2. 1 By: Prof. Y. Peter Chiu 9 / 1 / 2012 9 / 1 / 2012 Chapter 2 -A Forecasting

3. 2 §. F1: Introduction (1) “ My concern is with the future since I plan to spend the rest of my life there ” Charles F. Kettering (2) Forecasting is the process of predicting the future. (3) All business planning is based to some extent on a forecast

4. 3 (4) Most use of forecasting in 2 functional areas : (a) Marketing (b) Production In some cases the forecasts prepared by marketing may not meet the needs of production. (5) Can all events be accurately forecasted ? ~ NO ~ §. F1: Introduction

5. 4 (7) Demand is likely to be random in most circumstances, Can forecasting methods provide any value ? In most cases, the answer is “YES” (6) In POM, we are primarily interested in forecasting “product demand” §. F1: Introduction

6. 5 (8) Forecast Horizons in Operation Planning :(see Fig.2-1)  Short Term: ~ day-to-day planning or weeks  Intermediate Term: ~ weeks or months  Long Term: ~ months or years, ~ overall firm’s manufacturing strategy ~ capacity needs §. F1: Introduction

7. 6 §. F2: Characteristics of Forecasts (1) They are usually WRONG (2) A good forecast is more than a single number (3) Aggregate forecasts are more accurate

8. 7 (4) The longer the forecast horizon, the less accurate the forecast will be (5) Forecasts should not be used to the exclusion of known information §. F2: Characteristics of Forecasts

9. 8 §. F3: Subjective Forecasting Methods Methods (1) Sales force composites (2) Customer surveys (3) Jury of executive opinion (4) The Delphi method

10. 9 §. F4: Objective Forecasting Methods Time series (1) Time series : only past data, a “naive methods”  In time series analysis we attempt to isolate the patterns that arise most often, including  Trend ~ linear or nonlinear  Seasonality  Cycles ~ varies in length or magnitude  Randomness

11. 10 Fig.2-2 p.60

12. 11 (2) Causal models (2) Causal models : using other related data  is used to predict economic phenomena, e.g. GNP, GDP Causal models : Y= f (X 1, X 2,…, X n ) Phenomenon Variables we believe We wish to forecast to be related to Y Example: Y=α 0 +α 1 x 1 +α 2 x 2 +…+α n x n Econometric models Y ~ linear (X i )

13. 12 §. F4.1: Class Problems Discussion Chapter 2 : ( # 1, 2, 4, 6, 8, 9 ) p.59-60 Preparation Time : 15 ~ 20 minutes Discussion : 10 ~ 15 minutes Discussion : 10 ~ 15 minutes

14. 13 Notation Conventions : D 1, D 2, …, D t, as the observed values of demand periods 1, 2,…t, ● Time series methods use the past values to predict the future values, for most methods we can write a 0, a 1,…are weights where may be 1, 2, 3,… For one-step-ahead forecasts. i.e. ： forecast made in period t for period

15. 14 §. F5: Measures of Forecast Error (1) Mean Absolute Deviation ~ MAD (2) Mean Squared Error ~ MSE (3) Mean Absolute Percentage Error ~ MAPE

16. 15 §. F6: MAD (mean absolute deviation) [ 6.1] e i : errors over n periods. When forecast errors are Normally distributed, as is generally assumed, an estimate of the standard deviation of the forecast error,  e  1.25(MAD) §. F7: MSE (mean squared error) [ 7.1]

17. 16 §. F8: MAPE ( mean absolute percentage error ) [8.1] where for one-step-ahead forecasts

18. 17 Example 2.1 Example 2.1 p.62 Artel, a manufacturer of SRAMs (static random access memories), has production plants in Austin, Texas, and Sacramento, California. The managers of these plants are asked to forecast production yields (measured in percent) one week ahead for their plants. Based on six weekly forecasts, the firm’s management wishes to determine which manager is more successful at predicting his plant’s yields. The results of their predictions and actual yield rates are given in the following table. ◇

19. 18 Example 2.1 / solution ◇

20. 19 §. F 8.1 : Class Problems Discussion Chapter 2 : ( # 12, 13 ) Chapter 2 : ( # 12, 13 ) pp.63-64 Preparation Time : 25 ~ 35 minutes Discussion : 15 ~ 20 minutes Discussion : 15 ~ 20 minutes

21. 20 §. F9: Forecasting Methods for stationary time series (1) Moving average (1) Moving average of order N F t = (1/N) (D t-1 + D t-2 +.. + D t-N ) [ 9.1] (2) Exponential Smoothing F t =  D t-1 + (1 -  ) F t-1 [9.2a] or F t = F t-1 -  ( F t-1 - D t-1 ) [9.2b]

22. 21 Example 2.2 p. 64 QuarterEng.MA(3)MA(6) Failures 1 200 2 250 3 175 4 186 208 5 225 204 6 285 195 7 305 232 220 8 190 272 238 §. F10: MOVING AVERAGE MA(N) §. F10: MOVING AVERAGE MA(N) ： N-Period moving average A B A B ◇

23. 22 (A) one-step-ahead: (B) multiple-step-ahead: (C) [10.1] Example 2.2 / solution ◇

24. 23 Example 10.2: t=4 N=3 ∴ t+1=5 (D) MA lags behind the trend. [See Fig.2-4]

25. 24 Fig.2-4 p.66

26. 25 §. F11: Class Problems Discussion Chapter 2 : ( 16,17,18,19, 21) p.67 Preparation Time : 25 ~ 35 minutes Discussion : 15 ~ 20 minutes Discussion : 15 ~ 20 minutes

27. 26 §. F12: Exponential Smoothing New Forecast =  (current demand) + (1-  ) (last Forecast) F t =  D t-1 + (1-  ) (F t-1 ) [12.1] = F t-1 -  (F t-1 - D t-1 ) = F t-1 -  ． e t- 1 [12.2] 0 ≦  ≦ 1 the forecast in any period (t) is the forecast in period (t-1) minus some fraction of the observed forecast error in period (t-1)  

28. 27 [12.3] where a 0 =  ; a 1 =  (1 -  ) ; a 2 =  (1 -  ) 2 ; … ∴ a 0 > a 1 > a 2 > …, a i =  (1-  ) i  §. F12: Exponential Smoothing ∵ F t -1 =  D t-2 + (1-  ) F t-2 F t =  D t-1 + (1-  ) F t-1 =  D t-1 +  (1-  ) D t-2 + (1-  ) 2 F t-2 ∵ F t -2 =  D t-3 + (1-  ) F t-3 F t =  D t-1 +  (1-  ) D t-2 +  (1-  ) 2 D t-3 + (1-  ) 3 F t-3

29. 28 From  F t =  D t-1 + (1 -  ) F t-1 if  is large ~ variation form period to period if  is small ~ more stable In production application, stable forecasts are very desirable normally set  = 0.1 or 0.2 ( p.69 11-12 lines ) §. F12: Exponential Smoothing

30. 29 Example 2.3 Example 2.3 p.69 (F 2 ) (F 3 ) (F 4 ) ◇ Using [12.1] ∴ F 2 =  D t-1 + (1-  ) F t-1 = (0.1) (200) + (0.9) (200) =200 F 3 =  D t-1 + (1-  ) F t-1 = (0.1) D 2 + (0.9) F 2 = (0.1) (250) + (0.9) (200) = 205 F 4 = (0.1) D 3 + (0.9) F 3 = (0.1) (175) + (0.9) (205) = 202 The forecast are quite “STABLE”. See Fig.4 * INITIAL Value. Says=240. Then what-? F 2 = 236

31. 30 Fig.2-6 p.70

32. 31 §. F13: MA(3) v.s. ES(0.1) Example 13.1 (A) why N=3 for MA(3) why α=0.1 for ES(0.1) IF NOT N=3 or α≠0.1 … How to compare them? MAD=57.6 MSE=4215.6 MAD=49.2 MSE=3458.4

33. 32 (B) AVERAGE “AGE” OF DATA [13.1] → to have the same distribution of forecast errors. eg. α=0.1 N=19 α=0.5 N=3

34. 33 §. F14: Moving average v.s. exponential smoothing (1) stationary demand  constant +  (2) a single parameter, i.e. MA ~ N ES~  (3) lag behind a trend (4)  = 2 / (N+1) MA  ES in terms of the same level of accuracy (A) Similarities:

35. 34 (1) ES is a weighted average of all past data; MA ~ only the last N periods of data, outlier is washed out after N periods (advantage) (2) Using MA must save all N past data points; ES ~ needs to save only the last forecast F t-1 & D t-1 (advantage) (B) Difference:

36. 35 §. F15 : Class Problems Discussion Chapter 2 : ( # ) Chapter 2 : ( # 22, 24 ) p.73 2-27 ( 2-25 (a)(b) ; 2-27 ) Preparation Time : 20 ~ 25 minutes Discussion : 10 ~ 15 minutes

37. 36 THE END THE END