Calculating Forecast Sales using Exponential Smoothing

Exponential smoothing is a popular technique used in forecasting, particularly in time series analysis. It gives more weight to recent data points to predict future values. The formula for simple exponential smoothing is:

\( \text{New Forecast} = \text{Old Forecast} + \alpha \times (\text{Actual Sales} - \text{Old Forecast}) \)

Where:

• New Forecast is the forecast for the next period.
• Old Forecast is the forecast for the current period.
• Actual Sales is the actual sales value for the current period.
• \(\alpha\) (alpha) is the smoothing constant, a value between 0 and 1.

In this problem, we are given the following information for December 2002:

• Forecast sales for December 2002: 25
• Actual sales for December 2002: 20
• Exponential smoothing constant (\(\alpha\)): 0.2

We need to calculate the forecast sale for January 2003 using this information. Here, December 2002 is the "current period", and January 2003 is the "next period".

Using the exponential smoothing formula:

\( \text{Forecast for Jan 2003} = \text{Forecast for Dec 2002} + \alpha \times (\text{Actual Sales in Dec 2002} - \text{Forecast for Dec 2002}) \)

Let's substitute the given values into the formula:

\( \text{Forecast for Jan 2003} = 25 + 0.2 \times (20 - 25) \)

Now, perform the calculation step-by-step:

\( \text{Forecast for Jan 2003} = 25 + 0.2 \times (-5) \)

\( \text{Forecast for Jan 2003} = 25 - 1 \)

\( \text{Forecast for Jan 2003} = 24 \)

Therefore, the forecast sale for January 2003 is 24.

Let's summarise the calculation in a table:

The calculation shows that the forecast for January 2003 is 24.