Computer sales over the past 4 months have been 35, 34, 38, and 44 units.
Using a 3-month moving average, forecast sales for the next month.
Using a 3-month weighted moving average with the weights 3, 2, and 1, and with the most weight on the most recent data, forecast the next period’s sales.
Calculate the forecast using exponential smoothing with an alpha of 1 and a first period’s forecast of 35.
The fifth period’s sales were actually 46 units. Based on this exercise, which forecasting method would you use going forward? Be sure to show all of your work.
To answer these questions, we will follow the given methods and calculations step by step:
1. Three-Month Moving Average Forecast:
The three-month moving average forecast simply calculates the average of the past three months' actual sales. Here is how to calculate it:
- Month 1: (35 + 34 + 38) / 3 = 35.67
- Month 2: (34 + 38 + 44) / 3 = 38.67
The forecast for the next month will be the average of the most recent three months' actual sales, which is 38.67 units.
2. Three-Month Weighted Moving Average Forecast:
The three-month weighted moving average assigns weights to each of the past three months' actual sales values, with the most weight on the most recent value. Here is how to calculate it:
- Month 1: (35 * 1 + 34 * 2 + 38 * 3) / (1 + 2 + 3) = 36.17
- Month 2: (34 * 1 + 38 * 2 + 44 * 3) / (1 + 2 + 3) = 40.5
The forecast for the next month will be the weighted average of the most recent three months' actual sales, which is 40.5 units.
3. Exponential Smoothing Forecast:
Exponential smoothing utilizes a smoothing factor (alpha) to assign different weights to the most recent actual sales and the previous forecast. The formula for calculation is:
Forecast = alpha * (Most recent actual sales) + (1 - alpha) * (Previous forecast)
Given alpha = 1, and the first period's forecast = 35, we can calculate the forecast for the fifth period as follows:
- Fifth period forecast = 1 * 46 + (1 - 1) * 35 = 46
The forecast for the fifth period using exponential smoothing is 46 units.
Based on this exercise, to decide which forecasting method to use going forward, we should compare the forecasted values with the actual sales. Let's compare:
- Three-Month Moving Average Forecast for the fifth period: 38.67 (actual: 46)
- Three-Month Weighted Moving Average Forecast for the fifth period: 40.5 (actual: 46)
- Exponential Smoothing Forecast for the fifth period: 46 (actual: 46)
Comparing the forecasted values with the actual sales, we can see that the Exponential Smoothing Forecast provides the most accurate forecast for the fifth period, as it matches the actual value exactly. Thus, based on this exercise, the Exponential Smoothing method would be the preferred forecasting method going forward.