Call Center Arrivals: When to Jointly Forecast Multiple Streams?

Ye, Han; Luedtke, James; Shen, Haipeng

doi:10.1111/poms.12888

Cited by 7 publications

(4 citation statements)

References 23 publications

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“…Quantitative studies on the benefit of precisely modeling uncertainty are performed also in contexts different than energy generation planning, such as call center demand prediction. In [39], a time-series model is developed, and it is shown that under some dependence condition of call center demand streams, performing a joint forecast is more beneficial than building a single prediction model for each stream separately. More specifically, three types of inter-stream dependence are considered and modeled simultaneously, as well as certain data conditions where the multi-stream approach performs better than the single stream model are provided.…”

Section: Literature Reviewmentioning

confidence: 99%

On the Impact of Deep Learning-based Time-series Forecasts on Multistage Stochastic Programming Policies

Wang¹,

Çevik²,

Bodur³

2020

Preprint

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Multistage stochastic programming provides a modeling framework for sequential decisionmaking problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling. Traditionally, statistical forecasting techniques with simple forms, e.g., (first-order) autoregressive time-series models, are used to extract scenarios to be added to optimization models to represent the uncertain future. However, often times, the performance of these forecasting models are not thoroughly assessed. Motivated by the advances in probabilistic forecasting, we incorporate a deep learning-based global time-series forecasting method into multistage stochastic programming framework, and compare it with the cases where a traditional forecasting method is employed to model the uncertainty. We assess the impact of more accurate forecasts on the quality of two commonly used look-ahead policies, a deterministic one and a two-stage one, in a rolling-horizon framework on a practical problem. Our results illustrate that more accurate forecasts contribute substantially to the model performance, and enable obtaining high-quality solutions even from computationally cheap heuristics. They also show that the probabilistic forecasting capabilities of deep learning-based methods can be especially beneficial when used as a (conditional) sampling tool for scenario-based models, and to predict the worst-case scenario for risk-averse models.

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Section: Literature Reviewmentioning

confidence: 99%

On the Impact of Deep Learning-based Time-series Forecasts on Multistage Stochastic Programming Policies

Wang¹,

Çevik²,

Bodur³

2020

Preprint

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“…Empirical research has shown that the rates at which customers arrive are not known with certainty ahead of time, and hence must be forecasted. Statistical models have sought to better characterize the distribution of arrival rates, by time of day, as they evolve; see, for example, Weinberg, Brown and Stroud, 2007, Shen and Huang, 2008a, Shen and Huang, 2008b, Aldor-Noiman, Feigin and Mandelbaum, 2009, Matteson et al, 2011, Taylor, 2012, Ibrahim and L'Ecuyer, 2013, Ibrahim et al, 2016a, Ye, Luedtke and Shen, 2019. Data-Driven forecasting and stochastic programming (SP) framework is proposed by Gans et al (2015) to cope with arrival-rate uncertainty, integrating statistics and operations management.…”

Section: Diving Deeper Into the Main Building Blocks Ofmentioning

confidence: 99%

“…Forecasting of arrivals has been well surveyed by Ibrahim et al (2016a) for service systems with one arrival stream. However, ServNets more often than not have multiple arrival streams, that are furthermore dependent, which is a scenario studied in Ibrahim and L'Ecuyer (2013), Ye, Luedtke and Shen (2019). One must also study the impact of interstream dependence on operational decisions, such as agent pooling, in a similar spirit to what Gans et al (2015) did for single-arrival stream systems.…”

Section: 33mentioning

confidence: 99%

Statistical Theory Powering Data Science

Cai¹,

Mandelbaum²,

Nagaraja³

et al. 2019

Statist. Sci.

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Statisticians are finding their place in the emerging field of data science. However, many issues considered "new" in data science have long histories in statistics. Examples of using statistical thinking are illustrated, which range from exploratory data analysis to measuring uncertainty to accommodating nonrandom samples. These examples are then applied to service networks, baseball predictions and official statistics.

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“…It is found that the overdispersion can sometimes be explained by the strong autocorrelation of arrival counts over successive periods during the day (Ibrahim et al, 2016; Ibrahim & L'Ecuyer, 2013; Shen & Huang, 2008; Ye et al, 2019). Such intraday dependencies may arise due to a variety of reasons.…”

Section: Introductionmentioning

confidence: 99%

Staffing many‐server queues with autoregressive inputs

Sun

Liu

2020

Naval Research Logistics

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Recent studies reveal significant overdispersion and autocorrelation in arrival data at service systems such as call centers and hospital emergency departments. These findings stimulate the needs for more practical non‐Poisson customer arrival models, and more importantly, new staffing formulas to account for the autocorrelative features in the arrival model. For this purpose, we study a multiserver queueing system where customer arrivals follow a doubly stochastic Poisson point process whose intensities are driven by a Cox–Ingersoll–Ross (CIR) process. The nonnegativity and autoregressive feature of the CIR process makes it a good candidate for modeling temporary dips and surges in arrivals. First, we devise an effective statistical procedure to calibrate our new arrival model to data which can be seen as a specification of the celebrated expectation–maximization algorithm. Second, we establish functional limit theorems for the CIR process, which in turn facilitate the derivation of functional limit theorems for our queueing model under suitable heavy‐traffic regimes. Third, using the corresponding heavy traffic limits, we asymptotically solve an optimal staffing problem subject to delay‐based constraints on the service levels. We find that, in order to achieve the designated service level, such an autoregressive feature in the arrival model translates into notable adjustment in the staffing formula, and such an adjustment can be fully characterized by the parameters of our new arrival model. In this respect, the staffing formulas acknowledge the presence of autoregressive structure in arrivals. Finally, we extend our analysis to queues having customer abandonment and conduct simulation experiments to provide engineering confirmations of our new staffing rules.

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Call Center Arrivals: When to Jointly Forecast Multiple Streams?

Cited by 7 publications

References 23 publications

On the Impact of Deep Learning-based Time-series Forecasts on Multistage Stochastic Programming Policies

On the Impact of Deep Learning-based Time-series Forecasts on Multistage Stochastic Programming Policies

Statistical Theory Powering Data Science

Staffing many‐server queues with autoregressive inputs

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