## 2 Literature Review  
Efficient management of operations in manufacturing industries and services is important [19; 20; 21; 22; 23] and requires an accurate prediction of customer demand as this directly influences strategic, tactical and operational decisions. More specifically, a higher level of forecasting accuracy aids the manufacturer in formulating the appropriate production plan, restoring balance, scheduling the production line and maintaining proper inventory level as well as satisfying customer demand on time [24]. In the domain of forecasting, the time series is a set of values for one or more variables presented through consecutive time increments [25] and used in engineering, science, economics, finance, meteorology, telecommunication, etc. The hours, days and months are contemplated as the periods of the historical observation and/or the time series [26]. The forecasting methods featuring these time series are mainly categorized as regression, smoothing and decomposition techniques [27], among which, the exponential smoothing approaches are found to be the most widely used due to its robustness [9; 28], simplicity [9] and the small number of required variables [2; 9]. These favourable characteristics justifying the ease of implementation and cost effectiveness of this class of forecasting method [2; 29; 30] have attracted numerous researchers to dig continuously for further improvement [31]. Among these exponential smoothing approaches, the three most commonly adopted and addressed in literature can be named as simple exponential smoothing [10]; double exponential smoothing and/or [PERSON]'s method [11]; and triple exponential smoothing and/or the Holt-Winters method [5]. Simple exponential smoothing is renowned for its simplicity and ease of use, whereas [PERSON]'s method gives better results for the time series having trend components. Despite having superior performance for such cases, [PERSON]'s method loses its executive while dealing with seasonal time series [32]. However, in the presence of both the seasonality and the trend in time series, the Holt-Winters method shows better performance with minimal computational effort [24]. Two forms of Holt-Winters method (additive and multiplicative) are found to be the most widely adopted approaches in literature for seasonal demand forecasting, among which the additive forecasting method is observed to be suitable apparently for a situation where the seasonal peak adopts a consistent pattern throughout the demand horizon, and the latter fits well for a dynamic increase or decrease of the seasonal peak. However, during the implementation of these techniques, difficulties are encountered in determining the initial values of the time-series parameters (i.e., level, growth rate and seasonal index), quantifying the optimal values of smoothing constants, as well as using the intricate recursive computational processes [24; 31; 33]. As a consequence, and similar to the other time-series forecasting techniques, several approaches and modifications have also been proposed to improve the accuracy of the conventional Holt-Winters method by featuring the relevant issues. For instance, [PERSON] and [PERSON] in 2001 [34] proposed a modified Holt-Winters model for forecasting UK air passengers, where the values of the smoothing constants were determined by minimizing the mean square error (_MSE_). In the research of [PERSON] and [PERSON] in 2011 [35], the _MSE_ is also used as a performance measure and is a prerequisite for determining the appropriate trio of the smoothing constants. On the other hand, to estimate the initial values of the level, growth rate and seasonality, [PERSON] and [PERSON] in 1991 [17] considered these three parameters as the autonomous variables, and determined their initial values by minimizing one-step-ahead forecasting errors. [PERSON] et al. in 2006 [24] also computed the initial values of these three time-series parameters by minimizing the forecast error.