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Bina Nusantara Model Ramalan Pertemuan 14: Mata kuliah: K0194-Pemodelan Matematika Terapan Tahun: 2008

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Bina Nusantara Learning Outcomes Mahasiswa akan dapat menghubungkan masalah aplikasi ramalan dengan berbagai metoda yang ada.

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Bina Nusantara Outline Materi: Moving Average Eksponesial trend Regression trend Contoh..

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Bina Nusantara MA is a series of arithmetic means. Used if little or no trend. Used often for smoothing. MA n n Demand in previous periods periods Moving Average Method

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Bina Nusantara You’re manager of a museum store that sells historical replicas. You want to forecast sales (in thousands) for months 4 and 5 using a 3-period moving average. Month 14 Month 2 6 Month 35 Month 4? Month 5? Moving Average Example

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Bina Nusantara Moving Average Forecast MonthResponse Y i Moving Total (n=3) Moving Average (n=3) 14NA 26 35 4? 5? 4+6+5=15 15/3=5 6 ?

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Bina Nusantara Actual Demand for Month 4 = 3

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Bina Nusantara Moving Average Forecast MonthResponse Y i Moving Total (n=3) Moving Average (n=3) 14NA 26 35 43 15 5 576+5+3=1414/3=4.667 6 ?

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Bina Nusantara Actual Demand for Month 5 = 7 MonthResponse Y i Moving Total (n=3) Moving Average (n=3) 14NA 26 35 43 15 5 576+5+3=1414/3=4.667 6 ?

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Bina Nusantara Moving Average Forecasts MonthResponse Y i Moving Total (n=3) Moving Average (n=3) 14NA 26 35 434+6+5=1515/3=5.0 576+5+3=1414/3=4.667 6 ? 5+3+7=1515/3=5.0

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Bina Nusantara Gives more emphasis to recent data. Weights decrease for older data. Weights sum to 1.0. –May be based on intuition. –Sum of digits weights: numerators are consecutive. 3/6, 2/6, 1/6 4/10, 3/10, 2/10, 1/10 WMA = Σ [(Weight for period n) (Demand in period n)] ΣWeights Weighted Moving Average Method

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Bina Nusantara Weighted Moving Average: 3/6, 2/6, 1/6 MonthResponse Y i Weighted Moving Average 14 NA 26 35 4 31/6 = 5.167 5 6 ? ? ?

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Bina Nusantara Weighted Moving Average: 3/6, 2/6, 1/6 MonthResponse Y i Weighted Moving Average 14 NA 26 35 43 31/6 = 5.167 57 6 ? 25/6 = 4.167 32/6 = 5.333

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Bina Nusantara Increasing n makes forecast: – Less sensitive to changes. – Less sensitive to recent data. Weights control emphasis on recent data. Do not forecast trend well. Require historical data. Moving Average Methods

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Bina Nusantara Form of weighted moving average. –Weights decline exponentially. –Most recent data weighted most. Requires smoothing constant ( ). –Usually ranges from 0.05 to 0.5 –Should be chosen to give good forecast. Involves little record keeping of past data. Exponential Smoothing Method

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Bina Nusantara F t = F t-1 + (A t-1 - F t-1 ) –F t = Forecast value for time t –A t-1 = Actual value at time t-1 – = Smoothing constant Need initial forecast F t-1 to start. –Could be given or use moving average. Exponential Smoothing Equation

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Bina Nusantara You want to forecast product demand using exponential smoothing with =.10. Suppose in the most recent month (month 6) the forecast was 175 and the actual demand was 180. Month 6180 Month 7 ? Month 8? Month 9? Month 10? Exponential Smoothing Example

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Bina Nusantara α F t = F t -1 + α ( A t -1 - F t -1 ) Month Actual Forecast,F t ( αααα =.10) 6180 175.00 (Given) 7? 175.00 +.10(180 - 175.00) = 175.50 8? 9? 10? 11 ? Exponential Smoothing - Month 7

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Bina Nusantara Exponential Smoothing - Month 8 α F t = F t -1 + α ( A t -1 - F t -1 ) Actual Forecast, F t ( α =.10) 180175.00 (Given) 168 175.00 +.10(180 - 175.00) = 175.50 ? 175.50 +.10(168 - 175.50) = 174.75 ? ? ? Month 6 7 8 9 10 11

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Bina Nusantara Exponential Smoothing Solution α F t = F t -1 + α ( A t -1 - F t -1 ) Actual Forecast, F t ( α =.10) 180 175.00 (Given) 168 175.00 +.10(180 - 175.00) = 175.50 159 175.50 +.10(168 - 175.50) = 174.75 ? 174.75 +.10(159 - 174.75) = 173.18 ? ? Month 6 7 8 9 10 11

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Bina Nusantara 173.18 +.10(175 - 173.18) = 173.36 Exponential Smoothing Solution α F t = F t -1 + α ( A t -1 - F t -1 ) Actual Forecast, F t ( α =.10) 180 175.00 (Given) 168 175.00 +.10(180 - 175.00) = 175.50 159 175.50 +.10(168 - 175.50) = 174.75 175 174.75 +.10(159 - 174.75) = 173.18 190 ? 173.36 +.10(190 - 173.36) = 175.02 Month 6 7 8 9 10 11

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Bina Nusantara αIncreasing α makes forecast: – More sensitive to changes. – More sensitive to recent data. α α controls emphasis on recent data. Do not forecast trend well. –Trend adjusted exponential smoothing - p. 90-93 Exponential Smoothing Methods

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Bina Nusantara F t = A t - 1 + (1- ) A t - 2 + (1- ) 2 A t - 3 +... Forecast Effects of Smoothing Constant Weights Prior Period 2 periods ago (1 - ) 3 periods ago (1 - ) 2 == = 0.10 = 0.90 10% 9% 8.1% 90%9%0.9%

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Bina Nusantara Choosing - Comparing Forecasts A good method has a small error. Choose to produce a small error. Error = Demand - Forecast Error > 0 if forecast is too low Error < 0 if forecast is too high MAD = Mean Absolute Deviation : Average of absolute values of errors. MSE = Mean Squared Error : Average of squared errors. MAPE = Mean Absolute Percentage Error : Average of absolute value of percentage errors.

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Bina Nusantara Mean Absolute Deviation (MAD) Mean Squared Error (MSE) Forecast Error Equations

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Bina Nusantara Mean Absolute Percentage Error (MAPE) Forecast Error Equations

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Bina Nusantara MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5 MSE F1 = 31/4 = 7.75 F2 = 26/4 = 6.5 MAPE F1 = 0.171 = 17.1% F2 = 0.156 = 15.6% Forecast Error Example Actual F1 F1 error 20 19 1 18 2 10 15 -5 13 -3 24 22 2 21 3 20 21 18 2 F2 F2 error

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Bina Nusantara MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5 MSE F1 = 31/4 = 7.75 F2 = 26/4 = 6.5 MAPE F1 = 0.171 = 17.1% F2 = 0.156 = 15.6% Which Forecast is Best?

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Bina Nusantara

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