# Question

Quality Bikes is a wholesale firm that specializes in the distribution of bicycles. In the past, the company has maintained ample inventories of bicycles to enable filling orders immediately, so informal rough forecasts of demand were sufficient to make the decisions on when to replenish inventory. However, the company’s new president, Marcia Salgo, intends to run a tighter ship. Scientific inventory management is to be used to reduce inventory levels and minimize total variable inventory costs. At the same time, Marcia has ordered the development of a computerized forecasting system based on statistical forecasting that considers seasonal effects. The system is to generate three sets of forecasts—one based on the moving-average method, a second based on the exponential smoothing method, and a third based on exponential smoothing with trend. The average of these three forecasts for each month is to be used for inventory management purposes.

The following table gives the available data on monthly sales of 10-speed bicycles over the past three years. The last column also shows monthly sales this year, which is the first year of operation of the new forecasting system.

(a) Determine the seasonal factors for the 12 months based on past sales.

(b) After considering seasonal effects, apply the moving-average method based on the most recent three months to forecast monthly sales this year.

(c) After considering seasonal effects, apply the exponential smoothing method to forecast monthly sales this year. Use an initial estimate of 420 and a smoothing constant of α = 0.2.

(d) After considering seasonal effects, apply exponential smoothing with trend to forecast monthly sales this year. Use initial estimates of 420 for the expected value and 0 for the trend, along with smoothing constants of α = 0.2 and α = 0.2.

(e) Compare both the MAD and MSE values obtained in parts (b), (c), and (d).

(f) Calculate the combined forecast for each month by averaging the forecasts for that month obtained in parts (b), (c), and (d). Then calculate the MAD for these combined forecasts.

(g) Based on these results, what is your recommendation for how to do the forecasts next year?

The following table gives the available data on monthly sales of 10-speed bicycles over the past three years. The last column also shows monthly sales this year, which is the first year of operation of the new forecasting system.

(a) Determine the seasonal factors for the 12 months based on past sales.

(b) After considering seasonal effects, apply the moving-average method based on the most recent three months to forecast monthly sales this year.

(c) After considering seasonal effects, apply the exponential smoothing method to forecast monthly sales this year. Use an initial estimate of 420 and a smoothing constant of α = 0.2.

(d) After considering seasonal effects, apply exponential smoothing with trend to forecast monthly sales this year. Use initial estimates of 420 for the expected value and 0 for the trend, along with smoothing constants of α = 0.2 and α = 0.2.

(e) Compare both the MAD and MSE values obtained in parts (b), (c), and (d).

(f) Calculate the combined forecast for each month by averaging the forecasts for that month obtained in parts (b), (c), and (d). Then calculate the MAD for these combined forecasts.

(g) Based on these results, what is your recommendation for how to do the forecasts next year?

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