00 Bias 860 MAD 1500 MAPD 008 There is really no way to determine if this is an

00 bias 860 mad 1500 mapd 008 there is really no way

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Cumulative error 86.00 Bias 8.60 MAD 15.00 MAPD 0.08 There is really no way to determine if this is an accurate forecast method unless it is com- pared with some other method. 12-22. See Problem 12-21 solution for tracking signal values. The forecast appears to be biased low (i.e., actual demand exceeds the forecast).
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12-23. 239.38; There does not seem to be any high or low bias in the forecast. 12-24. Year Error Cumula- tive Error Running MAD Tracking Signal 1 2 250 250 250.00 1.00 3 –300 –50 275.00 –0.18 4 –524.4 –574.4 358.13 –1.60 5 –154.8 –729.4 307.30 –2.37 6 –523.34 –1,252.54 350.51 –3.57 7 –908.52 –2,161.06 443.51 –4.87 8 –360.91 –2,521.97 431.71 –5.84 The control chart suggests the forecast is not performing accurately and is consistently bi- ased high (i.e., the actual demand is consistently lower than the forecast).
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12-25. a. Month Deman d Foreca s t Error D F Run- n i n g MAD Cumula- tive Error Tracking Signal March 120 April 110 120.0 –10.00 10.00 10.00 –10.0 –1.00 May 150 116.0 34.00 34.00 22.00 24.0 1.09 June 130 129.6 0.40 0.40 14.80 24.4 1.65 July 160 129.7 30.30 30.30 18.67 54.7 2.93 August 165 141.8 23.20 23.20 19.58 77.9 3.98 Septem- b er 140 151.1 –11.10 11.10 18.17 66.8 3.67 October 155 146.7 8.30 8.30 16.76 75.1 4.48 Novem- b er 150.0 75.10 117.30 Bias 10.73 MAD 16.76 MAPD 0.1038 Cumulative error 75.10 b. Month Demand 3-Month Moving Average Error D F March 120 April 110 May 150 June 130 126.67 3.33 3.33 July 160 130.00 30.00 30.00 Month Demand 3-Month Moving Average Error D F August 165 146.67 18.33 18.33 Septem- ber 140 151.67 –11.67 11.67 October 155 155.00 0.00 0.00 November 153.33 39.99 63.33
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Bias 8.00 MAD 12.67 MAPD 0.08 MSE 276.64 Cumulative error 39.99 The 3-month moving average seems to provide a better forecast. c. The tracking signal moves beyond the 3 MAD control limit for July and continues in- creasing indicating the forecast is consistently biased low. 12-26. The 3-month moving average forecast appears to be more accurate. Month Demand Forecast t t D F Month Demand Forecast t t D F January 9 9.00 August 11 9.27 1.73 Febru- a r y 7 9.00 2.00 September 12 9.62 2.38 March 10 8.60 1.40 October 10 10.09 0.09 April 8 8.88 0.88 November 14 10.07 3.92 May 7 8.70 1.70 December 16 10.86 5.14 June 12 8.36 3.64 January 11.88 July 10 9.09 0.91 Moving Average Forecast (Prob. 12-1a) Exponentially Smoothed (Prob. 12-20) Mad 1.89 2.16 12.27. MAD 1.79 Cumulative error 12.36 According to these measures, the forecast appears to be fairly accurate. Year Deman d ForecastError Running MAD Cumula- tive Error Tracking Signal 1 16.8 16.8 0 2 14.1 16.8 2.7 2.70 2.7 1.00 3 15.3 15.7 0.4 1.55 3.1 2.00 4 12.7 15.5 2.8 1.97 5.9 3.00 5 11.9 14.4 2.5 2.10 8.4 4.00 6 12.3 13.4 1.1 1.90 9.5 5.00 7 11.5 12.9 1.4 1.82 10.9 6.00 8 10.4 12.4 1.6 1.79 12.5 7.00
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The tracking signal goes outside of the control limits beginning in year 4, indicating a forecast that is biased high. Linear trend model: Year Demand Forecast 1 16.80 15.87 2 14.10 15.10 3 15.30 14.33 4 12.70 13.56 5 11.90 12.79 6 12.30 12.02 7 11.50 11.24 8 10.80 10.47 9 9.70 MAD 0.68 The linear trend line forecast appears to be more accurate for MAD. 12-28. 49.95 0.428 , y x where occupancy y rate and wins. x Forecast if the Red Jays win 85 games: 49.95 .428 85 86.3 occupancy rate. yes; .8626 r 12-29. a. .51 .403 , y x where sales y and permits. x Forecast if 25 permits are filed: .51 .403 25 10.57 b. The correlation coefficient is .914 indicating a strong causal relationship.
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