Question

A store has the following demand figures for the last four years:

Year	Demand
1	100
2	150
3	98
4	112

What is the exponential smoothing forecast for year 5? Use alpha 0.3 and a forecast for year 2 of 100.

• 108.4
• 111.1
• 103.6
• 110.5

Answer 1

Using the exponential smoothing method the formula to calculate the forecast is as follows :

Ft = F(t-1) + $\alpha$ [A(t - 1) - F(t - 1)]

Where, Ft = forecast for period t

A(t - 1) = Actual value for period previous to t

F(t - 1) = forecast for period previous to t

$\alpha$ = smoothing constant

So using the above formula with $\alpha$ = 0.3 and year 2 forecast of 100, the forecast for year 3 through 5 are

• For year 3 = 100 + 0.3(150-100) = 100 + (0.3 x 50) = 100 + 15 = 115
• For year 4 = 115 + 0.3(98-115) = 115 + [0.3(-17)] = 115+(-5.1) = 115-5.1 = 109.9
• For year 5 = 109.9 + 0.3(112-109.9) = 109.9 + (0.3x2.1) = 109.9 + 0.63 = 110.53 or rounded to 110.5

So forecast for year 5 is 110.5