Question

Daily attendance at a movie theatre for the past six Fridays is given in Table 2. Table 2 Week Attendance 1 1200 2 1350 3 1400 4 1425 5 1475 6 1490 The forecast for week 5 is 1450 and α =0.20 a. Using exponential smoothing, calculate the forecast for week 7. [8 marks]

Answer 1

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Ft+1 = Ft + α(At – Ft)

Where,

Ft+1 is the forecast for period (t+1)

Ft is the forecast for period t

At is the actual for period t

α = 0.2

F5 = 1450

Using F5 and A5, we can calculate F6.

F5 = 1450

A5 = 1475

α = 0.2

Hence,

F6 = F5 + α(A5 – F5) = 1450 + 0.2*(1475-1450) = 1450 + 0.2*(25) = 1450 + 5 = 1455

Similarly, using F6 and A6, we can determine the forecast for week 7.

So,

F7 = F6 + α(A6 – F6)

F6 = 1455

A6 = 1490

α = 0.2

F7 = 1455 + 0.2*(1490-1455) = 1455 + 0.2*(35) = 1455 + 7 = 1462.

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