Reconsider Prob. 20.7-12. The economy is beginning to boom so the management of Transcontinental Airlines is predicting that the number of people flying will steadily increase this year over the relatively flat (seasonally adjusted) level of last year. Since the forecasting methods considered in Prob. 20.7-12 are relatively slow in adjusting to such a trend, consideration is being given to switching to exponential smoothing with trend. Subsequently, as the year goes on, management’s prediction proves to be true. The following table shows the average number of the passengers under consideration in each month of the new year.
(a) Repeat part (a) of Prob. 20.7-12 for the two years of data.
(b) After considering seasonal effects, apply exponential smoothing with trend to just the new year. Use initial estimates of 80 for the expected value and 2 for the trend, along with smoothing constants of α = 0.2 and ß = 0.2. Compare MAD for this method to the MAD values obtained in part (a).
(c) Repeat part (b) when exponential smoothing with trend is begun at the beginning of the first year and then applied to both years, just like the other forecasting methods in part (a). Use the same initial estimates and smoothing constants except change the initial estimate of trend to 0.
(d) Based on these results, which forecasting method would you recommend that Transcontinental Airlines use hereafter?
Transcontinental Airlines maintains a computerized forecasting system to forecast the number of customers in each fare class who will fly on each flight in order to allocate the available reservations to fare classes properly. For example, consider economy-class customers flying in midweek on the noon flight from New York to Los Angeles. The following table shows the average number of such passengers during each month of the year just completed. The table also shows the seasonal factor that has been assigned to each month based on historical data.
(a) After considering seasonal effects, compare the MAD values for the last-value method, the averaging method, the movingaverage method (based on the most recent three months), and the exponential smoothing method (with an initial estimate of 80 and a smoothing constant of α = 0.2) when they are applied retrospectively to the past year.
(b) Use the forecasting method with the smallest MAD value to forecast the average number of these passengers flying in January of the new year.
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