# 10.8 Scenarios and Exercises

## 10.8.1 Choice of Appropriate Forecasting Techniques

Figure 10.8.1.1 shows historical demand curves for four different products. What forecasting technique for each product do you propose to apply to forecast future demand?

Fig. 10.8.1.1      Historical demand curves for four products.

Solution:

• Product 1: demand with linear trend —> linear regression
• Product2: constant demand without trend —> moving average forecasting or first-order exponential smoothing
• Product 3: seasonal fluctuations with trend —> linear regression or second-order exponential smoothing with seasonality
• Product 4: constant demand with seasonal fluctuation —> moving average forecasting, or first-order exponential smoothing, with seasonality

## 10.8.2 Moving Average Forecasting Technique

The person in your firm responsible for forecasting has been absent for three months, so your supervisor asks you to forecast the demand of the most important product. The information you get is a table (see Figure 10.8.2.1) showing the historical data on the demand for the product (January to October) and the forecast for the period January to July based on the moving average forecasting technique.

Fig. 10.8.2.1      Demand and forecast with moving average forecasting technique.

a. Forecast the demand just as your colleague does. Therefore, you have to calculate the parameter n from the historical forecast data.

Solution:   n = 4

b. Calculate the forecast for August, September, and October as well as for the following month, November.

Solution:  Forecast August = (207+199+175+111) / 4 = 173; forecast September: 145; forecast October: 125; forecast November: 129.

##### c. Compute the standard deviation Sigma of the forecast from January to October and decide if the applied technique fits this product.

Solution: Sigma = 53.87 and variation coefficient = 53.87 / 152.6 » 0.35. A variation coefficient of 0.35 stands for a relatively low quality of the forecast. Therefore, the applied technique is not appropriate for this product. Try a value other than n = 4, or with additional seasonal index.

## 10.8.3 First-Order Exponential Smoothing

When you report to your supervisor that the moving average forecasting technique is not suitable for the product, he remembers that your colleague in charge of forecasting had been working on introducing the first-order exponential smoothing technique for this product. Therefore, your supervisor gives you the information in Figure 10.8.3.1.

Fig. 10.8.3.1      Demand and forecast using first-order exponential smoothing technique.

The Figure shows the demand for the product (January to October) and the forecast using the first-order exponential smoothing technique with α = 0.3 of the product (January to July). To evaluate your supervisor’s suggestion, you execute the following steps:

a. Compute the forecast for August, September, and October and for the following month, November.

Solution:    Forecast August = 0.3*111+0.7*179 = 159; forecast September: 140; forecast October: 134; forecast November: 151.

b. Calculate the mean absolute deviation (MAD) for November assuming MAD(Jan) = 18 and the smoothing parameter α.

c. In the preceding exercise, could you have obtained a result comparable to the one for the parameter α calculated above by changing n, that is, the number of observed values?

Solution:   Yes, by choosing a value of n = (2 – 0.3)/0.3 = 5.67 (see the formula in Figure 10.2.3.1).

d. Decide whether the chosen first-order exponential smoothing technique with parameter α calculated above is appropriate for this product.

Solution:  Since the demand fluctuates, it would be better to increase α. More­over, the first-order exponential smoothing technique does not fit this demand curve well. Therefore, it is worth considering another fore­casting technique, e.g., with short-term seasonality.

e. What can you say in general about the choice of α depending on the product life cycle?

Solution:    At the beginning and the end of the product (market) life cycle, α should be relatively high, e.g., α = 0.5. For a well-established product, the a often chosen α is around 0.1.

## 10.8.4 Moving Average Forecast versus First-Order Exponential Smoothing Forecast

Figure 10.2.2.6 showed the effect of different values of the smoothing con­stant α . Figure 10.2.3.1 shows the necessary relationship between the num­ber of observed values and the smoothing constant α. You can view the comparison using the interactive exercise below.

Comparing Moving Average Forecast versus First-Order Exponential Smoothing Forecast
This exercise demonstrates the different types of demand forecast.
The first graph calculates the forecast using first-order exponential smoothing while the second is calculated by a method of your choice. Play with the different parameters and use the calculate-button to see the according changes.
The initial setting marks the 11th and 12th month of the current yeat as unknown (="-"). You may also change these parameters.

In the red section at the top of the Web page, you can choose different values for the smoothing constant α . In the lower, green section you can choose either a different value for the smoothing constant a for comparison with the red curve or choose the number of values for the moving average forecast and compare the results of the technique with exponential smoothing (the red curve). Clicking on the “calculate” icon executes your input choice.