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Capacity Sizing Under Parameter Uncertainty: Safety Staffing Principles Revisited


  • Achal Bassamboo

    () (Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

  • Ramandeep S. Randhawa

    () (Marshall School of Business, University of Southern California, Los Angeles, California 90089)

  • Assaf Zeevi

    () (Graduate School of Business, Columbia University, New York, New York 10027)


We study a capacity sizing problem in a service system that is modeled as a single-class queue with multiple servers and where customers may renege while waiting for service. A salient feature of the model is that the mean arrival rate of work is random (in practice this is a typical consequence of forecasting errors). The paper elucidates the impact of uncertainty on the nature of capacity prescriptions, and relates these to well established rules-of-thumb such as the square-root safety staffing principle. We establish a simple and intuitive relationship between the incoming load (measured in Erlangs) and the extent of uncertainty in arrival rates (measured via the coefficient of variation) that characterizes the extent to which uncertainty dominates stochastic variability or vice versa. In the former case it is shown that traditional square-root safety staffing logic is no longer valid, yet simple capacity prescriptions derived via a suitable newsvendor problem are surprisingly accurate.

Suggested Citation

  • Achal Bassamboo & Ramandeep S. Randhawa & Assaf Zeevi, 2010. "Capacity Sizing Under Parameter Uncertainty: Safety Staffing Principles Revisited," Management Science, INFORMS, vol. 56(10), pages 1668-1686, October.
  • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:10:p:1668-1686

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    References listed on IDEAS

    1. Athanassios N. Avramidis & Alexandre Deslauriers & Pierre L'Ecuyer, 2004. "Modeling Daily Arrivals to a Telephone Call Center," Management Science, INFORMS, vol. 50(7), pages 896-908, July.
    2. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    3. Otis B. Jennings & Avishai Mandelbaum & William A. Massey & Ward Whitt, 1996. "Server Staffing to Meet Time-Varying Demand," Management Science, INFORMS, vol. 42(10), pages 1383-1394, October.
    4. Itay Gurvich & Mor Armony & Avishai Mandelbaum, 2008. "Service-Level Differentiation in Call Centers with Fully Flexible Servers," Management Science, INFORMS, vol. 54(2), pages 279-294, February.
    5. J. Michael Harrison & Assaf Zeevi, 2005. "A Method for Staffing Large Call Centers Based on Stochastic Fluid Models," Manufacturing & Service Operations Management, INFORMS, vol. 7(1), pages 20-36, September.
    6. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
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    Cited by:

    1. Tolga Tezcan & Banafsheh Behzad, 2012. "Robust Design and Control of Call Centers with Flexible Interactive Voice Response Systems," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 386-401, July.
    2. Josh Reed & Bo Zhang, 0. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 0, pages 1-34.
    3. Hu, Xiangling & Motwani, Jaideep G., 2014. "Minimizing downside risks for global sourcing under price-sensitive stochastic demand, exchange rate uncertainties, and supplier capacity constraints," International Journal of Production Economics, Elsevier, vol. 147(PB), pages 398-409.
    4. Li, Gang & Huang, Feng Feng & Cheng, T.C.E. & Zheng, Quan & Ji, Ping, 2014. "Make-or-buy service capacity decision in a supply chain providing after-sales service," European Journal of Operational Research, Elsevier, vol. 239(2), pages 377-388.
    5. repec:spr:queues:v:86:y:2017:i:1:d:10.1007_s11134-017-9519-0 is not listed on IDEAS
    6. repec:spr:queues:v:87:y:2017:i:1:d:10.1007_s11134-017-9526-1 is not listed on IDEAS


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