniques

(Cont.)

•

Penggunaan model kuantitatif membutuhkan:

 Data kondisi masa lalu

 Data tersebut dapat dikuantifisir

 Diasumsikan pola data masa lalu akan berlanjut pada masa yang akan datang

•

Data yang digunakan untuk keperluan

perencanaan produksi:

 Paling baik menggunakan data permintaan  Menggunakan data jumlah unit penjualan

 Kalau tidak dimiliki data penjualan gunakan data jumlah unit produksi

9

Forecasting Techniques

(Cont.)

Components of Time Series Data should be plotted to detect:

 Trend variations: increasing or decreasing

 Cyclical variations: wavelike movements that are longer than a year (e.g., business cycle)

 Seasonal variations: show peaks & valleys that repeat over a consistent interval such as hours, days, weeks, months, years, or seasons

 Random variations: due to unexpected or unpredictable events

Forecasting Techniques (Cont.)

Causal Models

-External variables are identified that are related to demand

Simple regression. Only one explanatory variable is used

& is similar to the linear trend model. The difference is that the xvariable is no longer time but an explanatory variable.

Ŷ = b₀₊b₁x

where

Ŷ = forecast or dependent variable

x = explanatory or independent variable

b₀= intercept of the line

b₁= slope of the line

Forecasting Techniques (Cont.)

Cause & Effect Models (Cont.)

Multiple regression.Several explanatory variables are

used to make the forecast. Ŷ = b0 + b1x1+ b2x2+ . . . bkxk

where

Ŷ = dependent variable

x_k= kth explanatory variable

b₀= intercept of the line

b_k= regression coefficient of the

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12

Implementing Quantitative Forecasting

Determine Method

•Time Series

•Causal Model

Collect data: <Ind.Vars; Obs. Dem.>

Fit an analytical model to the data:

F(t+1) = f(X1, X2,…)

Use the model for forecasting future demand

Monitor error: e(t+1) = D(t+1)-F(t+1)

Model Valid? Update Model

Parameters

Yes No

- Determine functional form - Estimate parameters - Validate

13

Prosedur Peramalan

•

Plot data permintaan vs. waktu

•

Pilih beberapa metoda peramalan

•

Evaluasi kesalahan peramalan

•

Pilih metoda peramalan dengan kesalahan

peramalan terkecil

•

Verifikasi

•

Intepretasi hasil peramalan

Pola Data

Components of Time Series

Data should be plotted to detect:

 Trend variations: increasing or decreasing  Cyclical variations: wavelike movements that

are longer than a year (e.g., business cycle)  Seasonal variations: show peaks & valleys that

repeat over a consistent interval such as hours, days, weeks, months, years, or seasons

 Random variations: due to unexpected or

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16

Contoh Teknik Peramalan

• Konstan

• Regresi linier

• Siklis

b

Kriteria Performansi Peramalan

•

Mean Square Error (MSE)

dengan:

dt = data aktual pada periode t Dt‘ = nilai ramalan pada periode t n = banyaknya periode

MSE

Kriteria Performansi Peramalan

•

Standard error of estimate (SEE)

dengan:

f = derajat kebebasan –1 : untuk data konstan

–2 : untuk data linier

–3 : untuk data kuadratis

SEE t t

Kriteria Performansi Peramalan

•

Persentase Kesalahan

•

Mean Absolute Percentage Error (MAPE)

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Contoh

•

Dari data 12 bulan terakhir tercata penjualan produk X:

•

Gambar diagram Pencar:

t 1 2 3 4 5 6 7 8 9 10 11 12

dt 140 159 136 157 173 181 177 188 154 179 180 160

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Metoda Konstan

t dt dt' e = dt - dt' _e2 SEE 1 140 165.33 -25.33 641.61 2 159 165.33 -6.33 40.07 3 136 165.33 -29.33 860.25 4 157 165.33 -8.33 69.39 5 173 165.33 7.67 58.83 6 181 165.33 15.67 245.55 7 177 165.33 11.67 136.19 8 188 165.33 22.67 513.93 9 154 165.33 -11.33 128.37 10 179 165.33 13.67 186.87 11 180 165.33 14.67 215.21 12 160 165.33 -5.33 28.41

3124.68 17

Metoda Konstan

a N

t t

n

t

d

1 '

SEE

n f

dt dt

t

n ₂

1

3124 68 12 1 3124 68

11 16 85 17

(

')

.

165.33 a

Metoda Linier

t dt t . dt t2 dt'=156+1.t e = dt - dt' e2

1 140 140 1 157 -17 289

2 159 318 4 158 1 1

3 136 408 9 159 -23 529

4 157 628 16 160 -3 9

5 173 865 25 161 12 144

6 181 1086 36 162 19 361 7 177 1239 49 163 14 196 8 188 1504 64 164 24 576 9 154 1386 81 165 -11 121 10 179 1790 100 166 13 169 11 180 1980 121 167 13 169 12 160 1920 144 168 -8 64

78 1984 13264 647 2628

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24

Metoda Linier

b

12 13264 1984 78 12 647

157168 154752 7764 6084

2416

Metoda Kuadratis

t dt t.dt t2 t2.dt t4 dt'

e=dt-Metoda Kuadratis

b

1984 182 12 28910 12 4550

361088 346920 33124 54600

14168

21476 0 6597 0 66

1984 0 66 182 12

1984 120 12 12

SEE 5737 27

12 3

5737 27 9 25 25 25

.

Pemilihan Metoda Terbaik & Hasil Peramalan

•

Metode yang dipilih adalah metode peramalan

linier

•

Dt' = 156 + t

Konstan Linier Siklis

SEE 17 16 25

t 13 14 15 16 17 18 19 20 21 22 23 24

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Metoda Peramalan Lainnya

•

Moving average method

 Simple moving average

•

Exponential smoothing

 Simple exponential smoothing

•

Winters model

29

Simple Moving Average

•

Forecast Ft is average of nprevious observations or actuals Dt :

•

Note that the npast observations are equally

weighted. t

n t i

i t

n t t

t t

D

n

F

D

n

F

1 1

1

1 )

(

1 

Simple Moving Average

•

Include nmost recent observations

•

Weight equally

•

Ignore older observations

weight

today

1 2 3

...

n

1/n

Moving Average

Internet Unicycle Sales

0 50 100 150 200 250 300 350 400 450

Apr-01 Sep-02 Jan-04 May-05 Oct-06 Feb-08 Jul-09 Nov-10 Apr-12 Aug-13

U

n

it

s

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32

Contoh

Data penjualan PC (personal computer) selama lima bulan terakhir adalah

Bulan (t) 1 2 3 4 5 Penjualan (D) 823 872 834 900 867

Berapa perkiraan jumlah penjualan PC untuk 3 bulan ke depan ?

33

Moving average 3 bln

Asumsi actual demand bln 6 = 934 dan bln 7 = 854

Bulan (t) 1 2 3 4 5 6 7 8

Penjualan (D) 823 872 834 900 867 934 854

Peramalan (F) 843 869 867 900 885

Error (D-F)2 ₃₂₄₉ ₃ ₄₄₈₉ ₂₁₄₇

MSE 2471.9

Exponential Smoothing I

•

Include all past observations

•

Weight recent observations much more

heavily than very old observations:

weight

today Decreasing weight given

to older observations

Exponential Smoothing: Math

1

)

1 (

_t

t

aD

a

F



2 1

2 2 1

)

1 (

)

1 (

)

1 (

)

1 (

t t

D

a

D

F

D

(10)

36

Exponential Smoothing: Math

•

Thus, new forecast is weighted sum of old forecast

and actual demand

•

Notes:

 Only 2 values (Dt and Ft-1 ) are required, compared with nfor moving average

 Parameter a determined empirically (whatever works best)

 Rule of thumb: < 0.5

 Typically, = 0.2 or = 0.3 work well

•

Forecast for kperiods into future is:

1

Exponential Smoothing

Internet Unicycle Sales (1000's)

0

Jan-03 May-04 Sep-05 Feb-07 Jun-08 Nov-09 Mar-11 Aug-12

Month

Contoh Exponential Smoothing

Time yt =0.1 Error

Verifikasi Peramalan

•

Dilakukan untuk memverifikasi apakah fungsi

peramalan yang digunakan mewakili pola data yang ada.

•

Metoda verifikasi: moving range chart

•

Moving Range

•

Average moving range

•

Control limits

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Verifikasi Peramalan

• Pengujian Out of control

 Dari 3 titik yang berurutan, 2 titik atau lebih di Daerah A

 Dari 5 titik yang berurutan, 4 titik atau lebih di Daerah B

 Dari 8 titik yang berurutan seluruhnya berada atau di bawah center line

 Satu titik di luar batas kontrol

• Bila kondisi out-of-control terjadi, tindakan yang bisa diambil :

 Perbaiki ramalan dengan

mencakup data baru (sistem sebab baru)

 Tunggu evidence selanjutnya

center line UCL

Contoh Verifikasi (1)

•Dt' = 156 + t

Contoh Verifikasi (2)