CALL CENTERS (CENTRES) - Faculty of Industrial Engineering and ...

Keywords: M(n)/M(n)/s + GI system, Limited waiting times, Finite buffer, Virtual waiting
times, Blocking-, Abandon probability, Impatience rates, Asymptotic results, M(n)/M(n)/s
system with waiting place dependent impatient rates, Markovian approximation
87. Brusco, Michael J. and Larry W. Jacobs. Optimal models for meal-break and start-time flexibility
in continuous tour scheduling, Management Science, 46 (12), 2000, 1630–1641.
Abstract. A compact integer-programming model is presented for large-scale continuous tour
scheduling problems that incorporate meal-break window, start-time band, and start-time interval
policies. For practical scheduling environments, generalized set-covering formulations
(GSCF) of such problems often contain hundreds of millions of integer decision variables, usually
precluding identification of optimal solutions. As an alternative, an implicit integer-programming
model has been prevented that frequently has fewer than 1,500 variables and can be formulated
and solved using PC-based hardware and software platforms. An empirical study using laborrequirement
distributions for customer service representatives at a Motorola Inc. call center was
used to demonstrate the importance of having a model that can evaluate tradeoffs among the
various scheduling policies.
Keywords: Continuous tour scheduling, Integer programming, Meal-break window, Start-time
band, Generalized set-covering, Customer service, Workforce scheduling, Production control
88. Easton, Fred F. Labor requirements for multi-server multi-class finite queues. Working paper,
Robert H. Brethen Operations Management Institute, School of Management, Syracuse University,
Syracuse, NY, USA, June 2000.
Abstract. Most of North American’s 70,000 call centers use Erlang queueing models to determine
appropriate staffing levels for each period their systems operate. These standard queueing
models (M/M/C or M/M/C/N) assume a one-stage single-queue service, FCFS priority, multiple
identical servers, and exponential inter-arrival times and service times. If a call center
provides two or more types of service, each with distinct mean service times, its workforce
management system typically averages the interarrival and service times over all calls. These
parameters are then automatically passed to a M/M/C/∞ or a M/M/C/N model to determine
the minimum staff needed to assure a prescribed level of service.
In this research we consider a multi-server finite Poisson queueing system that provides two
types of service, classified H2/H2/C/N. We decompose the two arrival streams and show that
the system is reversible, allowing efficient computation of its two-dimensional state probabilities.
The model enables us to better understand the magnitude of the staffing errors that result when
standard Erlang models are applied to multi-class queueing systems. For example, we find that
when an equal number of callers arrive for each of two classes of service, but the mean service
rate for one class is nine times faster than the other, M/M/C/N can recommend a staffing level
that is less than one-half the minimum number of employees actually needed to provide the
desired level of service.
89. Jongbloed, Geurt and Ger Koole. Managing uncertainty in call centers using Poisson mixtures.
Working paper, Vrije Universiteit, Division of Mathematics and Computer Science, Amsterdam,
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