Forecasting-2 Forecasting -2 Exponential Smoothing Ardavan Asef-Vaziri Based on Operations management: Stevenson Chapter 7 Operations Management: Jacobs and Chase Demand Forecasting Supply Chain Management: Chopra and Meindl in a Supply.
Download ReportTranscript Forecasting-2 Forecasting -2 Exponential Smoothing Ardavan Asef-Vaziri Based on Operations management: Stevenson Chapter 7 Operations Management: Jacobs and Chase Demand Forecasting Supply Chain Management: Chopra and Meindl in a Supply.
Forecasting-2 Forecasting -2 Exponential Smoothing Ardavan Asef-Vaziri Based on Operations management: Stevenson Chapter 7 Operations Management: Jacobs and Chase Demand Forecasting Supply Chain Management: Chopra and Meindl in a Supply Chain Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 1 Forecasting-2 Time Series Methods Moving Average Discard old records Assign same weight for recent records Assign different weights Weighted moving average Ft 1 0.4At 0.3At 1 0.2 At 2 0.1At 3 Exponential Smoothing Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 2 Forecasting-2 Exponential Smoothing Ft 1 Ft α( At Ft ) Ft 1 Ft αAt αFt Ft 1 (1 α) Ft αAt Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 3 Forecasting-2 Exponential Smoothing t At Ft 1 100 100 2 150 100 α=0.2 3 110 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. A1 F2 F3 =(1-α)F2 + α A2 F3 =0.8(100) + 0.2(150) F3 =80 + 30 = 110 F3 =(1-α)F2 + α A2 A1 F2 Ardavan Asef-Vaziri F2 & A2 F3 A1 & A2 F3 6/4/2009 Exponential Smoothing 4 Forecasting-2 Exponential Smoothing α=0.2 t At Ft 1 100 100 3 2 150 120 100 110 4 112 F4 =(1-α)F3 + α A3 F4 =0.8(110) + 0.2(120) F4 =88 + 24 = 112 F4 =(1-α)F3 + α A3 A3 & F3 F4 A1 & A2 F3 A1& A2 & A3 F4 Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 5 Forecasting-2 Example: Forecast for week 9 using a = 0.1 Week Demand 1 200 2 250 3 175 4 186 5 225 6 285 7 305 8 190 Forecast 200 F3 1 a F2 aA2 0.9 * 200 0.1* 250 205 Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 6 Forecasting-2 Week 4 Week Demand Forecast 1 200 2 250 200 3 175 205 4 186 5 225 6 285 7 305 8 190 F4 1 a F3 aA3 0.9 * 205 0.1*175 202 Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 7 Forecasting-2 Exponential Smoothing Week Demand 1 200 2 250 200 3 175 205 4 186 202 5 225 200 6 285 203 7 305 211 8 190 220 Ardavan Asef-Vaziri 6/4/2009 Forecast Exponential Smoothing 8 Forecasting-2 Two important questions How to choose a? Large a or Small a When does it work? When does it not? What is better exponential smoothing OR moving average? Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 9 Forecasting-2 The Same Example: a = 0.4 Week Demand 1 200 2 250 200 3 175 220 4 186 202 5 225 196 6 285 207 7 305 238 8 190 265 Ardavan Asef-Vaziri 6/4/2009 Forecast Exponential Smoothing 10 Forecasting-2 Comparison 350 300 250 Demand 200 alpha = 0.1 150 alpha = 0.4 100 50 0 1 2 3 4 5 6 7 8 week Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 11 Forecasting-2 Comparison As a becomes larger, the predicted values exhibit more variation, because they are more responsive to the demand in the previous period. A large a 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. Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 12 Forecasting-2 Comparison Forecast for 0.1 alpha AD Forecast for 0.4 alpha AD Week Demand 1 200 2 250 200.00 50.00 200.00 50.00 3 175 205.00 30.00 220.00 45.00 4 186 202.00 16.00 202.00 16.00 5 225 200.40 24.60 195.60 29.40 6 285 202.86 82.14 207.36 77.64 7 305 211.07 93.93 238.42 66.58 8 190 220.47 30.47 265.05 75.05 46.73 51.38 Choose the forecast with lower MAD. Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 13 Forecasting-2 Which a to choose? In general want to calculate MAD for many different values of a 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. Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 14 Forecasting-2 All Pieces of Data are Taken into Account in ES Ft = a At–1 + (1 – a) Ft–1 Ft–1 = a At–2 + (1 – a) Ft–2 Ft = aAt–1+(1–a)aAt–2+(1–a)2Ft–2 Ft–2 = a At–3 + (1 – a) Ft–3 Ft = aAt–1+(1–a)aAt–2+(1–a)2a At–3 + (1 – a) 3 Ft–3 = aAt–1+(1–a)aAt–2+(1–a)2aAt–3 +(1–a)3aAt–4 +(1–a)4aAt–5+(1–a)5aAt–6 +(1–a)6aAt–7+… A large number of data are taken into account– All data are taken into account in ES. Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 15 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 1/ a. 1n)/2 = 1/ a a = 2/(n+1) If we set a = 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. Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 16 Forecasting-2 Compute MAD & TS Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Ardavan Asef-Vaziri 6/4/2009 At 13400 14100 14700 15100 13400 16000 12700 15400 13000 16200 16100 13500 14900 15200 15200 15800 16100 16400 15300 15900 16300 15500 15800 16000 Alpha = 0.50 Ft 13912 13656 13878 14289 14695 14047 15024 13862 14631 13815 15008 15554 14527 14713 14957 15078 15439 15770 16085 15692 15796 16048 15774 15787 Dev -512 444 822 811 -1295 1953 -2324 1538 -1631 2385 1092 -2054 373 487 243 722 661 630 -785 208 504 -548 26 213 AD 512 444 822 811 1295 1953 2324 1538 1631 2385 1092 2054 373 487 243 722 661 630 785 208 504 548 26 213 MAD = 927 MAD 512 478 593 647 777 973 1166 1212 1259 1371 1346 1405 1326 1266 1198 1168 1138 1110 1093 1048 1022 1001 959 927 Sum Dev -512 -68 754 1565 271 2223 -100 1438 -193 2191 3284 1230 1603 2089 2333 3054 3715 4346 3561 3768 4272 3724 3750 3963 TS -1.000 -0.142 1.272 2.418 0.348 2.286 -0.086 1.186 -0.153 1.598 2.440 0.875 1.209 1.651 1.948 2.616 3.265 3.916 3.259 3.594 4.178 3.721 3.912 4.273 Exponential Smoothing 17 Forecasting-2 Data Table Excel Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 At 13400 14100 14700 15100 13400 16000 12700 15400 13000 16200 16100 13500 14900 15200 15200 15800 16100 16400 15300 15900 16300 15500 15800 16000 Alpha = 0.50 Ft 13912 13656 13878 14289 14695 14047 15024 13862 14631 13815 15008 15554 14527 14713 14957 15078 15439 15770 16085 15692 15796 16048 15774 15787 Dev -512 444 822 811 -1295 1953 -2324 1538 -1631 2385 1092 -2054 373 487 243 722 661 630 -785 208 504 -548 26 213 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 AD 512 444 822 811 1295 1953 2324 1538 1631 2385 1092 2054 373 487 243 722 661 630 785 208 504 548 26 213 927 1017 897 886 901 927 960 997 1036 1078 1130 Ardavan Asef-Vaziri MAD = 927 MAD 512 478 593 647 777 973 1166 1212 1259 1371 1346 1405 1326 1266 1198 1168 1138 1110 1093 1048 1022 1001 959 927 Sum Dev -512 -68 754 1565 271 2223 -100 1438 -193 2191 3284 1230 1603 2089 2333 3054 3715 4346 3561 3768 4272 3724 3750 3963 TS -1.000 -0.142 1.272 2.418 0.348 2.286 -0.086 1.186 -0.153 1.598 2.440 0.875 1.209 1.651 1.948 2.616 3.265 3.916 3.259 3.594 4.178 3.721 3.912 4.273 927 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Data, what if, Data table This is a one variable Data Table Min, conditional formatting 6/4/2009 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 927 1017 897 886 901 927 960 997 1036 1078 1130 886 Exponential Smoothing 18 Forecasting-2 Office Button Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 19 Forecasting-2 Add-Inns Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 20 Forecasting-2 Not OK, but GO, then Check Mark Solver Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 21 Forecasting-2 Data Tab/ Solver Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 22 Forecasting-2 Target Cell/Changing Cells Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 23 Forecasting-2 Optimal a Minimal MAD Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 24 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. Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 25 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) Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 26 Forecasting-2 Measures of Forecast Error Mean AbsoluteDeviation(MAD) E t # of Observations Et 100 At Mean AbsolutePercentageError(MAPE ) # of Observations Mean Squared Error(MSE) 2 E t # of Observations 1.25MAD is an estimate Standard Deviation of Error MSE is also anotherestimateStandardDeviationof Error Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 27