A dry cleaner uses exponential smoothing to forecast equipment usage at its main

Question

A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage was forecasted to be 51 percent of capacity; actual usage was 52 percent of capacity. A smoothing constant of .15 is used. a. Prepare a forecast for September. (Round your final answer to 2 decimal places.)

Forecast for September___________ percent of capacity

b. Assuming actual September usage of 58 percent, prepare a forecast for October usage. (Round your answer to 2 decimal places.)

Forecast for October ________ percent of capacity

Explanation / Answer

Forecast for period t can be expressed as per following formula :

Ft = alpha x At-1 + ( 1 – alpha) x Ft-1 = 0.15 x At-1 + 0.85 x Ft-1

Where,

Ft, Ft-1 = Forecasts for period t and t-1 respectively

At-1 = Actual usage for period t-1

Alpha = smoothing constant = 0.15

Answer to question a :

Following data are provided :

At-1 = Actual usage for August = 52 percent

Ft-1 = Forecast for period August = 51 percent

Therefore ,

Ft ( Forecast for period September )

= 0.15 x 52 + 0.85 x 51

= 7.8 + 43.35

= 51.15

Forecast for September = 51.15 percent of capacity

Answer to question b :

At-1 = Actual September usage = 58 percent

Ft-1 = Forecast for September = 51.15 percent

Forecast for October ( Ft )

= 0.15 x 58 + 0.85 x 51.15

= 8.7 + 43.4775

= 52.1775 ( 52.18 % rounded to 2 decimal places )

Forecast for October = 52.18 percent of capacity

Forecast for September = 51.15 percent of capacity

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