1. Exponential Smoothing 1 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Chapter 7 Demand Forecasting in a Supply Chain Forecasting -2 Exponential Smoothing Ardavan Asef-Vaziri Based on Operations management: Stevenson Operations Management: Jacobs and Chase Supply Chain Management: Chopra and Meindl

2. Exponential Smoothing 2 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Time Series Methods  Moving Average  Discard old records  Assign same weight for recent records  Assign different weights  Weighted moving average  Exponential Smoothing

3. Exponential Smoothing 3 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Exponential Smoothing

4. Exponential Smoothing 4 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Exponential Smoothing α=0.2 t At Ft 1 100 A1  F2 2 100 Since I have no information for F1, I just enter A1 which is 100. Alternatively we may assume the average of all available data as our forecast for period 1. 150 F3 =(1-α)F2 + α A2 F3 =0.8(100) + 0.2(150) F3 =80 + 30 = 110 3 110 F2 & A2  F3 A1  F2A1 & A2  F3 F3 =(1-α)F2 + α A2

5. Exponential Smoothing 5 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Exponential Smoothing α=0.2 t At Ft 1 100 F4 =(1-α)F3 + α A3 F4 =0.8(110) + 0.2(120) F4 =88 + 24 = 112 A3 & F3  F4 A1 & A2  F3A1& A2 & A3  F4 2 150 100 3 110 4 112 120 F4 =(1-α)F3 + α A3

6. Exponential Smoothing 6 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Example: Forecast for week 9 using  = 0.1 WeekDemand Forecast 1200 2250200 3175 4186 5225 6285 7305 8190

7. Exponential Smoothing 7 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Week 4 WeekDemandForecast 1200 2250200 3175205 4186 5225 6285 7305 8190

8. Exponential Smoothing 8 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Exponential Smoothing WeekDemandForecast 1200 2250200 3175205 4186202 5225200 6285203 7305211 8190220

9. Exponential Smoothing 9 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Two important questions  How to choose  ? Large  or Small  When does it work? When does it not?  What is better exponential smoothing OR moving average?

10. Exponential Smoothing 10 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 The Same Example:  = 0.4 WeekDemandForecast 1200 2250200 3175220 4186202 5225196 6285207 7305238 8190265

11. Exponential Smoothing 11 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Comparison

12. Exponential Smoothing 12 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Comparison  As  becomes larger, the predicted values exhibit more variation, because they are more responsive to the demand in the previous period.  A large  seems to track the series better.  Value of stability  This parallels our observation regarding MA: there is a trade-off between responsiveness and smoothing out demand fluctuations.

13. Exponential Smoothing 13 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Comparison WeekDemand Forecast for 0.1 alpha AD Forecast for 0.4 alphaAD 1200 2250200.0050.00200.0050.00 3175205.0030.00220.0045.00 4186202.0016.00202.0016.00 5225200.4024.60195.6029.40 6285202.8682.14207.3677.64 7305211.0793.93238.4266.58 8190220.4730.47265.0575.05 46.73 51.38 Choose the forecast with lower MAD.

14. Exponential Smoothing 14 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Which  to choose?  In general want to calculate MAD for many different values of  and choose the one with the lowest MAD.  Same idea to determine if Exponential Smoothing or Moving Average is preferred.  Note that one advantage of exponential smoothing requires less data storage to implement.

15. Exponential Smoothing 15 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 All Pieces of Data are Taken into Account in ES F t = a A t–1 + (1 – a) F t–1 F t–1 = a A t–2 + (1 – a) F t–2 F t = aA t–1 +(1–a)aA t–2 +(1–a) 2 F t–2 F t–2 = a A t–3 + (1 – a) F t–3 F t = aA t–1 +(1–a)aA t–2 +(1–a) 2 a A t–3 + (1 – a) 3 F t–3 = aA t–1 +(1–a)aA t–2 +(1–a) 2 aA t–3 +(1–a) 3 aA t–4 +(1–a) 4 aA t–5 +(1–a) 5 aA t–6 +(1–a) 6 aA t–7 +… A large number of data are taken into account– All data are taken into account in ES.

16. Exponential Smoothing 16 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 What is better? Exponential Smoothing or Moving Average  Age of data in moving average is (1+ n)/2   Age of data in exponential smoothing is about    n)/2 = 1/    = 2/(n+1)  If we set  = 2/(n +1), then moving average and exponential smoothing are approximately equivalent.  It does not mean that the two models have the same forecasts.  The variances of the errors are identical.

17. Exponential Smoothing 17 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Compute MAD & TS

18. Exponential Smoothing 18 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Data Table Excel Data, what if, Data table Min, conditional formatting This is a one variable Data Table

19. Exponential Smoothing 19 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Office Button

20. Exponential Smoothing 20 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Add-Inns

21. Exponential Smoothing 21 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Not OK, but GO, then Check Mark Solver

22. Exponential Smoothing 22 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Data Tab/ Solver

23. Exponential Smoothing 23 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Target Cell/Changing Cells

24. Exponential Smoothing 24 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Optimal  Minimal MAD

25. Exponential Smoothing 25 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 NOTE – The following pages are not recorded Note: The following discussion – from the next page up to the end of this set of slides – are not recorded.

26. Exponential Smoothing 26 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Measures of Forecast Error; Additional Indices Error: difference between predicted value and actual value (E)  Mean Absolute Deviation (MAD)  Tracking Signal (TS)  Mean Square Error (MSE)  Mean Absolute Percentage Error (MAPE)

27. Exponential Smoothing 27 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 7-1-27 Measures of Forecast Error