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Dimensioning Large-Scale Membership Services

Author

Listed:
  • Francis de Véricourt

    (European School of Management and Technology, Berlin 10178, Germany)

  • Otis B. Jennings

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

Motivated by workforce planning problems in health care, professional, warranty, and repair services, we propose modeling service centers that are exclusively dedicated to fixed client constituencies as closed multiserver queueing systems, a framework we refer to as membership services . We provide fluid and diffusion approximations of the number of users within the membership who are requesting service. The approximations are obtained via many-server limit theorems, where the limiting regime assumptions of each theorem correspond to a particular staffing strategy a manager might employ. Accordingly, we propose staffing rules designed to meet a certain desired performance criterion. In particular, when the objective is to minimize the staffing size subject to a constraint on the probability of delay for a service-requesting customer, we suggest staffing rules inspired by the so-called quality- and efficiency-driven (QED), or Halfin-Whitt, limiting regime. Numerical evaluations of our proposed QED scheme indicate that, although justified for large systems, the staffing rule performs well for memberships of all sizes.

Suggested Citation

  • Francis de Véricourt & Otis B. Jennings, 2008. "Dimensioning Large-Scale Membership Services," Operations Research, INFORMS, vol. 56(1), pages 173-187, February.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:1:p:173-187
    DOI: 10.1287/opre.1070.0464
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    References listed on IDEAS

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    1. J. Michael Harrison & Assaf Zeevi, 2004. "Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Heavy Traffic Regime," Operations Research, INFORMS, vol. 52(2), pages 243-257, April.
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    Cited by:

    1. Amy R. Ward & Mor Armony, 2013. "Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers," Operations Research, INFORMS, vol. 61(1), pages 228-243, February.
    2. Petar Momčilović & Amir Motaei, 2018. "QED limits for many-server systems under a priority policy," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 125-159, October.
    3. Avishai Mandelbaum & Sergey Zeltyn, 2009. "Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers," Operations Research, INFORMS, vol. 57(5), pages 1189-1205, October.
    4. Fiona Sloothaak & James Cruise & Seva Shneer & Maria Vlasiou & Bert Zwart, 2021. "Complete resource pooling of a load-balancing policy for a network of battery swapping stations," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 65-120, October.
    5. Francis de Véricourt & Otis B. Jennings, 2011. "Nurse Staffing in Medical Units: A Queueing Perspective," Operations Research, INFORMS, vol. 59(6), pages 1320-1331, December.
    6. Ingolfsson, Armann & Almehdawe, Eman & Pedram, Ali & Tran, Monica, 2020. "Comparison of fluid approximations for service systems with state-dependent service rates and return probabilities," European Journal of Operational Research, Elsevier, vol. 283(2), pages 562-575.
    7. Carri W. Chan & Galit Yom-Tov & Gabriel Escobar, 2014. "When to Use Speedup: An Examination of Service Systems with Returns," Operations Research, INFORMS, vol. 62(2), pages 462-482, April.
    8. Ramandeep S. Randhawa & Sunil Kumar, 2009. "Multiserver Loss Systems with Subscribers," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 142-179, February.

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