1 f 10 47505956453 2 f 10 47x01 50x015 59x025 56x05

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1) F 10 = (47+50+59+56)/4=53 2) F 10 = (47x0.1) +(50x0.15) +(59x0.25) +(56x0.5) = 55 3) F 10 = 60+0.2(56-60) =59.2
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b) If the forecasts for period 1 to period 9 were 30, 35, 42, 42, 40, 50, 53, 61, 59, respectively, determine the bias, MAD and tracking signal. How would you improve the forecasting accuracy in this situation? Month 1 2 3 4 5 6 7 8 9 10 A i 26 32 39 40 38 47 50 59 56 F i 30 35 42 42 40 50 53 61 59 e i -4 -3 -3 -2 -2 -3 -3 -2 -3 Bias= (Σ ei)/9= (-25)/9= -2.7 MAD= (ΣІeiІ)/9 = 25/9= +2.7 TS= (-2.7)/2.7= -1 Any Suggestion?
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Exercise #3 Assume that you are forecasting a weekly demand for Item A using the simple exponential smoothing method. You are now at the end of week 9. The forecasting for week 9 is 1008 units, and the actual demand in week 9 is 1024 units. The smooth constant α is 0.2. Update Bias t 2 MAD t = BIAS t = BIAS t-1 +1/N (E t – E t-N ) MAD t = MAD t-1 +1/N (|E t | -| E t-N |) a) Develop a forecast for week 10. F 9 =1008, A 9 =1024;, 2=0.2 F 10 =F 9 +2(A 9 –F 9 ) = 1008+0.2(1024-1008)=1011
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At the end of week 10, you learned that the actual demand in week 10 was only 631 units. You use the last 4 periods in computing Bias and MAD, and the forecasting error in week 6 was -90 units. The Bias and MAD calculated in week 9 were -50 and 60 units respectively. Compute the Tracking Signal for week 10 Known: A 10 =631, BIAS 9 = -50, MAD 9 =60 F 10 =1011, E 6 =-90 E 10 = (A 10 – F 10 )=(631-1011)=-380 BIAS 10 = BIAS 9 + ¼ (E 10 – E 6 ) = -50+ ¼ (-380+90) = -50 -72.50= -122.50 MAD 10 = MAD 9 + ¼ (|E 10 |-|E 6 |)= 60+ ¼ (380-90) 60 + 72.50= 132.50 TS 10 = BIAS 10 / MAD 10 = (-122.50)/132.50= -0.924 Forecasting is very poor
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Excerscise#4 Assume that you are forecasting a weekly demand for Item B using the simple exponential smoothing method. You are now at the end of week 9 is 501 units, and the forecasting for week 9 is 501 units, and the actual demand in week 9 is 506 units. The smooth constant α is 0.3 a) Develop a forecast for week 10. F 9 = 501, A 9 = 506, 2=0.3 F 10 = F 9 +2(A 9 –F 9 )=501+0.3(506-501)=502.50
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b) At the end of week 10, you learned that the actual demand in week 10 was only 515. You use the last 3 periods in computing Bias and MAD, and the forecasting error in week 7 was +10 units. The Bias and MAD calculated in week 9 were 2 and 18. Compute the Tracking Signal for week 10. Known: A 10 =515, F 10 =502.5, E 7 =+10 MAD 9 = 18, BIAS 9 = 2 E 10 =(A 10 –F 10 ) = 515 - 502.50 =12.5 BIAS 10 = BIAS 9 1/3(E 10 – E 7 ) = 2+0.83 = 2.83 MAD 10 = MAD 9 +1/3 (|E 10 |- |E 7 |) =18+1/3 (12.5-10) =18.83 TS 10 = 2.83/18.83 = 0.15 (Forecasting is “Ok”)
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Forecast Error Measurements Forecast error is the difference between the forecast and the actual demand 1. Cumulative sum of forecast errors (CFE) 2. Average forecast error equals (Bias=CFE/n) 3. Mean squared error (MSE) 4. Standard deviation (MAD) 5. Mean absolute deviation (MAD) 6. Mean absolute percent error MAPE) 7. Tracking signal = CFE / MAD Criteria for evaluating Forecasting Models Minimize Bias Minimize MAD or MSE Meet managerial expectations of changes Minimize the forecast error last period Use holdout set (data from more recent periods) as a final test Techniques for Improving Forecasting: Combine forecasts Focus forecasting Research indicates that: Simple techniques often perform as well or better than sophisticated procedures There is no one best forecasting technique for all products and/or services
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Elements of Time Series Analysis
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