The sales of a product during the last four years were 840, 860, 850, 870 units. The forecast for the fourth year was 855. If the forecast for the fifth year, using simple exponential smoothening, is equal to the forecast using the three period moving average, what will be the value of exponential smoothening constant?

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BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

The given sales data for the last four years are: 840, 860, 850, and 870 units.

The three-period moving average is given by:

\( F_5 = \frac{A_2 + A_3 + A_4}{3} \)

\( F_5 = \frac{860 + 850 + 870}{3} \)

\( F_5 = \frac{2580}{3} = 860 \)

The simple exponential smoothing equation is:

\( F_5 = \alpha A_4 + (1 - \alpha) F_4 \)

Where:

A₄ = 870 (Actual sales in Year 4)

F₄ = 855 (Forecast for Year 4)

F₅ = 860 (Forecast for Year 5 using both methods)

Calculation:

Substituting values in the equation:

\( 860 = \alpha (870) + (1 - \alpha)(855) \)

Expanding:

\( 860 = 870\alpha + 855 - 855\alpha \)

\( 860 - 855 = (870 - 855) \alpha \)

\( 5 = 15\alpha \)

\( \alpha = \frac{5}{15} = \frac{1}{3} \)