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Refining Square-Root Safety Staffing by Expanding Erlang C

Author

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  • A. J. E. M. Janssen

    (Eindhoven University of Technology and EURANDOM, 5600 MB Eindhoven, The Netherlands)

  • J. S. H. van Leeuwaarden

    (Eindhoven University of Technology and EURANDOM, 5600 MB Eindhoven, The Netherlands)

  • Bert Zwart

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

We apply a new corrected diffusion approximation for the Erlang C formula to determine staffing levels in cost minimization and constraint satisfaction problems. These problems are motivated by large customer contact centers that are modeled as an M / M / s queue with s the number of servers or agents. The proposed staffing levels are refinements of the celebrated square-root safety-staffing rule and have the appealing property that they are as simple as the conventional square-root safety-staffing rule. In addition, we provide theoretical support for the empirical fact that square-root safety-staffing works well for moderate-sized systems.

Suggested Citation

  • A. J. E. M. Janssen & J. S. H. van Leeuwaarden & Bert Zwart, 2011. "Refining Square-Root Safety Staffing by Expanding Erlang C," Operations Research, INFORMS, vol. 59(6), pages 1512-1522, December.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:6:p:1512-1522
    DOI: 10.1287/opre.1110.0991
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    References listed on IDEAS

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    1. Avishai Mandelbaum & Petar Momčilović, 2008. "Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 561-586, August.
    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.
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    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ramandeep S. Randhawa, 2016. "Optimality gap of asymptotically derived prescriptions in queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 131-155, June.
    2. Bo Zhang & Johan S. H. van Leeuwaarden & Bert Zwart, 2012. "Staffing Call Centers with Impatient Customers: Refinements to Many-Server Asymptotics," Operations Research, INFORMS, vol. 60(2), pages 461-474, April.
    3. Galit B. Yom-Tov & Avishai Mandelbaum, 2014. "Erlang-R: A Time-Varying Queue with Reentrant Customers, in Support of Healthcare Staffing," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 283-299, May.
    4. Eugene Furman & Adam Diamant & Murat Kristal, 2021. "Customer Acquisition and Retention: A Fluid Approach for Staffing," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4236-4257, November.
    5. Matthieu Jonckheere & Balakrishna J. Prabhu, 2018. "Asymptotics of insensitive load balancing and blocking phases," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 243-278, April.
    6. Heemskerk, M. & Mandjes, M. & Mathijsen, B., 2022. "Staffing for many-server systems facing non-standard arrival processes," European Journal of Operational Research, Elsevier, vol. 296(3), pages 900-913.
    7. Frank Karsten & Marco Slikker & Geert-Jan van Houtum, 2015. "Resource Pooling and Cost Allocation Among Independent Service Providers," Operations Research, INFORMS, vol. 63(2), pages 476-488, April.
    8. Liu, Zhongyi & Liu, Jingchen & Zhai, Xin & Wang, Guanying, 2019. "Police staffing and workload assignment in law enforcement using multi-server queueing models," European Journal of Operational Research, Elsevier, vol. 276(2), pages 614-625.
    9. Ying Chen & John J. Hasenbein, 2017. "Staffing large-scale service systems with distributional uncertainty," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 55-79, October.
    10. 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.
    11. Josh Reed & Bo Zhang, 2017. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 61-94, June.
    12. Britt Mathijsen & Bert Zwart, 2017. "Transient error approximation in a Lévy queue," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 269-304, April.
    13. Ragavendran Gopalakrishnan & Sherwin Doroudi & Amy R. Ward & Adam Wierman, 2016. "Routing and Staffing When Servers Are Strategic," Operations Research, INFORMS, vol. 64(4), pages 1033-1050, August.
    14. Jayakrishnan Nair & Adam Wierman & Bert Zwart, 2016. "Provisioning of Large-Scale Systems: The Interplay Between Network Effects and Strategic Behavior in the User Base," Management Science, INFORMS, vol. 62(6), pages 1830-1841, June.
    15. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    16. Eugene Furman & Alex Cressman & Saeha Shin & Alexey Kuznetsov & Fahad Razak & Amol Verma & Adam Diamant, 2021. "Prediction of personal protective equipment use in hospitals during COVID-19," Health Care Management Science, Springer, vol. 24(2), pages 439-453, June.
    17. Llanos R. L. F., 2016. "A study on call/contact centers' inbound and outbound management process," South Asian Journal of Management Sciences (SAJMS), Iqra University, Iqra University, vol. 10(2), pages 1-10, Fall.
    18. Galit B. Yom-Tov & Carri W. Chan, 2021. "Balancing admission control, speedup, and waiting in service systems," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 163-219, February.

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