# Exponential Smoothing Methods

In these methods, the weight assigned to a previous period’s demand decreases exponentially as that data gets older. Thus, recent demand data receives a higher weight than does older demand data.

When to use exponential smoothing:

Exponential smoothing methods are particularly attractive for production and operations applications that involve forecasting for a large number of items. These methods work best under the following conditions:

1) The forecasting horizon is relatively short; for example, a daily, weekly, or monthly demand needs to be forecasted
2) There is little outside information available about cause and effect relationships between the demand of an item and independent factors that influence it.
3) Small effort in forecasting is desired. Effort is measured by both a method’s ease of application and by the computational requirements (time, storage) needed to implement it
4) Updating of the forecast as new data become available is easy and can be accomplished by simply inputting the new data.
5) It is desired that the forecast is adjusted for randomness (fluctuation in demand are smoothed) and tracks trends and seasonality.

Basic Exponential Smoothing Model:

The simplex exponential smoothing model is applicable when there is no trend or seasonality component in the data. Thus, only the horizontal component of demand is present and, because of randomness, the demand fluctuates around an average demand which we will call the base. If the base is constant from period to period, then all fluctuations in demand must be due to randomness. In reality, fluctuations in demand are caused by both changes in the base and random noise. The key objective in exponential smoothing models is to estimate the base and use that estimates for forecasting.

In the basic exponential smoothing model, the base for the current period St is estimated by modifying the previous base by adding or subtracting to it a fraction α (alpha) of the difference between the actual current demand Dt and the previous base St-1. The estimate of the new base is then

New base = Previous base + α(New demand – Previous base).

Or, stated in symbols,

St = St – 1 + α(Dt – St-1) ——————-Eq (1)

The smoothing constant, α, is between 0 and 1, with commonly used values of 0.01 to 0.30.

Another interpretation of Eq (1) is that new base is estimated by modifying the previous base, St-1, by correcting for the observed error in period t. We call (Dt–St-1) an observed error for period t because Dt is the actual demand for period t and St-1is our forecast for period t.

Eq (1) can be rearranged as follows:

New base = α(New demand) + (1 – α) (Previous base)

St = αDt + ( 1 – α) St-1———————-Eq (2) Thus, the new base is estimated by simply taking a weighted average of the new demand Dt and the previous St-1

To Illustrate the application of this model, suppose α =0.10, SJan = 50 units, and DFeb = 60 units. The new base for February is computed by using Eq (2)

SFeb = 0.1DFeb+ 0.95SJan
= 0.1(60) + 0.9 (50)
= 51 units

So far, we have seen how we can estimate a new base from the information about new demand and the previous base once α has been specified. We now need to make forecast for the next (or, more generally, for some specified future period). In the basic exponential smoothing model, since trend and seasonality components are not included in the model, direct extrapolation of St, to infer forecast is justified. Therefore, the forecasts for any future period is taken directly as the computed value of St. Table shows the computations and forecasts for the first several months of demand data for a product. It is useful to split the process of forecasting using exponential smoothing models in two steps.

Step 1: estimate the new St using Eq (2)
Step 2: Forecast made in period t for T periods ahead, Ft,T in the basic exponential smoothing model is simply St

Ft,T = St

Usually T = 1; that is, the forecast is made for only one period ahead.