Perencanaan dan Pengendalian Produksi IE 2353

  Forecasting Peramalan Permintaan _25.00

• The process of predicting the values of a
_20.00 certain quantity, Q, over a certain time _{15.00 Series1 Series2} horizon, T, based on past trends and/or a _Series3 number of relevant factors. ^{10.00 Series4} 5.00<
• _0.00

  An estimate of future demand &amp; provides _{1 4 7 10 13 16 19 22 25 28 31 34 37 40} the basis for planning decisions

• Goal is to minimize forecast error

  Forecast error: difference between

• Perencanaan dan Pengendalian Produksi

  IE 2353 forecast and actual demand

  Pratya Poeri S

  1 Sistem Peramalan Demand

  Data Historis

• Observed demand (O)=Systematic component

  (S) + Random component (R)

   Systematic component: Expected value of demand Data checked for

   accuracy and Random component: The part of the forecast that deviate reasonableness from the systematic component

  Tujuan Update sesuai

  Demand forecasting is based on:

• model kebutuhan

  Knowledge of

   extrapolating to the future past trends observed in the

  changed condition

  company sales;

  Pembandingan Forecast

   understanding the impact of various factors on the

  dengan kondisi (Prediction)

  company future sales:

  aktual

• – market data
• – strategic plans of the company

  Feedback on

• – technology trends

  forecast

• – social/economic/political factors

  accuracy

• – environmental factors
• – etc

  Characteristics of Forecast Forecasting Techniques

  They are almost always going to be wrong

  Qualitative forecasting is based on opinion &amp; intuition.

• A good forecast also gives some measure of error
• Forecasting aggregate units is generally easier
• Quantitative forecasting uses mathematical

  than forecasting individual units models &amp; historical data to make forecasts.

  Forecasts made future out into the future are less among all the quantitative forecasting models. accurate

•  Time series models are the most frequently used
• A forecasting technique should not be used to the exclusion of know information

  4

  5 (Cont.)

  Forecasting Techniques (Cont.)

  Forecasting Techniques Quantitative Methods Qualitative Forecasting Methods

• Time series forecasting- based on the assumption that the

  Used when data are limited, unavailable, or not future is an extension of the past. Historical data is used to currently relevant. Incorporate factors like the predict future demand. forecaster’s intuition, emotions, personal

• Cause &amp; Effect forecasting- assumes that one or more experience, and value system.

  factors (independent variables) predict future demand.

  It is generally recommended to use a combination of Four qualitative models used are: quantitative &amp; qualitative techniques.

  1. Jury of executive opinion

  2. Delphi method

  3. Sales force composite

  4. Consumer survey

• Penggunaan model kuantitatif membutuhkan:

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

• Data yang digunakan untuk keperluan perencanaan produksi:

   Random variations : due to unexpected or unpredictable events

  (Cont.)

   Data kondisi masa lalu  Data tersebut dapat dikuantifisir  Diasumsikan pola data masa lalu akan berlanjut pada masa yang akan datang

   Paling baik menggunakan data permintaan  Menggunakan data jumlah unit penjualan  Kalau tidak dimiliki data penjualan gunakan data jumlah unit produksi

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

  Components of Time Series

  Data should be plotted to detect:

8 Forecasting Techniques

  9 Forecasting Techniques (Cont.)

  Forecasting Techniques (Cont.) Cause &amp; Effect Models (Cont.)

• + b

  independent variable x k

  b _{k = regression coefficient of the}

  = intercept of the line

  Ŷ = dependent variable x _{k = kth explanatory variable} b

  where

  k x k

  2

  2 x

  1

  1 x

  Ŷ = b + b

  Multiple regression. Several explanatory variables are used to make the forecast.

• + . . . b

  1

  = slope of the line

  b

  = intercept of the line

  b

  = explanatory or independent variable

  where

  1 x

  Ŷ = b + b

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

  Simple regression . Only one explanatory variable is used

  xternal variables are identified that are related to demand

  E

  Forecasting Techniques (Cont.) Causal Models -

  Ŷ = forecast or dependent variable x Implementing Quantitative Forecasting Prosedur Peramalan

  Plot data permintaan vs. waktu

• Determine Method
• Time Series •Causal Model
• Pilih beberapa metoda peramalan

  Collect data: &lt;Ind.Vars; Obs. Dem.&gt;

• Determine Evaluasi kesalahan peramalan

  Fit an analytical model functional form to the data:

• Estimate parameters

  F(t+1) = f(X1, X2,…)

• Validate

  Pilih metoda peramalan dengan kesalahan

  Use the model for

  peramalan terkecil

  forecasting future demand Update Model

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

• Verifikasi
• Intepretasi hasil peramalan

  No Model Yes

  12

  13 Valid? Pola Data

  Components of Time Series

  Data should be plotted to detect:

   Trend variations : increasing or decreasing

  : wavelike movements that

   Cyclical variations

  are longer than a year (e.g., business cycle) : show peaks &amp; valleys that

   Seasonal variations

  repeat over a consistent interval such as hours, days, weeks, months, years, or seasons : due to unexpected or

   Random variations

  unpredictable events

• Mean Square Error (MSE)
>Konstan
• Regresi linier
• Siklis

  1

  ( ' ) Kriteria Performansi Peramalan

  dengan:

  f = derajat kebebasan

  SEE t t n f d D _t ⁿ

  2

  1 ( ' )

  Kriteria Performansi Peramalan

  ( )

  Mean Absolute Percentage Error (MAPE) ^{t t t t}

  PE d D d

  ( x ) %

  '

  100 MAPE n ^{t t n}

  PE

  1

  2

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

  MSE t t t n n d D

  D a a d t n t t n

  b N t dt dt t N t n a dt N b t N dt b t ^{t n t n t n t n t n t n} t t

  .

  .

  ( ) ^{1 1 1 2} ₁ ² _{1 1}

  1 ^ ^ ^

  ( )

  1 ^

  dengan:

  ( ) cos

  D t a u t

  N v sin

  2 t N

  2 ^ ^

  ( ) D t a bt

16 Contoh Teknik Peramalan

  17 Kriteria Performansi Peramalan

• Standard error of estimate (SEE)
• Persentase Kesalahan •
• – 1 : untuk data konstan
• – 2 : untuk data linier
• – 3 : untuk data kuadratis
• Dari data 12 bulan terakhir tercata penjualan produk X:

• Gambar diagram Pencar:

  165.33 a Metoda Linier

  a N t t n t d d

  1 ' SEE n f dt dt t n

  2

  1

  3124 68 12 1 3124 68

  11 16 85 17

  ( ') .

  . .

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

  28.41 3124.68

  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 t 6.5 dt 165.33

  17 Metoda Konstan

  10 179 165.33 13.67 186.87 11 180 165.33 14.67 215.21 12 160 165.33 -5.33

  t

  9

  1

  2

  3

  4

  5

  6

  7

  8

  10

  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

  11

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

  21 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

20 Contoh

• 6 140 -840 36 5040 1296 118.36 21.64 468.29
• 5 159 -795 25 3975 625 127.82 31.18 972.19
• 4 136 -544 16 2176 256 143.88 -7.88
• 3 157 -471 9 1413
• 2 173 -346 4 692
• 1 181 -181 1 181

  5737 27 12 3 5737 27

  ( ) SEE

  ' . . .

  . ( ) . .

  ( )( ) ( ) ( ) . .

  182 . .

  155 32 2 2 0 66 ^{2 2}

  12 1984 120 12 12 155 32

  1984 0 66 182

  14168 21476 0 6597 0 66

  1984 182 12 28910 12 4550 361088 346920 33124 54600

  404 182 2 22 2 2

  2 c = dt _t=1 ⁿ b c a dt t t

  ( ) ^{1 2} ₁ ^{2 1 2 1 2} ₁ ⁴ _{1 1 2 1}

  b t dt N dt n a dt C N ^{t n t n t n t n t n t n t n t n} t t t t t t . .

  9 25 25 25 .

  Pemilihan Metoda Terbaik &amp; Hasil Peramalan

  . .

  18

  24 Dt' 169 170 171 172 173 174 175 176 177 178 179 180

  23

  22

  21

  20

  19

  17

  Konstan Linier Siklis SEE

  16

  15

  14

  13

  25 t

  16

  17

  7 Metoda Kuadratis

  35.52 4 179 716 16 2864 1256 161.48 17.52 306.95 5 180 900 25 4500 625 149.82 30.18 910.83 6 160 960 36 5760 1296 144.76 15.24 232.26 1984 404 182 28710 4550 5737.2

  1 152.46 28.54 814.53 1 177 177 1 171 1 156.86 20.14 405.62 2 188 376 4 752 16 158.4 29.6 876.16 3 154 462 9 1386 81 159.96 -5.96

  2

  b a dt b t dt t

  1

  1

  1

  2

  1

  1

  16 147.6 23.4 547.56

  1

  1

  ( )

  .

  .

  b N t dt dt t N t n a dt N b t N dt b t t n t n t n t n t n t n t t

  12 13264 1984 78 12 647 157168 154752 7764 6084

  2416 1680 1 44 1

  165 33 1 44 6 5 165 33 9 35 155 98 156 156 1

  2

  81 146.74 10.26 105.27

  62.09

  t dt t.dt t2 t2.dt t4 dt' e=dt- dt' e2

  25 Metoda Kuadratis

  ( ') .

  10 16 21 16

  2628 12 2 2628

  1

  2

  ( ) SEE n f dt dt t n

  '

  . . . ( . ) . . .

  ( ) ( )( ) ( ) .

  78

24 Metoda Linier

• Metode yang dipilih adalah metode peramalan li
• Dt' = 156 + t

  Simple Moving Average Metoda Peramalan Lainnya

  Forecast F is average of n previous Moving average method

  t

  observations or actuals D :  Simple moving average

  t

  1 F ( D D  D )

  1 t t 1 t 1 n

  Exponential smoothing

• t

  n

   Simple exponential smoothing

  t

  1 F D t 1 i

  Winters model

  i t 1 n

• n
• Note that the n past observations are equally weighted.

  28

  29 Simple Moving Average Moving Average

• Include n most recent observations
• Weight equally

  Internet Unicycle Sales n = 3

• Ignore older observations
_{450 400}

  weight _{300 350} 1/n _{U n it s 150 200 100 250 50} n ...

  2

  1

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

  _Month today Moving average 3 bln Contoh Bulan (t)

  1

  2

  3

  4

  5

  6

  7

  8 Data penjualan PC (personal computer) selama lima

  bulan terakhir adalah

  Penjualan (D) 823 872 834 900 867 934 854 Peramalan (F) 843 869 867 900 885 ₂ Error (D-F) 3249 3 4489 2147 Bulan (t)

  1

  2

  3

  4

  5 MSE 2471.9 Penjualan (D) 823 872 834 900 867

  Berapa perkiraan jumlah penjualan PC untuk 3 bulan ke

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

  depan ?

  32

  33 Exponential Smoothing I Exponential Smoothing: Math

  Include all past observations

• 2

  F D ( 1 ) D ( 1 ) D  t t t 1 t

  2

• Weight recent observations much more

   F D ( 1 ) D ( 1 a ) D t t t 1 t

  2

  heavily than very old observations:

  weight F aD a F

  ( 1 )

  1

  t t t Decreasing weight given to older observations today Exponential Smoothing: Math Exponential Smoothing

  F aD (1 a F ) t t t

1 Internet Unicycle Sales (1000's)

• Thus, new forecast is weighted sum of old forecast ₄₅₀ and actual demand Notes:
400<
• ₃₅₀

  = 0.2

   Only 2 values (D and F ) are required, compared with

  t t-1 ₃₀₀ n for moving average _{s 250}

   Parameter a determined empirically (whatever works it _{U n 200} best) ₁₅₀  Rule of thumb: &lt; 0.5 ₁₀₀

   Typically, = 0.2 or = 0.3 work well ⁵⁰

• Forecast for k periods into future is:

  F F t k t _{Jan-03 May-04 Sep-05 Feb-07 Jun-08 Nov-09 Mar-11 Aug-12 Month}

  36

  37 Contoh Exponential Smoothing Verifikasi Peramalan

• Dilakukan untuk memverifikasi apakah fungsi

  =0.1 Time yt Error

  peramalan yang digunakan mewakili pola data

  1

  71 yang ada.

  2

  70 71 -1

• Metoda verifikasi: moving range chart

  3

  69 70.9 -1.9

  4

  68 70.71 -2.71

  Moving Range

  5

  64 70.44 -6.44 MR d d d d t t t

• ' '

  1 t

  1

  6

  65 69.8 -4.8 MR

  72

  69.32

2.68 MR

  Average moving range

• 7

  n

  1

  8

  78

  69.58

  8.42

  9

  75

  70.43

  4.57

• Control limits

  UCL 2 .

  66 MR

  10

  75

  70.88

  4.12 2 .

  66 LCL MR

  11

  75

  71.29

  3.71

  12

  70 71.67 -1.67

• Pengujian Out of control
• Dt' = 156 + t
• Bila kondisi out-of-control

  12.82

  LCL UCL MR Contoh Verifikasi (2) _{38.45 25.63}

  11 159

  14

  38 45 .

  38 45 .

  45 .

  21 159

  7

  12 160 167

  15 10 179 165 -14 24 11 180 166 -14

  10

  10 9 154 164

  7 7 177 162 -15 5 8 188 163 -25

  20 5 173 160 -13 15 6 181 161 -20

  2

  24 4 157 159

  22

  18 3 136 158

  t Dt Dt' Dt'- Dt MR 1 140 156 16 2 159 157 -2

  41 Contoh Verifikasi (1)

   Perbaiki ramalan dengan mencakup data baru (sistem sebab baru)  Tunggu evidence selanjutnya ^{center line UCL LCL re g io n A re g io n B re g io n C re g io n A re g io n B re g io n C}

  terjadi, tindakan yang bisa diambil :

   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

40 Verifikasi Peramalan

• 38.45 ^{-12.82 -25.63}