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Models and Approximations for Call Center Design

Author

Listed:
  • David L. Jagerman

    (Rutgers University)

  • Benjamin Melamed

    (Rutgers University)

Abstract

A call center is a facility for delivering telephone service, both incoming and outgoing. This paper addresses optimal staffing of call centers, modeled as M/G/n queues whose offered traffic consists of multiple customer streams, each with an individual priority, arrival rate, service distribution and grade of service (GoS) stated in terms of equilibrium tail waiting time probabilities or mean waiting times. The paper proposes a methodology for deriving the approximate minimal number of servers that suffices to guarantee the prescribed GoS of all customer streams. The methodology is based on an analytic approximation, called the Scaling-Erlang (SE) approximation, which maps the M/G/n queue to an approximating, suitably scaled M/G/1 queue, for which waiting time statistics are available via the Pollaczek-Khintchine formula in terms of Laplace transforms. The SE approximation is then generalized to M/G/n queues with multiple types of customers and non-preemptive priorities, yielding the Priority Scaling-Erlang (PSE) approximation. A simple goal-seeking search, utilizing SE/PSE approximations, is presented for the optimal staffing level, subject to GoS constraints. The efficacy of the methodology is demonstrated by comparing the number of servers estimated via the PSE approximation to their counterparts obtained by simulation. A number of case studies confirm that the SE/PSE approximations yield optimal staffing results in excellent agreement with simulation, but at a fraction of simulation time and space.

Suggested Citation

  • David L. Jagerman & Benjamin Melamed, 2003. "Models and Approximations for Call Center Design," Methodology and Computing in Applied Probability, Springer, vol. 5(2), pages 159-181, June.
    • Handle: RePEc:spr:metcap:v:5:y:2003:i:2:d:10.1023_a:1024501601020
    DOI: 10.1023/A:1024501601020
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    References listed on IDEAS

    as
    1. Ward Whitt, 1999. "Improving Service by Informing Customers About Anticipated Delays," Management Science, INFORMS, vol. 45(2), pages 192-207, February.
    2. Per Hokstad, 1978. "Approximations for the M / G / m Queue," Operations Research, INFORMS, vol. 26(3), pages 510-523, June.
    3. Benjamin Melamed & Ward Whitt, 1990. "On Arrivals That See Time Averages," Operations Research, INFORMS, vol. 38(1), pages 156-172, February.
    4. David Y. Sze, 1984. "OR Practice—A Queueing Model for Telephone Operator Staffing," Operations Research, INFORMS, vol. 32(2), pages 229-249, April.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Gökçe Kahveciog̃lu & Barış Balcıog̃lu, 2016. "Coping with production time variability via dynamic lead-time quotation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 877-898, October.
    2. A. Baykal Hafızoğlu & Esma S. Gel & Pınar Keskinocak, 2013. "Expected Tardiness Computations in Multiclass Priority M / M / c Queues," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 364-376, May.
    3. Wei Xiong & Tayfur Altiok, 2009. "An approximation for multi-server queues with deterministic reneging times," Annals of Operations Research, Springer, vol. 172(1), pages 143-151, November.
    4. Sheridan, Patricia Kristine & Gluck, Erich & Guan, Qi & Pickles, Thomas & Balcıog˜lu, Barış & Benhabib, Beno, 2013. "The dynamic nearest neighbor policy for the multi-vehicle pick-up and delivery problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 49(C), pages 178-194.

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