Question

Jim's department at a local department store has tracked the sales of a product over the last ten weeks. Forecast demand using exponential smoothing with an alpha of 0.4, and an initial forecast of 28.0 for period.

Calculate the MAD. Calculate the tracking signal. What do you recommend?

Period Demand
1 24
2 23
3 26
4 36
5 26
6 30
7 32
8 26
9 25
10 28

Answer 1

The question covers the use of exponential smoothing for demand forecasting and examines the concept of price elasticity of demand for pricing decisions, as well as income elasticity to characterize types of goods.

Step-by-step explanation:

The student's question involves the process of predicting the demand using exponential smoothing with a smoothing factor (alpha) of 0.4 and computing the Mean Absolute Deviation (MAD) and the tracking signal. Since the actual demand values over ten weeks and the initial forecast are given, the student can apply the formula for exponential smoothing to update the forecast for each period. The MAD can then be calculated as the average absolute error over all available periods, and the tracking signal is the cumulative forecast errors divided by the MAD to check if the forecast is within acceptable control limits. If the tracking signal indicates the forecast is not accurate, adjustments to the model or the smoothing factor may be necessary.

The price elasticity of demand is important in making pricing decisions. An elasticity of 1.4 suggests that the price should be lowered to increase revenue, while an elasticity of 0.6 indicates that the price could be raised. An elasticity of 1 implies a unitary elasticity where changing the price won't significantly affect the total revenue.

Furthermore, income elasticity helps determine if a good is normal or inferior. A negative income elasticity, as seen with the bread consumption example, indicates that bread is an inferior good because as income rises consumption decreases.

Answer 2

To forecast the demand using exponential smoothing with an alpha of 0.4, start with the initial forecast of 28.0 for period 1. Calculate the MAD and Tracking Signal to evaluate the accuracy of the forecast and make recommendations.

Step-by-step explanation:

To forecast the demand using exponential smoothing with an alpha of 0.4, we start with the initial forecast of 28.0 for period 1. The formula for exponential smoothing is:

Forecast for period t = Alpha * Demand for period t + (1 - Alpha) * Forecast for period t-1

1. For period 2, the forecast would be 0.4 * 24 + (1 - 0.4) * 28 = 23.6
2. For period 3, the forecast would be 0.4 * 26 + (1 - 0.4) * 23.6 = 24.96
3. For period 4, the forecast would be 0.4 * 36 + (1 - 0.4) * 24.96 = 28.776
4. Continuing this process, we can calculate the forecasts for all ten periods.

The Mean Absolute Deviation (MAD) can be calculated by finding the absolute difference between the forecasted demand and the actual demand for each period, summing up the differences, and dividing by the number of periods. The Tracking Signal can be calculated by dividing the cumulative error by the standard deviation of the forecast errors. Based on the MAD and Tracking Signal, recommendations can be made regarding the accuracy of the forecast and any adjustments that may be needed.