forecasting, Holt-Winters method, Optimization


Exponential smoothing methods are very commonly used for forecasting demand because they are simple, fast and inexpensive. The Holt-Winters (HW) methods estimate three smoothing parameters, associated with level, trend and seasonal factors. The seasonal variation can be of either an additive or multiplicative form. The multiplicative version is used more widely and on average works better than the additive, but if a data series contains some values equal to zero, the multiplicative HW method may not be used. In this paper we propose an improved additive HW method and we treat the initial values for the level, trend and seasonal components as well as three smoothing constants as decision variables. Through our results we demonstrate that a considerable reduction in forecast error (mean square error) can be achieved. The presented new method is applied to the case of overnight stays of tourists in Republic of Slovenia and comparisons with other methods are made on this case study data.