1. Session 10a

2. Decision Models -- Prof. Juran2 Overview Forecasting Methods Exponential Smoothing –Simple –Trend (Holt’s Method) –Seasonality (Winters’ Method) Regression –Trend –Seasonality –Lagged Variables

3. Decision Models -- Prof. Juran3 Forecasting 1.Analysis of Historical Data Time Series (Extrapolation) Regression (Causal) 2.Projecting Historical Patterns into the Future 3.Measurement of Forecast Quality

4. Decision Models -- Prof. Juran4 Measuring Forecasting Errors Mean Absolute Error Mean Absolute Percent Error Root Mean Squared Error R-square

5. Decision Models -- Prof. Juran5 Mean Absolute Error

6. Decision Models -- Prof. Juran6 Mean Absolute Percent Error MAPE  *%100 n Y n i i i   1  Or, alternatively  *%100 n Y n i i i   1 ˆ 

7. Decision Models -- Prof. Juran7 Root Mean Squared Error

8. Decision Models -- Prof. Juran8 R -Square

9. Decision Models -- Prof. Juran9 Trend Analysis Part of the variation in Y is believed to be “explained” by the passage of time Several convenient models available in an Excel chart

10. Decision Models -- Prof. Juran10 Example: Revenues at GM

11. Decision Models -- Prof. Juran11 Right-click on the data series Superimpose a trend line on the graph:

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17. Decision Models -- Prof. Juran17 You can also show moving-average trend lines, although showing the equation and R -square are no longer options:

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20. Decision Models -- Prof. Juran20 Simple Exponential Smoothing

21. Decision Models -- Prof. Juran21 Why is it called “exponential”?

22. Decision Models -- Prof. Juran22 Example: GM Revenue

23. Decision Models -- Prof. Juran23 In this spreadsheet model, the forecasts appear in column G. Note that our model assumes that there is no trend. We use a default alpha of 0.10.

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25. Decision Models -- Prof. Juran25 We use Solver to minimize RMSE by manipulating alpha. After optimizing, we see that alpha is 0.350 (instead of 0.10). This makes an improvement in RMSE, from 4691 to 3653.

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27. Decision Models -- Prof. Juran27 Exponential Smoothing with Trend: Holt’s Method Weighted Current Trend Weighted Current Observation Weighted Current Level

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29. Decision Models -- Prof. Juran29 Holt’s model with optimized smoothing constants. This model is slightly better than the simple model ( RMSE drops from 3653 to 3568).

30. Decision Models -- Prof. Juran30 Exponential Smoothing with Seasonality: Winters’ Method

31. Decision Models -- Prof. Juran31 Weighted Current Seasonal Factor Weighted Seasonal Factor from Last Year

32. Decision Models -- Prof. Juran32 Winters’ model with optimized smoothing constants. This model is better than the simple model and the Holt’s model (as measured by RMSE ).

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34. Decision Models -- Prof. Juran34 Forecasting with Regression

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37. Decision Models -- Prof. Juran37 The most reasonable statistic for comparison is probably RMSE for smoothing models vs. standard error for regression models, as is reported here: The regression models are superior most of the time (6 out of 10 revenue models and 7 out of 10 EPS models). Which Method is Better?

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40. Decision Models -- Prof. Juran40 Time series characterized by relatively consistent trends and seasonality favor the regression model. If the trend and seasonality are not stable over time, then Winters’ method does a better job of responding to their changing patterns.

41. Decision Models -- Prof. Juran41 Lagged Variables Only applicable in a causal model Effects of independent variables might not be felt immediately Used for advertising’s effect on sales

42. Decision Models -- Prof. Juran42 Example: Motel Chain

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49. Decision Models -- Prof. Juran49 Here are measures of model fit for the non-regression models: The regression model has a standard error of only 213, which is much better than any of the other models.

50. Decision Models -- Prof. Juran50 Summary Forecasting Methods Exponential Smoothing –Simple –Trend (Holt’s Method) –Seasonality (Winters’ Method) Regression –Trend –Seasonality –Lagged Variables