Question

The number of items sold over a four-month period are: month 1 2 3 4 sales 5100 5500 5400 5600 Calculate the forecasts for the 4th and 5th months using 3-month weighted moving average method with weights of 0.6 for the most recent month and 0.3 for the next to the most recent month. Further, suppose that the exponential smoothing constant α=0.5. Then calculate the forecasts for 3rd, 4th and 5th months, using exponential smoothing method. Under the 3-month weighted moving average method, what is the forecast for the fourth month?

Answer 1

By using 3-month weighted moving average method -

Forecasts for the 4th month = 5400

Forecasts for the 5th month = 5530

By using Exponential smoothing method -

Forecasts for 3rd month = 5300

Forecast for 4th month = 5350

Forecast for 5th month = 5475

Explanation:

To find - Calculate the forecasts for the 4th and 5th months using 3-month weighted moving average method.

Calculate the forecasts for 3rd, 4th and 5th months, using exponential smoothing method.

Proof -

Given that,

month 1 2 3 4

sales 5100 5500 5400 5600

F(4) = 0.6 A(3) + 0.3 A(2) + 0.1 A(1)

= 0.6 [ 5400] + 0.3 [ 5500] + 0.1 [ 5100]

= 3240 + 1650 + 510

= 5400

⇒forecasts for the 4th month = 5400

Now,

F(5) = 0.6 A(4) + 0.3 A(3) + 0.1 A(2)

= 0.6 [ 5600] + 0.3 [ 5400] + 0.1 [ 5500]

= 3360 + 1620 + 550

= 5530

⇒forecasts for the 5th month = 5530

Now,

Given that, the exponential smoothing constant α=0.5

Month Sales Forecast

1 5100 5100

2 5500 5100 + 0.5(5100 - 5100) = 5100

3 5400 5100 + 0.5(5500 - 5100) = 5300

4 5600 5300 + 0.5(5400 - 5300) = 5350

5 5350 + 0.5(5600 - 5350) = 5475

∴ we get

By using Exponential smoothing method -

Forecasts for 3rd month = 5300

Forecast for 4th month = 5350

Forecast for 5th month = 5475