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عنوان فارسی مقاله:
پیش بینی ورودی مرکز تماس با استفاده از روش میانگین متحرک فصلی
عنوان انگلیسی مقاله:
Forecasting intraday call arrivals using the seasonal moving average method
سال انتشار : 2016
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بخشی از مقاله انگلیسی:
2. Univariate methods for forecasting intraday arrivals
The lack of research into time series forecasting methods for call centers first observed by Fildes and Kumar (2002), and detailed by Gans et al. (2003) and Mandelbaum (2006), has led to a recent surge in this area of research. The first empirical evaluation of univariate time series methods for call center arrivals by Taylor (2008a) evaluated several models not previously used for call center forecasting, including the double seasonal Holt-Winters exponential smoothing method and a multiplicative double seasonal ARMA model (Taylor, 2003). These methods were introduced specifically to model the double seasonal pattern inherent in intraday call arrival data1 (see Fig. 2). Since then, several advanced time series methods have been developed for modelling time series containing such features. These include numerous developments in exponential smoothing (see, for example, Taylor, 2003, 2008b, 2010, 2012; Taylor & Snyder, 2012), ARIMA modelling (see, for example, Antipov & Meade, 2002; Taylor, 2008a), regression including dynamic harmonic (Tych, Pedregal, Young, & Davies, 2002) and discount weighted regression (Taylor, 2010), singular vector decomposition (see, for example, Shen, 2009; Shen & Huang, 2005, 2008a,b), and the use of Gaussian linear mixed-effects models (Aldor-Noiman, Feigin, & Mandelbaum, 2009; Ibrahim & L'ecuyer, 2013). Despite the focus on more sophisticated methods of forecasting, the findings of Taylor (2008a) suggest that “to use more advanced methods may not be the solution”. The study found that for lead times up to about three days ahead, the double seasonal Holt-Winters and the double seasonal ARIMA methods performed well, but beyond short lead times and across all lead times simultaneously, the SMA method with weekly seasonality was best. While SMA with weekly seasonality did not produce the best accuracy in Taylor (2010), primarily because of poor performance at short lead times, it was observed to be the best performing method beyond four days ahead forecasting. Early evidence from Tandberg et al. (1995) in producing forecasts of hourly calls to a regional poison center in New Mexico also found that the SMA method performed well, outperforming Seasonal ARIMA. Further evidence outside of time series methods research was given by Ibrahim and L'Ecuyer (2013) who observed that at relatively long forecasting lead times, the SMA method outperformed a number of statistical models which included, fixed-effects, mixed-effects and bivariate mixed-effects models. It is therefore surprising that extensions of the Seasonal Moving Average method have not been considered, despite previous findings of residual autocorrelation when fitted to intraday arrivals, a clear indication that further improvements are possible (Brown et al., 2005; Taylor, 2008a). Additionally the method has not been systematically evaluated. This is remarkable given its preferred use in practice over more advanced methods which are difficult to implement, communicate to middle and top management, and which lack transparency. This study assesses the impact of the number of seasonal periods included in calculating the seasonal moving average to better understand the properties of this simple forecasting method. It also proposes a hybrid decomposition approach which in the first step models and forecasts the original series using the SMA method, and in the second step, models and forecasts the residuals of the SMA method using a linear or nonlinear model. The forecasts of the original and residual series are then combined to produce the final forecast. In estimating the nonlinear AR model we consider ANNs as they have shown promise in modelling data containing similar features of intraday and intraweek seasonality (Temraz, Salama, & Chikhani, 1997; Willis & Northcotegreen, 1983). They are flexible not requiring the prespecification of a particular model form and have been successfully employed in numerous forecasting applications (Adya & Collopy, 1998; Hamid & Iqbal, 2004; Zhang et al., 1998). They have however yielded mixed results when modelling intraday call arrivals (see, for example, Taylor & Snyder, 2012; Pacheco, Millan-Ruiz, & Velez, 2009; Millan-Ruiz, Pacheco, Hidalgo, & Velez, 2010), and selecting a single ANN can be difficult owing to the large number of factors which affecting network performance (Zhang & Berardi, 2001). Given the strengths and weaknesses in both approaches, a hybrid approach seems appealing, and may be an effective strategy in practice.
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