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Telephone call centers: Tutorial, review, and research prospects
 Mgmt
, 2003
"... Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments trad ..."
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Cited by 280 (15 self)
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Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value – and at the same time fundamentally limited – in their ability to characterize system performance. We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research. Acknowledgments The authors thank Lee Schwarz, Wallace Hopp and the editorial board of M&SOM for initiating this project, as well as the referees for their valuable comments. Thanks are also due to L. Brown, A. Sakov, H. Shen, S. Zeltyn and L. Zhao for their approval of importing pieces of [36, 112].
Contact centers with a callback option and realtime delay information
 Operations Research
, 2004
"... doi 10.1287/opre.1030.0088 ..."
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Coping with TimeVarying Demand When Setting Staffing Requirements for a Service System
, 2007
"... We review queueingtheory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the longrun steadystate behavior of stationary mode ..."
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Cited by 70 (25 self)
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We review queueingtheory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the longrun steadystate behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that timedependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, timelag refinements can improve traditional stationary independent periodbyperiod and peakhour approximations. Timevarying infiniteserver models help develop refinements, because closedform expressions exist for their timedependent behavior. More difficult cases with very long service times and other complicated features, such as endofday effects, can often be treated by a modifiedofferedload approximation, which is based on an associated infiniteserver model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned.
Server Staffing to Meet TimeVarying Demand
 Management Science
, 1996
"... We consider a multiserver service system with general nonstationary arrival and servicetime processes in which s(t), the number of servers as a function of time, needs to be selected to meet projected loads. We try to choose s(t) so that the probability of a delay (before beginning service) hits or ..."
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Cited by 68 (24 self)
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We consider a multiserver service system with general nonstationary arrival and servicetime processes in which s(t), the number of servers as a function of time, needs to be selected to meet projected loads. We try to choose s(t) so that the probability of a delay (before beginning service) hits or falls just below a target probability at all times. We develop an approximate procedure based on a timedependent normal distribution, where the mean and variance are determined by infiniteserver approximations. We demonstrate that this approximation is effective by making comparisons with the exact numerical solution of the Markovian M t / M / s t model.
Staffing of timevarying queues to achieve timestable performance
, 2005
"... Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform timedependent staffing for manyserver queues. Our aim is to achieve timestable performance in face of general timevarying arrival rates. It turns out that it suffices to target a stable probab ..."
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Cited by 67 (34 self)
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Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform timedependent staffing for manyserver queues. Our aim is to achieve timestable performance in face of general timevarying arrival rates. It turns out that it suffices to target a stable probability of delay. That procedure tends to produce timestable performance for several other operational measures. Motivated by telephone call centers, we focus on manyserver models with customer abandonment, especially the Markovian Mt/M/st + M model, having an exponential timetoabandon 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 simulationbased 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 squarerootstaffing rule, proposed by Jennings et al., which is based on the associated infiniteserver 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 infiniteserver 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
Improving Service by Informing Customers about Anticipated Delays
 Management Science
, 1999
"... This paper studies alternative ways to manage a multiserver system such as a telephone call center. Three alternatives can be described succinctly by: (i) blocking, (ii) reneging and (iii) balking. The first alternative – blocking – is to have no provision for waiting. The second alternative is to ..."
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Cited by 57 (8 self)
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This paper studies alternative ways to manage a multiserver system such as a telephone call center. Three alternatives can be described succinctly by: (i) blocking, (ii) reneging and (iii) balking. The first alternative – blocking – is to have no provision for waiting. The second alternative is to allow waiting, but neither inform customers about anticipated delays nor provide state information to allow arriving customers to predict delays. The second alternative tends to yield higher server utilizations. The first alternative tends to reduce to the second, without the firstcome firstserved service discipline, when customers can easily retry, as with automatic redialers in telephone access. The third alternative is to both allow waiting and inform customers about anticipated delays. The third alternative tends to cause balking when all servers are busy (abandonment upon arrival) instead of reneging (abandonment after waiting). Birthanddeath process models are proposed to describe the performance with each alternative. Algorithms are developed to compute the conditional distributions of the time to receive service and the time to renege given each outcome. Algorithms are also developed to help the service provider predict customer waiting times before beginning service, given estimated servicetime distributions and the elapsed service times of the customers in service. Better predictions may be obtained by classifying customers and thereby obtaining better estimates of their servicetime distributions.
Staffing a Call Center with Uncertain Arrival Rate and Absenteeism
 Production and Operations Management
"... This paper proposes simple methods for staffing a singleclass 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 multiserver queue with customer aba ..."
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Cited by 43 (5 self)
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This paper proposes simple methods for staffing a singleclass 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 multiserver queue with customer abandonment, allowing nonexponential servicetime and timetoabandon distributions. The goal is to maximize the expected net return, given throughput benefit and server, customerabandonment and customerwaiting 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 modelparameter vector, and then uncondition to get the desired results. Two recentlydeveloped approximations are used for the conditional performance measures: first, a deterministic fluid approximation and, second, a numerical algorithm based on a purely Markovian birthanddeath model, having statedependent death rates. Key words: modelparameter uncertainty; contact centers; employee absenteeism; customer abandonment; fluid models
A method for staffing large call centers based on stochastic fluid models
, 2004
"... We consider a call center model with m input flows and r pools of agents; the mvector λ of instantaneous arrival rates is allowed to be timedependent and to vary stochastically. Seeking to optimize the tradeoff between personnel costs and abandonment penalties, we develop and illustrate a practic ..."
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Cited by 38 (5 self)
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We consider a call center model with m input flows and r pools of agents; the mvector λ of instantaneous arrival rates is allowed to be timedependent and to vary stochastically. Seeking to optimize the tradeoff between personnel costs and abandonment penalties, we develop and illustrate a practical method for sizing the r agent pools. Using stochastic fluid models, this method reduces the staffing problem to a multidimensional newsvendor problem, which can be solved numerically by a combination of linear programming and Monte Carlo simulation. Numerical examples are presented, and in all cases the pool sizes derived by means of the proposed method are very close to optimal.
Uniform acceleration expansions for Markov chains with timevarying rates
 Ann. Appl. Probab
, 1998
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