Question

Ben Swanson, owner and manager of Swanson’s Department Store, has decided to use statistical forecasting to get a better handle on the demand for his major products. However, Ben now needs to decide which forecasting method is most appropriate for each category of product. One category is major household appliances, such as washing machines, which have a relatively stable sales level. Monthly sales of washing machines last year are shown below.

January 23 February 24 March 22

April 28 May 22 June 27

July 20 August 26 September 21

October 29 November 23 December 28

T (b) Use the last-value method retrospectively to determine what the forecasts would have been for the last 11 months of last year. What is MAD?

Answer 1

The last-value method uses the previous month's sales as the forecast for the next month. To calculate MAD, one must find the average of the absolute differences between the forecasted and actual sales figures over the 11 months.

Last-Value Method and MAD Calculation

The last-value method of forecasting is a technique where the actual sales of the last period are used as the forecast for the next period.

This method is simple and may be suitable for stable products such as major household appliances.

To retrospectively apply the last-value method for the 11 months of last year, we would use the sales figure from the previous month as the forecast for the current month.

For example, the forecast for February would be the actual sales figure from January, and so on.

To calculate the Mean Absolute Deviation (MAD), we take the absolute differences between the actual figures and the forecasted figures, then find the average of those absolute differences over the given period.

1. For February, the forecast would have been 23 (from January's actual sales), and the actual was 24, resulting in an absolute difference of 1.
2. Repeat this process for each month, using the previous month's actual sales as the forecast for the next month.
3. Add up all the absolute differences and divide by the number of forecasts to calculate MAD.

To calculate the MAD for Swanson's Department Store:

• For February's forecast (using January's actual): |24 - 23| = 1
• For March (using February's actual): |22 - 24| = 2
• For April (using March's actual): |28 - 22| = 6
• ... and so on for the remaining months.
• After calculating each month's absolute difference, add them and divide by 11 for the MAD.