Search

In this paper, we consider a two-stage call center staffing model. In the first stage, the interval staffing levels are set under arrival rate uncertainty. In the second stage, these initial staffing levels are corrected to the right value based on more precise arrival rate information. We show that this problem is of newsvendor type, where the costs are the initial staffing costs plus the second stage adaptation costs. We show that we should initially staff according to a quantile of the distributional forecast, rather than the mean. It is also shown that the errors in staffing are approximately linear in the forecasting errors. This leads to the conclusion that the weighted sum of errors should be the error measurement in call center forecasting, since minimizing, it minimizes the total staffing costs. In special cases where the costs are symmetric for over- and understaffing, this is equivalent to minimizing the weighted absolute percentage error. [ABSTRACT FROM AUTHOR]

Problem definition: We consider a revenue-generating call center with inbound and outbound calls, where service and sales activities are blended. For maximizing the call center's revenue, the call center manager exercises two levels of control: agent reservation for inbound calls and call outsourcing. Given the influence of waits on purchase probability, we investigate the strategy of outsourcing customers who have waited already as opposed to outsourcing customers directly at arrival. Academic/practical relevance: The main novelty of this article arises from the use of a single framework to investigate both the combination of agent reservation with outsourcing decisions, and a waiting time–based outsourcing strategy. The existing literature only considers these two strategies in isolation and is restricted to quantity-based decisions. From a practical viewpoint, our results aim to provide decision support tools that are directly implementable in a call center's routing software. Methodology: We apply a Markov decision process approach to optimize the manager's decisions. The particularity of our approach is that we use the experienced waiting time as a decision variable. Results: We prove that the optimal policy for reservation and outsourcing is of threshold type. Our main conclusion is that outsourcing customers after letting them wait in-house generates higher revenue than outsourcing calls at arrival. However, it is also detrimental to service quality. In addition, we identify contexts in which the difference between the two outsourcing strategies is significant. Managerial implications: Contrary to standard call center practices, which either consist of specialized teams for one type of call or only exercise one specific level of decision-making (reservation or outsourcing), we demonstrate the potential of partial outsourcing with partial reservation. Our study shows that the benefits of implementing our results are greatest in small congested call centers. [ABSTRACT FROM AUTHOR]

In radiotherapy, treatment needs to be delivered in time. Long waiting times can result in patient anxiety and growth of tumors. They are often caused by inefficient use of radiotherapy equipment, the linear accelerators (LINACs). However, making an efficient schedule is very challenging, especially when we have multiple types of patients, having different service requirements and waiting time constraints. Moreover, in radiotherapy a patient needs to go through a LINAC multiple times over multiple days, to complete the treatment. In this paper we model the radiotherapy treatment process as a queueing system with multiple queues, and we propose a new class of scheduling policies that are simple, flexible and fair to patients. Numerical experiments show that our new policy outperforms the commonly used policies. We also extend the policy to an adaptive one to deal with unknown and fluctuating arrival rates. Our adaptive policy turns out to be quite efficient in absorbing the effects caused by these changes. Due to the complexity of our problem, we select the parameters of the policies through simulation-based optimization heuristics. Our work may also have important implications for managers in other service systems such as call centers. [ABSTRACT FROM AUTHOR]

In the context of multi-channel call centers with inbound calls and emails, this article considers a threshold policy on the reservation of agents for the inbound calls. We study a general non-stationary model where calls arrive according to a non-homogeneous Poisson process. The optimization problem consists in maximizing the throughput of emails under a constraint on the waiting time of inbound calls. An efficient adaptive threshold policy is proposed that is easy to implement in the automatic call distributor. This scheduling policy is evaluated through a comparison with the optimal performance measures found in the case of a constant arrival rate and also with other intuitive adaptive threshold policies in the general non-stationary case. [ABSTRACT FROM PUBLISHER]

We study call routing policies for call centers with multiple call types and multiple agent groups. We introduce new weight-based routing policies where each pair (call type, agent group) is given a matching priority defined as an affine combination of the longest waiting time for that call type and the longest idle time or the number of idle agents in that agent group. The coefficients in this combination are parameters to be optimized. This type of policy is more flexible than traditional ones found in practice, and it performs better in many situations. We consider objective functions that account for the service levels, the abandonment ratios, and the fairness of occupancy across agent groups. We select the parameters of all considered policies via simulation-based optimization heuristics. This requires only the availability of a simulation model of the call center, which can be much more detailed and realistic than the models used elsewhere in the literature to study the optimality of certain types of routing rules. We offer a first numerical study of realistic routing rules that takes into account the complexity of real-life call centers. [ABSTRACT FROM AUTHOR]

An important feature of call center modeling is the presence of impatient customers. This article considers single-skill call centers including customer abandonments. A number of different service-level definitions are structured, including all those used in practice, and the explicit computation of their performance measures is performed. Based on data from different call centers, models are defined that extend the common Erlang A model. It is shown that the proposed models fit reality very well. [ABSTRACT FROM PUBLISHER]

We consider a multi-period staffing problem in a single-shift call center. The call center handles inbound calls, as well as some alternative back-office jobs. The call arrival process is assumed to follow a doubly non-stationary stochastic process with a random mean arrival rate. The inbound calls have to be handled as quickly as possible, while the back-office jobs, such as answering emails, may be delayed to some extent. The staffing problem is modeled as a generalized newsboy-type model under an expected cost criterion. Two different solution approaches are considered. First, by discretization of the underlying probability distribution, we explicitly formulate the expected cost newsboy-type formulation as a stochastic program. Second, we develop a robust programming formulation. The characteristics of the two methods and the associated optimal solutions are illustrated through a numerical study based on real-life data. In particular we focus on the numerical tractability of each formulation. We also show that the alternative workload of back-office jobs offers an interesting flexibility allowing to decrease the total operating cost of the call center. [ABSTRACT FROM AUTHOR]

In practice, call center service levels are reported over periods of finite length that are usually no longer than 24 hours. In such small periods the service level has a large variability. It is therefore not sufficient to base staffing decisions only on the expected service level. In this paper we consider the classical M/M/s queueing model that is often used in call centers. We develop accurate approximations for the service-level distribution based on extensive simulations. This distribution is used for a service-level variability-controlled staffing approach to circumvent the shortcomings of the traditional staffing based on the expected service level. [ABSTRACT FROM AUTHOR]

We consider an inbound call center with a fixed reward per call and communication and agent costs. By controlling the number of lines and the number of agents, we can maximize the profit. Abandonments are included in our performance model. Monotonicity results for the maximization problem are obtained, which lead to an efficient optimization procedure. We give a counterexample to the concavity in the number of agents, which is equivalent to saying that the law of diminishing returns does not hold. Numerical results are given. [ABSTRACT FROM AUTHOR]

We study a simple method for staffing in multiskill call centers. The method has short computation times and determines nearly optimal staffing levels. It is in both views competitive to other methods from the literature. Because of the fast and accurate performance of the method, many different scenarios can be analyzed, and our method can be used for both tactical and strategic capacity management decisions. [ABSTRACT FROM AUTHOR]

This paper introduces a new method for shift scheduling in multiskill call centers. The method consists of two steps. First, staffing levels are determined, and next, in the second step, the outcomes are used as input for the scheduling problem. The scheduling problem relies on a linear programming model that is easy to implement and has short computation times, i.e., a fraction of a second. Therefore, it is useful for different purposes and it can be part of an iterative procedure: for example, one that combines shifts into rosters. [ABSTRACT FROM AUTHOR]

Temporary overload situations in queues can be approximated by fluid queues. We strengthen earlier results on the comparison of multi-server tandem systems with their fluid limits. At the same time we give conditions under which economies of scale hold. We apply the results to call centers. [ABSTRACT FROM AUTHOR]

We study a shift scheduling problem for call centers with an overall service level objective. We prove a property of this problem, called multimodularity, that ensures that a local search algorithm terminates with a globally optimal solution. We report on computations performed using real call center data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This is a survey of some academic research on telephone call centers. The surveyed research has its origin in, or is related to, queueing theory. Indeed, the "queueing-view" of call centers is both natural and useful. Accordingly, queueing models have served as prevalent standard support tools for call center management. However, the modem call center is a complex socio-technical system. It thus enjoys central features that challenge existing queueing theory to its limits, and beyond. [ABSTRACT FROM AUTHOR]

We model a call centre as a queueing model with Poisson arrivals having an unknown varying arrival rate. We show how to compute prediction intervals for the arrival rate, and use the Erlang formula for the waiting time to compute the consequences for the occupancy level of the call centre. We compare it to the current practice of using a point estimate of the arrival rate (assumed constant) as forecast. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]