پیش بینی ورودی مرکز تماس با استفاده از روش میانگین متحرک فصلی  Forecasting intraday call arrivals using the seasonal moving average method

1. Introduction Accurate and robust forecasts of inbound calls volumes as a measure of service demand is of primary importance to managing call centers effectively and efficiently, be it for scheduling agents efficiently in 15‐ or 30-min intervals during the day or within a week, or determining the quantity, and timing of hiring and training (Aksin, Armony, & Mehrotra, 2007; Gans, Koole, & Mandelbaum, 2003). Call centers employ millions of individuals around the world accounting for N70% of all customer-business interactions (Brown et al., 2005). With 60–80% of a call center’s operating budget comprising of human resource costs (Aksin et al., 2007) the accurate forecasting of inbound calls, even those corresponding to a single product or service such as a medical emergency hotline, can have substantial socio-economic implications. plications. Time series forecasting research has recently focused on developing rather sophisticated methods for forecasting inbound call arrivals. However there has been overwhelming evidence (Ibrahim & L’ecuyer, 2013; Tandberg, Easom, & Qualls, 1995; Taylor, 2008a, 2010) that such methods are outperformed by the simple Seasonal Moving Average (SMA) method particularly at longer forecast horizons where capacity planning decisions are made. Despite its attractiveness, the performance of the SMA method has not been systematically evaluated, nor have extensions been investigated. This study evaluates the performance of the SMA method systematically varying the number of seasonal periods included in the average to assess its impact on forecasting accuracy across different data frequencies of 5 min, half-hourly and hourly recorded call arrivals. The SMA method is compared to ‘simple’ and advanced benchmarks including seasonal ARIMA and the double seasonal Holt-Winters exponential smoothing method of Taylor (2003) forecasting 5 min to two weeks ahead. A new hybrid forecasting method is proposed which combines the strengths of the simple SMA method, capable of robustly capturing the intraday and intraweek seasonal pattern in intraday call arrivals, and the data driven nonlinear capabilities of ANNs in modelling potential nonlinear and nonparametric features of the residuals (Zhang, Patuwo, & Hu, 1998). Such an approach would allow call center managers the ability to observe both the short‐ and long-term trends in call arrivals in a single forecast, and facilitate easier use of judgmental adjustments in that it separates out the seasonal weekly and daily fluctuations from the rest of the series highlighting its main components. Both linear autoregressive (AR) and nonlinear ANNs are evaluated as in practice it is often difficult to determine whether a series is generated from a linear or nonlinear process, and/or whether any one method will produce better forecasts than the other. This is especially true for the case of the three Banks considered in this study, whose service demand are likely affected by both structural and behavioral changes in response to financial and economic stimuli. Data on inbound service demand is obtained from call centers of a US bank (Weinberg, Brown, & Stroud, 2007.), a UK bank (Taylor, 2008a), and a bank in Israeli (Mandelbaum, Sakov, & Zeltyn, 2000). These represent 5 min, half-hourly, and hourly observations of call arrivals respectively and facilitate evaluation of performance across increasing sampling frequency. These three series have a signifi- cant impact on the cost of operations of these call centers, representing a major aspect of inbound call traffic and affecting capacity planning and scheduling decisions. It is hypothesized that by using ANNs, complex autocorrelation structures in the data may be modelled more accurately. The rest of the paper is organized as follows. In Section 2, a review of the literature on univariate forecasting for intraday arrivals is performed. This is followed in Section 3, by a discussion of the Seasonal Moving Average method and development of the proposed hybrid approach. Section 4 provides a description of the intraday call arrival datasets followed by Section 5 which describes the experimental design and benchmarks method. Section 6 presents the results and findings, while Section 7 discusses briefly the implications of practice. Finally, Section 8 presents a summary and concluding remarks.