Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective

Abstract

In this article, we introduce staffing strategies for the Erlang‐A queuing system in call center operations with uncertain arrival, service, and abandonment rates. In doing so, we model the system rates using gamma distributions that create randomness in operating characteristics used in the optimization formulation. We divide the day into discrete time intervals where a simulation based stochastic programming method is used to determine staffing levels. More specifically, we develop a model to select the optimal number of agents required for a given time interval by minimizing an expected cost function, which consists of agent and abandonment (opportunity) costs, while considering the service quality requirements such as the delay probability. The objective function as well as the constraints in our formulation are random variables. The novelty of our approach is to introduce a solution method for the staffing of an operation where all three system rates (arrival, service, and abandonment) are random variables. We illustrate the use of the proposed model using both real and simulated call center data. In addition, we provide solution comparisons across different formulations, consider a dynamic extension, and discuss sensitivity implications of changing constraint upper bounds as well as prior hyper‐parameters. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 460–478, 2016

Bayesian modeling of abandonments in ticket queues

“…Gurvich et al (2008) use delay probabilities as constraints in their objective function, and Feldman et al (2008) consider those as targets to be achieved. Aktekin and Ekin (2016) develop a staffing strategy using an augmented probability simulation-based stochastic optimization model, where both the objective function and the constraints are random. It is possible to implement an approach similar to the latter work using our abandonment-prediction framework.…”

“…Most studies on call center abandonments adopt a queuing theory perspective. Brown et al (), Aldor‐Noiman, Feigin, and Mandelbaum (), Aktekin and Soyer (), Aksin, Ata, Emadi, & Su (), Aktekin and Ekin (), and Yu, Allon, and Bassamboo () are among the few recent works that use statistical inferences to model call center abandonment behavior. Following this recent line of work, we introduce a counting process model to describe customer abandonment behavior in TQs and to analyze interval‐censored abandonment data.…”

“…The Bayesian model uses gamma processes (see van Noortwick ()), which have not been considered previously in the queueing literature. Although there is a rich body of literature on Bayesian queueing analyses, starting in the 1990s (eg, see Armero, ; Ramirez‐Cobo, Lillo, Wilson, & Wiper, ; Aktekin & Soyer, ; Rios Insua, Ruggeri, & Wiper, ; Aktekin & Ekin, ), nonparametric Bayesian models for queues have only recently gained attention. Furthermore, the nonparametric approaches proposed by Aktekin () and Ventz and Muliere () do not consider queueing systems with abandonments.…”

Evaluating the Performance of the Erlang Models for Call Centers

“…develop a scheduling algorithm using a stochastic programming model that is based on uncertain arrival rate forecasts. Aktekin and Ekin (2016) develop staffing strategies for a call center model where arrival rate, service time, and abandonment distributions are all uncertain. Heching and Squillante (2014) apply a two-stage stochastic optimization approach to optimize service delivery centers.…”

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

“…APS can be more efficient, since it performs the expectation and optimization simultaneously. For instance, Aktekin and Ekin () utilize the APS approach of Ekin et al () to solve for their call center staffing model with random arrival, service, and abandonment rates. In their application, the probabilities of abandonment and delay are functions of both decision variables and random parameters, hence indirect decision dependency exists.…”