مدل سازی و پیش بینی مرکز تماس های ورودی: بررسی ادبیات و یک مطالعه موردی ورودی   Modeling and forecasting call center arrivals: A literature survey and a case study

1. Introduction The call center services industry is large and important, with more than 2.7 million agents working in the United States and 2.1 million agents working in Europe, the Middle East, and Africa (Akşin, Armony, & Mehrotra, 2007). Managing a call center efficiently is a challenging task, because managers have to make staffing and scheduling decisions in order to balance staffing costs and service quality, which always conflict, in the presence of uncertainty as to arriving demand. Most staffing or scheduling plans start with the forecasting of customer call arrivals, which are highly stochastic. Accurate forecasts of call arrivals are key for the achievement of optimal operationalefficiency, since under-forecasting leads to under-staffing and therefore long customer waits, while over-forecasting results in money being wasted on over-staffing. The customer arrivals process is nontrivial. This process can be modeled as a Poisson arrival process, and has been shown to possess several features (Akşin et al., 2007; Cez¸ ik & L’Ecuyer, 2008; Gans, Koole, & Mandelbaum, 2003; Garnett, Mandelbaum, & Reiman, 2002; Wallace & Whitt, 2005). One of the most important of these features is the fact that the arrival rate is time-varying, which adds to the complexity of the forecasting process. Call arrival rates may exhibit intraday, weekly, monthly, and yearly seasonalities. While a time-inhomogeneous Poisson arrival process can easily capture time dependence in call arrival data, it often fails to capture other characteristics. For one thing, call center arrivals typically exhibit a significant dispersion relative to the Poisson distribution. Thus, a doubly stochastic Poisson arrival process may be more appropriate, e.g., see Aldor-Noiman, Feigin, and Mandelbaum (2009);Avramidis, Deslauriers, and L’Ecuyer (2004); Ding and Koole (2015) and Ibrahim and L’Ecuyer (2013). For another, call center arrivals also exhibit different types of dependencies, including intraday (within-day), interday, and inter-type dependence, e.g., see Aldor-Noiman et al. (2009); Avramidis et al. (2004); Channouf and L’Ecuyer (2012); Shen and Huang (2008b); Tanir and Booth (1999) and Whitt (1999b). A reasonable forecasting model needs to account appropriately for some or all of the types of dependencies that exist in real data. In the presence of intraday and interday dependence in call arrival rates, standard time series models may be applied for forecasting call arrivals, for example autoregressive integrated moving average (ARIMA) models and exponential smoothing (Hyndman, Koehler, Ord, & Snyder, 2008). In addition, some recent papers have proposed fixed-effects models (Ibrahim & L’Ecuyer, 2013; Shen & Huang, 2008b; Taylor, 2008; Weinberg, Brown, & Stroud, 2007) and mixed-effects models (Aldor-Noiman et al., 2009; Ibrahim & L’Ecuyer, 2013) to account for the within-day dependence, interday dependence, and inter-type dependence of call arrivals. Dimension reduction (Shen & Huang, 2005, 2008a,b) and Bayesian techniques (Aktekin & Soyer, 2011; Soyer&Tarimcilar, 2008;Weinberg et al., 2007) have also been adopted in the literature.