Call centers are an increasingly important part of today’s business world, employing millions of agents across the globe and serving as a primary customer-facing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several domains, including forecasting, capacity planning, queueing, and personnel scheduling. In addition, as telecommunications and information technology have advanced over the past several years, the operational challenges faced by call center managers have become more complicated. Issues associated with human resources management, sales, and marketing have also become increasingly relevant to call center operations and associated academic research. In this paper, we provide a survey of the recent literature on call center operations management. Along with traditional research areas, we pay special attention to new management challenges that have been caused by emerging technologies, to behavioral issues associated with both call center agents and customers, and to the interface between call center operations and sales and marketing. We identify a handful of broad themes for future investigation while also pointing out several very specific research opportunities.

Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform time-dependent staffing for many-server queues. Our aim is to achieve time-stable performance in face of general time-varying arrival rates. It turns out that it suffices to target a stable probability of delay. That procedure tends to produce time-stable performance for several other operational measures. Motivated by telephone call centers, we focus on many-server models with customer abandonment, especially the Markovian Mt/M/st + M model, having an exponential time-to-abandon distribution (the +M), an exponential servicetime distribution and a nonhomogeneous Poisson arrival process. We develop three different methods for staffing, with decreasing generality and decreasing complexity: First, we develop a simulation-based iterativestaffing algorithm (ISA), and conduct experiments showing that it is effective. The ISA is appealing because it applies to very general models and is automatically validating: we directly see how well it works. Second, we extend the square-root-staffing rule, proposed by Jennings et al., which is based on the associated infinite-server model. The rule dictates that the staff level at time t be st = mt + β √ mt, where mt is the offered load (mean number of busy servers in the infinite-server model) and the constant β reflects the service grade. We show that the service grade β in the staffing formula can be represented as a function of the target delay probability α by

This paper proposes simple methods for staffing a single-class call center with uncertain arrival rate and uncertain staffing due to employee absenteeism. The arrival rate and the proportion of servers present are treated as random variables. The basic model is a multi-server queue with customer abandonment, allowing non-exponential service-time and time-to-abandon distributions. The goal is to maximize the expected net return, given throughput benefit and server, customer-abandonment and customer-waiting costs, but attention is also given to the standard deviation of the return. The approach is to approximate the performance and the net return, conditional on the random model-parameter vector, and then uncondition to get the desired results. Two recently-developed approximations are used for the conditional performance measures: first, a deterministic fluid approximation and, second, a numerical algorithm based on a purely Markovian birth-and-death model, having state-dependent death rates. Key words: model-parameter uncertainty; contact centers; employee absenteeism; customer abandonment; fluid models

Call centers are an increasingly important part of today’s business world, employing millions of agents across the globe and serving as a primary customer-facing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several areas, including forecasting, capacity planning, queueing, and personnel scheduling. In addition, as telecommunications and information technology have advanced over the past several years, the operational challenges faced by call center managers have become more complicated as a result. Issues associated with human resources management, sales, and marketing have also become increasingly relevant to call center operations and associated academic research. In this paper, we provide a survey of the recent literature on call center operations management. Along with traditional research areas, we pay special attention to new management challenges that have been caused by emerging technologies, to behavioral issues associated with both call center agents and customers, and to the interface between call center operations and sales and marketing. We identify a handful of broad themes for future investigation while also pointing out several very specific research opportunities.

Abstract: In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic limits for two-parameter stochastic processes. We

To describe the congestion in large-scale service systems, we introduce and analyze a non-Markovian open network of many-server fluid queues with customer abandonment, proportional routing and time-varying model elements. A proportion of the fluid completing service at each queue is routed immediately to each other queue, while the fluid not routed to other queues leaves the network. The fluid queue network serves as an approximation for the corresponding non-Markovian open network of many-server queues with Markovian routing, where all model elements may be time varying. We establish the existence of a unique vector of (net) arrival rate functions at each queue and the associated time-varying performance. In doing so, we provide the basis for an efficient algorithm, even for networks with many queues. Key words: queues with time-varying arrivals; queueing networks; many-server queues; deterministic fluid model; customer abandonment; non-Markovian queues. History: Submitted on February 7, 2010 1.

Telephone call centers and their generalizations- customer contact centers- usually handle sev-eral types of customer service requests (calls). Since customer service representatives (agents) have different call-handling abilities and are typically cross-trained in multiple skills, contact centers exploit skill-based routing (SBR) to assign calls to appropriate agents, aiming to re-spond properly as well as promptly. Established agent-staffing and SBR algorithms ensure that agents have the required call-handling skills and that call routing is performed so that constraints are met for standard congestion measures, such as the percentage of calls of each type that abandon before starting service and the percentage of answered calls of each type that are delayed more than a specified number of seconds. We propose going beyond tra-ditional congestion measures to focus on the expected value derived from having particular agents handle various calls. Expected value might represent expected revenue or the likelihood of first-call resolution. Value might also reflect agent call-handling preferences. We show how value-based routing (VBR) and preference-based routing (PBR) can be introduced in the con-text of an existing SBR framework, based on static-priority routing using a highly-structured

Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative real-time delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the last customer to enter service (LES), (ii) the delay experienced so far by the customer at the head of the line (HOL), and (iii) the delay experienced by the customer to have arrived most recently among those who have already completed service (RCS). We compare these delay-history estimators to the estimator based on the queue length (QL), which requires knowledge of the mean interval between successive service completions in addition to the queue length. We characterize performance by the mean squared error (MSE). We do analysis and conduct simulations for the standard GI/M/s multi-server queueing model, emphasizing the case of large s. We obtain analytical results for the conditional distribution of the delay given the observed HOL delay. An approximation to its mean value serves as a refined estimator. For all three candidate delay estimators, the MSE relative to the square of the mean is asymptotically negligible in the many-server and classical heavy-traffic limiting regimes.

We introduce and analyze a deterministic fluid model that serves as an approximation for the Gt/GI/st + GI many-server queueing model, which has a general time-varying arrival process (the Gt), a general service-time distribution (the first GI), a time-dependent number of servers (the st) and allows abandonment from queue according to a general abandonment-time distribution (the +GI). This fluid model approximates the associated queueing system when the arrival rate and number of servers are both large. We characterize performance in the fluid model over alternating intervals in which the system is overloaded and underloaded (including critically loaded). For each t ≥ 0 and y ≥ 0, we determine the amount of fluid that is in service (in queue) at time t and has been so for time at most y. We obtain the service content density by applying the Banach contraction fixed point theorem. We also determine the time-varying potential waiting time, i.e., the virtual waiting time of a quantum of fluid arriving at a specified time, assuming that it will not abandon. The potential waiting time is determined by an ordinary differential equation. We show that a time-varying service capacity can be chosen to stabilize delays at any fixed target. Key words: queues with time-varying arrivals; nonstationary queues; many-server queues; deterministic fluid model; fluid approximation; queues with abandonment; non-Markovian queues.

stitute a large industry worldwide, where the majority of customer-firm interactions take place. There are thousands of call centers in the world, with sizes in terms of full time employees ranging from a few to several thousand. Datamonitor estimates that the 2.5 million agent positions in the