**Exponential Smoothing**

in the tow previous forecasting methods that have just been presented, a major issue h the need to continually carry a large amount of historical data. Never the less in man apparitions (perhaps even in most) the most recent data points tend to be more indicative of the future in comparison to those in the distant past. If this premise is valid-that the importance of data diminishes as the past becomes more distant-then exponential smoothing may be the most logical and easiest method to use. The reason this is called “exponential smoothing” is because each increment in the past is decreased by (I – 0′), as shown below:

Therefore, the exponents 0, I, 2, 3 … , and so on give this method its name. Exponential smoothing is the most commonly used of all forecasting techniques. It is an integral part of virtually all computerized forecasting programs, and is widely used for ordering inventory in retail firms, wholesale companies, and other service operations. Exponential smoothing accomplishes virtually everything that can be done with moving average forecasts. but requires significantly less data. The exponential smoothing constant alpha (a) is a value between 0 and 1. If the actual demand tends to be relatively stable over time, we would choose a relatively small value for 0′ to decrease the effects of short-term or random fluctuations, which is similar to having a moving average that involves a large number of periods. If the actual demand tends to fluctuate rapidly, we would choose a relatively large value for 0′ to keep up with these changes. This is similar to using a moving average with a small number of periods. The major reasons that exponential smoothing techniques have become so well accepted

are

I. Exponential smoothing models are surprisingly accurate.

2. Formulating an exponential smoothing model is relatively easy.

3. The user can readily understand how the model works.

4. There is very little computation required to use the model.

5. Computer storage requirements are small because of the limited use of historical data.

In the exponential smoothing method only three pieces of data are needed to forecast the future: the most recent forecast, the actual demand that occurred for that forecast period and a smoothing constant alpha . As described above this smoothing constant determines the level of smoothing and the speed of reaction to differences between forecasts and actual occurrences. The value for the constant is arbitrary and is determined by both the nature of the item being forecasted and the manager’s sense of what constitutes a good response rate. However error measuring techniques such as MAD (which is discussed later in this chapter) can be used to evaluate different values for until that value is found that minimizes the historical error. For example if a firm produced a standard item with relatively stable demand the reaction rate to differences between actual and forecast demand would tend to be small perhaps just a few percentage points. However if the firm were experiencing growth it would be desirable to have a higher reaction rate to give greater importance to recent growth experience. The more rapid the growth the higher the reaction rate should be. Sometimes users of the simple moving average switch to exponential

smoothing but like to keep the forecasts about the same as the imple moving average. In this case, a is approximated by 2(n + I) where II was the number of time periods that were used in the moving average. The equation for an exponential smoothing forecast is