Call Center Arrivals Research Articles

Forecasting call center arrivals using temporal memory networks and gradient boosting algorithm

Forecasting call center arrivals using temporal memory networks and gradient boosting algorithm

Comparing deep and shallow neural networks in forecasting call center arrivals

AbstractForecasting volumes of incoming calls is the first step of the workforce planning process in call centers and represents a prominent issue from both research and industry perspectives. We investigate the application of Neural Networks to predict incoming calls 24 hours ahead. In particular, a Machine Learning deep architecture known as Echo State Network, is compared with a completely different rolling horizon shallow Neural Network strategy, in which the lack of recurrent connections is compensated by a careful input selection. The comparison, carried out on three different real world datasets, reveals better predictive performance for the shallow approach. The latter appears also more robust and less demanding, reducing the inference time by a factor of 2.5 to 4.5 compared to Echo State Networks.

Beyond the beaten paths of forecasting call center arrivals: on the use of dynamic harmonic regression with predictor variables

Modern call centers require precise forecasts of call and e-mail arrivals to optimize staffing decisions and to ensure high customer satisfaction through short waiting times and the availability of qualified agents. In the dynamic environment of multi-channel customer contact, organizational decision-makers often rely on robust but simplistic forecasting methods. Although forecasting literature indicates that incorporating additional information into time series predictions adds value by improving model performance, extant research in the call center domain barely considers the potential of sophisticated multivariate models. Hence, with an extended dynamic harmonic regression (DHR) approach, this study proposes a new reliable method for call center arrivals’ forecasting that is able to capture the dynamics of a time series and to include contextual information in form of predictor variables. The study evaluates the predictive potential of the approach on the call and e-mail arrival series of a leading German online retailer comprising 174 weeks of data. The analysis involves time series cross-validation with an expanding rolling window over 52 weeks and comprises established time series as well as machine learning models as benchmarks. The multivariate DHR model outperforms the compared models with regard to forecast accuracy for a broad spectrum of lead times. This study further gives contextual insights into the selection and optimal implementation of marketing-relevant predictor variables such as catalog releases, mail as well as postal reminders, or billing cycles.

Call me maybe: Methods and practical implementation of artificial intelligence in call center arrivals’ forecasting

Machine learning (ML) techniques within the artificial intelligence (AI) paradigm are radically transforming organizational decision-making and businesses’ interactions with external stakeholders. However, in time series forecasting for call center management, there is a substantial gap between the potential and actual use of AI-driven methods. This study investigates the capabilities of ML models for intra-daily call center arrivals’ forecasting with respect to prediction accuracy and practicability. We analyze two datasets of an online retailer’s customer support and complaints queue comprising half-hourly observations over 174.5 weeks. We compare practically relevant ML approaches and the most commonly used time series models via cross-validation with an expanding rolling window. Our findings indicate that the random forest (RF) algorithm yields the best prediction performances. Based on these results, a methodological walk-through example of a comprehensive model selection process based on cross-validation with an expanding rolling window is provided to encourage implementation in individual practical settings.

Data Analytics Driven Controlling: Bridging Statistical Modeling and Managerial Intuition

Strategic planning in a corporate environment is often based on experience and intuition, although internal data is usually available and can be a valuable source of information. Predicting merger & acquisition (M&A) events is at the heart of strategic management, yet not sufficiently motivated by data analytics driven controlling. One of the main obstacles in using e.g. count data time series for M&A seems to be the fact that the intensity of M&A is time varying at least in certain business sectors, e.g. communications. We propose a new automatic procedure to bridge this obstacle using novel statistical methods. The proposed approach allows for a selection of adaptive windows in count data sets by detecting significant changes in the intensity of events. We test the efficacy of the proposed method on a simulated count data set and put it into action on various M&A data sets. It is robust to aberrant behavior and generates accurate forecasts for the evaluated business sectors. It also provides guidance for an a-priori selection of fixed windows for forecasting. Furthermore, it can be generalized to other business lines, e.g. for managing supply chains, sales forecasts, or call center arrivals, thus giving managers new ways for incorporating statistical modeling in strategic planning decisions.

Call Center Arrivals: When to Jointly Forecast Multiple Streams?

We consider call centers that have multiple (potentially inter‐dependent) demand arrival streams. Workforce management of such labor intensive service systems starts with forecasting future arrival demand. We investigate the question of whether and when to jointly forecast future arrivals of the multiple streams. We first develop a general statistical model to simultaneously forecast multi‐stream arrival rates. The model takes into account three types of inter‐stream dependence. We then show with analytical and simulation studies how the forecasting benefits of the multi‐stream forecasting model vary by the type, direction, and strength of inter‐stream dependence. In particular, we find that it is beneficial to simultaneously forecast multi‐stream arrivals (instead of separately forecasting each stream), when there exists inter‐stream lag dependence among daily arrival rates. Empirical studies, using two real call center datasets further demonstrate our findings, and provide operational insights into how one chooses forecasting models for multi‐stream arrivals.

Modeling and forecasting call center arrivals: A literature survey and a case study

The effective management of call centers is a challenging task, mainly because managers consistently face considerable uncertainty. One important source of this uncertainty is the call arrival rate, which is typically time-varying, stochastic, dependent across time periods and call types, and often affected by external events. The accurate modeling and forecasting of future call arrival volumes is a complicated issue which is critical for making important operational decisions, such as staffing and scheduling, in the call center. In this paper, we review the existing literature on modeling and forecasting call arrivals. We also discuss the key issues for the building of good statistical arrival models. In addition, we evaluate the forecasting accuracy of selected models in an empirical study with real-life call center data. We conclude with a summary of possible future research directions in this important field.

Forecasting Call Center Arrivals: Fixed-Effects, Mixed-Effects, and Bivariate Models

We consider different statistical models for the call arrival process in telephone call centers. We evaluate the forecasting accuracy of those models by describing results from an empirical study analyzing real-life call center data. We test forecasting accuracy using different lead times, ranging from weeks to hours in advance, to mimic real-life challenges faced by call center managers. The models considered are (i) a benchmark fixed-effects model that does not exploit any dependence structures in the data; (ii) a mixed-effects model that takes into account both interday (day-to-day) and intraday (within-day) correlations; and (iii) two new bivariate mixed-effects models, for the joint distribution of the arrival counts to two separate queues, that exploit correlations between different call types. Our study shows the importance of accounting for different correlation structures in the data.

Density Forecasting of Intraday Call Center Arrivals Using Models Based on Exponential Smoothing

A key input to the call center staffing process is a forecast for the number of calls arriving. Density forecasts of arrival rates are needed for analytical call center models, which assume Poisson arrivals with a stochastic arrival rate. Density forecasts of call volumes can be used in simulation models and are also important for the analysis of outsourcing contracts. A forecasting method, which has previously shown strong potential, is Holt–Winters exponential smoothing adapted for modeling the intraday and intraweek cycles in intraday data. To enable density forecasting of the arrival volume and rate, we develop a Poisson count model, with gamma distributed arrival rate, which captures the essential features of this exponential smoothing method. The apparent stationary level in our data leads us to develop versions of the new model for series with stationary levels. We evaluate forecast accuracy up to two weeks ahead using data from three organizations. We find that the stationary level models improve prediction beyond approximately two days ahead, and that these models perform well in comparison with sophisticated benchmarks. This is confirmed by the results of a call center simulation model, which demonstrates the use of arrival rate density forecasting to support staffing decisions. This paper was accepted by Yossi Aviv, operations management.

Modeling latent sources in call center arrival data

In this paper, we discuss issues that arise in the analysis of call center arrivals that are mostly linked to individual ads. More specifically, we consider the case where there is no complete linkage between the calls and the advertisements that led to the calls. The ability to model and infer such latent call arrival sources is important from a marketing as well as an operations point of view since knowledge of the linkage improves forecasting performance of the model. We pose this as a missing data problem and develop a data augmentation algorithm for the Bayesian analysis. We implement the proposed algorithm to simulated and actual call center arrival data and discuss its performance.

Interday Forecasting and Intraday Updating of Call Center Arrivals

Accurate forecasting of call arrivals is critical for staffing and scheduling of a telephone call center. We develop methods for interday and dynamic intraday forecasting of incoming call volumes. Our approach is to treat the intraday call volume profiles as a high-dimensional vector time series. We propose first to reduce the dimensionality by singular value decomposition of the matrix of historical intraday profiles and then to apply time series and regression techniques. Our approach takes into account both interday (or day-to-day) dynamics and intraday (or within-day) patterns of call arrivals. Distributional forecasts are also developed. The proposed methods are data driven, appear to be robust against model assumptions in our simulation studies, and are shown to be very competitive in out-of-sample forecast comparisons using two real data sets. Our methods are computationally fast; it is therefore feasible to use them for real-time dynamic forecasting.

A Comparison of Univariate Time Series Methods for Forecasting Intraday Arrivals at a Call Center

Predictions of call center arrivals are a key input to staff scheduling models. It is, therefore, surprising that simplistic forecasting methods dominate practice, and that the research literature on forecasting arrivals is so small. In this paper, we evaluate univariate time series methods for forecasting intraday arrivals for lead times from one half-hour ahead to two weeks ahead. We analyze five series of intraday arrivals for call centers operated by a retail bank in the United Kingdom. A notable feature of these series is the presence of both an intraweek and an intraday seasonal cycle. The methods considered include seasonal autoregressive integrated moving average (ARIMA) modeling; periodic autoregressive modeling; an extension of Holt-Winters exponential smoothing for the case of two seasonal cycles; robust exponential smoothing based on exponentially weighted least absolute deviations regression; and dynamic harmonic regression, which is a form of unobserved component state-space modeling. Our results indicate strong potential for the use of seasonal ARIMA modeling and the extension of Holt-Winters for predicting up to about two to three days ahead and that, for longer lead times, a simplistic historical average is difficult to beat. We find a similar ranking of methods for call center data from an Israeli bank.

Interday Forecasting and Intraday Updating of Call Center Arrivals

Interday Forecasting and Intraday Updating of Call Center Arrivals

Modeling Daily Arrivals to a Telephone Call Center

We develop stochastic models of time-dependent arrivals, with focus on the application to call centers. Our models reproduce three essential features of call center arrivals observed in recent empirical studies: a variance larger than the mean for the number of arrivals in any given time interval, a time-varying arrival intensity over the course of a day, and nonzero correlation between the arrival counts in different periods within the same day. For each of the new models, we characterize the joint distribution of the vector of arrival counts, with particular focus on characterizing how the new models are more flexible than standard or previously proposed models. We report empirical results from a study on arrival data from a real-life call center, including the essential features of the arrival process, the goodness of fit of the estimated models, and the sensitivity of various simulated performance measures of the call center to the choice of arrival process model.