A ski repair shop at a resort in colorado sells replacement poles each season. T

Question

A ski repair shop at a resort in colorado sells replacement poles each season. The shop needs to develop a forecast of next season's sales so that they can place an order for poles with their supplier well in advance of the beginning of the season. Sales data for the past five years are shown below. Compare the forecasts given by the following models.

Year 1 1 2 3 4 5

Sales (units) 350 375 355 375 390

Develop forecasts using: a. 5 year moving average

b. a weighted moving average model with weights of 0.2, 0.2, 0.1, 0.3, and 0.3 for years 1 through 5 respectively.

c. an exponential smoothing model with year 1 forecast of 380 and alpa=0.3

Explanation / Answer

a) five year moving average = Average of previous five years = (350+375+355+375+390)/5 = 369

b) Weighted moving average = 350*.2+375*.2+355*.1+375*.3+390*.3 = 410

c) Exponential smoothing forecast is calculated by following formula

Ft = Ft-1 + alpha *(At-1 - Ft-1) , where Ft is the forecast in period t, and At is the actual data in period t

Forecast for year 2 = 380+0.3*(350-380) = 371

Forecast for year 3 = 371+0.3*(375-371) = 372.2

Forecast for year 4 = 372+0.3*(355-372) = 367

Forecast for year 5 = 367+0.3*(375-367) = 369

Forecast for year 6 = 369+0.3*(390-369) = 376

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