4. Tyrell Garden Supply is a manufacturer of outdoor gardening equipment and sto

Question

4. Tyrell Garden Supply is a manufacturer of outdoor gardening equipment and storage devices. Tyrell Garden Supply’s storage shed sales for the past year is given in the table below: Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Shed Sales 10 12 13 16 19 23 26 30 28 18 16 14 a. What are the forecasts for January (next year), using a two-period and three-period moving average? [10 points] b. Compute MAPE for the two- and three-period moving average models and compare your results. What is the best number of periods for the moving average model based on MAPE? [10 points] c. Find the best single exponential smoothing model by evaluating the MSE from 0.1 to 0.9, in increments of 0.1. [10 points]

Explanation / Answer

a. Forecast for January using a two period moving average = (sales of november+december)/2 = (16+14)/2 = 15

Forecast for January using a three period moving average = (sales of october+november+december)/3 = (18+16+14)/3 = 16

b. MAPE = [100*sum of absolute value of deviations/actual]/n

MAPE for 2 period moving average:

Thus MAPE = 248.71/10 = 24.87

MAPE for 3 period moving average:

Thus MAPE = 303.13/9 = 33.68

As MAPE is lower in case of 2 period moving average the better number is 2 period.

c. MSE = sum of (forecast errors)^2/n

exponential smoothing forecast formula: forecast = last period's forecast+alpha*(last period's actual demand - last period's forecast)

The forcast calculation for alpha = 0.1 is shown below alongwith MSE: (note that forecast for January has been taken as its actual)

Thus MSE = 808.59/12 = 67.38. Similarly MSE for other alphas are computed in the above manner. The result is:

As MSE is lowest at 16.30 when alpha is 0.90, the best exponential smoothing model is when alpha is 0.9

Month Sales 2 month moving average 2 month moving average forecast Absolute deviation 100*(absolute deviation/actual) January 10.00 February 12.00 11.00 March 13.00 12.50 11.00 2.00 15.38 April 16.00 14.50 12.50 3.50 21.88 May 19.00 17.50 14.50 4.50 23.68 June 23.00 21.00 17.50 5.50 23.91 July 26.00 24.50 21.00 5.00 19.23 August 30.00 28.00 24.50 5.50 18.33 September 28.00 29.00 28.00 0.00 0.00 October 18.00 23.00 29.00 11.00 61.11 November 16.00 17.00 23.00 7.00 43.75 December 14.00 15.00 17.00 3.00 21.43 Total 248.71

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