Reconsider Prob. 27.7-11. For each of the forecasting methods specified in parts (b), (c), and (d), use the corresponding procedure in the forecasting area of your IOR Tutorial to obtain the requested forecasts. After examining the accompanying graph that plots both the demand data and forecasts, write a one-sentence description for each method of whether its plot of forecasts tends to lie below or above or at about the same level as the demands being forecasted. Then use these conclusions to select one of the methods to recommend using hereafter.
(a) Note how the sales level is shifting significantly from month to month—first trending upward and then dipping down before resuming an upward trend. Assuming that similar patterns would continue in the future, evaluate how well you feel each of the five forecasting methods introduced in Secs. 27.4 and 27.6 would perform in forecasting future sales.
(b) Apply the last-value method, the averaging method, and the moving-average method (with n = 3) retrospectively to last year’s sales and compare their MAD values. Then compare their MSE values.
(c) Using an initial estimate of 120, apply the exponential smoothing method retrospectively to last year’s sales with α = 0.1, 0.2, 0.3, 0.4, and 0.5. Compare both MAD and MSE for these five values of the smoothing constant α.
(d) Using initial estimates of 120 for the expected value and 10 for the trend, apply exponential smoothing with trend retrospectively to last year’s sales. Use all combinations of the smoothing constants where α = 0.1 or 0.3 or 0.5 and β = 0.1 or 0.3 or 0.5. Compare both MAD and MSE for these nine combinations.
(e) Which one of the above forecasting methods would you recommend that management use? Using this method, what is the forecast of total sales for January of the New Year?

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