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

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

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

4. 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

5. 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

6. 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 ?

7. Bina Nusantara Actual Demand for Month 4 = 3

8. 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 ?

9. 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 ?

10. 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

11. 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

12. 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 ? ? ?

13. 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

14. 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

15. 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

16. 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

17. 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

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

19. 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

20. 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

21. 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

22. 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

23. 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%

24. 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.

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

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

27. 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

28. 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?

29. Bina Nusantara