orecasting can be broadly considered as a method or a technique for estimating many future aspects of a business or other operations. All forecasting methods can be divided into two broad categories: qualitative and quantitative. Many forecasting techniques use past or historical data in the form of time series. A time series is simply a set of observations measured at successive points in time or over successive periods of time and forecasts essentially provide future values of the time series on a specific variable such as sales volume. Exponential smoothing is one the time series techniques which is widely used in forecasting. Exponential smoothing gives greater weight to more recent observations and takes into account all previous observations. In ordinary terms, an exponential weighting scheme assigns the maximum weight to the most recent observation and the weights decline in a systematic manner as older and older observations are included. Weight in the exponential smoothing technique is given by exponential smoothing constant ( ?? ). Forecast values are varied with the values of this constant. So, forecast errors are also depended on ?? . Many authors used exponential smoothing method in forecasting. has shown that exponential smoothing remains appropriate under more general conditions, where the variance is allowed to grow or contract with corresponding movements in the underlying level. Taylor (2003) investigated a new damped multiplicative trend approach. Gardner (2006) No research paper has found which determine the optimal value of exponential smoothing constant. In this paper, mean square error (MSE) and mean absolute deviation (MAD) are considered to determine the forecast error and to minimize MSE and MAD, optimal values of exponential smoothing constant are determined.

Different forecasting techniques and time series analysis are described by Montgomery and Johnson (1976). From Montgomery and Johnson (1976), forecast at period t is given for exponential smoothing

About-Department of Industrial and Production Engineering Bangladesh University of Engineering and Technology Email: [email protected] F Where, ?? ?? = Forecast at period ?? ?? ???1 = Actual value of period ?? ? 1 ?? = Exponential smoothing constant From (1), for different period, it can be written as,

(2)

And so on?.. The most commonly used measures of forecast accuracy are discussed by Mentzer and Kahn (1995). In this paper, mean square error and mean absolute deviation are considered to measure forecast accuracy. Now Mean Square Error (MSE) can be determined as,

This can be written as,

Again, Mean Absolute Deviation (MAD) is given by,

This can be written as,

Now Trial and Error method is used to find minimum value of exponential smoothing constant. Putting the different values within 0 to 1 for exponential smoothing constant, MSE and MAD are calculated.

III.

The method is described by considering a problem. A company's historical sales data are given for some previous periods. Actual values of sales are given in Table 1. 1. MAD is decreased with increasing ?? up to 0.83 and after that MAD is increased. Variation of MAD with ?? is shown in Figure 2. The value of exponential smoothing constant is 0.88 and 0.83 for minimum MSE and MAD respectively. To find the optimal value of exponential smoothing constant, minimum values of MSE and MAD are selected and corresponding value of exponential smoothing constant is the optimal value for this problem.

Minimum values of MSE and MAD and corresponding value of exponential smoothing constant is given in Table 4.

An exponential smoothing technique is widely used by many organizations to predict the future events. But problems are raised to assign the value of exponential smoothing constant. In this paper, this problem is solved by determining the optimal value of exponential smoothing constant. Mean square error and mean absolute deviation are minimized to get optimal value of the constant and optimal values are 0.88 and 0.83 for minimum mean square error and mean absolute deviation respectively. In this method, any organization can compute the optimal value of exponential smoothing constant to enhance the accuracy of forecasting. This work can be extended to minimize some other forecast errors such as mean absolute percent error (MAPE), cumulative forecast error (CFE) etc.

©2011 Global Journals Inc. (US) a sale at sixth period is also forecasted. Forecasts at sixth period are 12.455 thousand and 12.068 thousands for minimum MSE and MAD respectively. is shown is Table 5. From the five period actual values, From the optimal value of ??, forecast values for different period are determined using equation ( 1