Question

Given the following sales data:

week 1: 20

week 2: 29

week 3: 34

week 4: 21

week 5: 22

Forecast sales for week 6 using an exponential smoothing forecast with alpha = 0.4. Intialize using F(2) = [ A(1) + A(2) ] / 2.

Your Answer:

Answer 1

Here we have to first calculate the initial forecast that is the forecast for week 2(F2) = [A(1) + A(2)]/2 = (Actual sales in week 1 + actual sales in week 2)/2 = (20+29)/2 = 49/2 = 24.5

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

Ft = F(t-1) + [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

= smoothing constant

So using the above formula with =0.4 and week 2 forecast of 24.5 the forecast for week 3 through 6 are

• For week 3 = 24.5+0.4(29-24.5) = 24.5+1.8 = 26.3
• For week 4 = 26.3+0.4(34-26.3) = 26.3+3.08 = 29.38
• For week 5 = 29.38+0.4(21-29.38) = 29.38+(-3.352) = 29.38-3.352 = 26.028
• For week 6 = 26.028+0.4(22-26.028) = 26.028+(-1.6112) = 26.028-1.6112 = 24.4168

So the forecast for week 6 = 24.4168