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Service-Level Differentiation in Call Centers with Fully Flexible Servers


  • Itay Gurvich

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

  • Mor Armony

    () (Stern School of Business, New York University, New York, New York 10012)

  • Avishai Mandelbaum

    () (The William Davidson Faculty of Industrial Engineering and Management, Technion Institute of Technology, Haifa 32000, Israel)


We study large-scale service systems with multiple customer classes and many statistically identical servers. The following question is addressed: How many servers are required (staffing) and how does one match them with customers (control) to minimize staffing cost, subject to class-level quality-of-service constraints? We tackle this question by characterizing scheduling and staffing schemes that are asymptotically optimal in the limit, as system load grows to infinity. The asymptotic regimes considered are consistent with the efficiency-driven (ED), quality-driven (QD), and quality-and-efficiency-driven (QED) regimes, first introduced in the context of a single-class service system. Our main findings are as follows: (a) Decoupling of staffing and control, namely, (i) staffing disregards the multiclass nature of the system and is analogous to the staffing of a single-class system with the same aggregate demand and a single global quality-of-service constraint, and (ii) class-level service differentiation is obtained by using a simple idle-server-based threshold-priority (ITP) control (with state-independent thresholds); and (b) robustness of the staffing and control rules: our proposed single-class staffing (SCS) rule and ITP control are approximately optimal under various problem formulations and model assumptions. Particularly, although our solution is shown to be asymptotically optimal for large systems, we numerically demonstrate that it performs well also for relatively small systems.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:2:p:279-294
    DOI: 10.1287/mnsc.1070.0825

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    References listed on IDEAS

    1. Gérard P. Cachon & Martin A. Lariviere, 2001. "Contracting to Assure Supply: How to Share Demand Forecasts in a Supply Chain," Management Science, INFORMS, vol. 47(5), pages 629-646, May.
    2. Joseph M. Milner & Tava Lennon Olsen, 2008. "Service-Level Agreements in Call Centers: Perils and Prescriptions," Management Science, INFORMS, vol. 54(2), pages 238-252, February.
    3. Vinayak Deshpande & Morris A. Cohen & Karen Donohue, 2003. "A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes," Management Science, INFORMS, vol. 49(6), pages 683-703, June.
    4. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    5. Rodney B. Wallace & Ward Whitt, 2005. "A Staffing Algorithm for Call Centers with Skill-Based Routing," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 276-294, August.
    6. 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.
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    Cited by:

    1. Itay Gurvich & Ward Whitt, 2009. "Queue-and-Idleness-Ratio Controls in Many-Server Service Systems," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 363-396, May.
    2. Itay Gurvich & Mor Armony & Constantinos Maglaras, 2009. "Cross-Selling in a Call Center with a Heterogeneous Customer Population," Operations Research, INFORMS, vol. 57(2), pages 299-313, April.
    3. Iannoni, Ana Paula & Chiyoshi, Fernando & Morabito, Reinaldo, 2015. "A spatially distributed queuing model considering dispatching policies with server reservation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 49-66.
    4. Terekhov, Daria & Christopher Beck, J., 2009. "An extended queueing control model for facilities with front room and back room operations and mixed-skilled workers," European Journal of Operational Research, Elsevier, vol. 198(1), pages 223-231, October.
    5. Edward Hult & Houyuan Jiang & Daniel Ralph, 2014. "Exact computational approaches to a stochastic uncapacitated single allocation p-hub center problem," Computational Optimization and Applications, Springer, vol. 59(1), pages 185-200, October.
    6. Youngsoo Kim & Ramayya Krishnan & Linda Argote, 2012. "The Learning Curve of IT Knowledge Workers in a Computing Call Center," Information Systems Research, INFORMS, vol. 23(3-part-2), pages 887-902, September.
    7. 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.
    8. Sandjai Bhulai & Taoying Farenhorst-Yuan & Bernd Heidergott & Dinard Laan, 2012. "Optimal balanced control for call centers," Annals of Operations Research, Springer, vol. 201(1), pages 39-62, December.
    9. Jouini, Oualid & Pot, Auke & Koole, Ger & Dallery, Yves, 2010. "Online scheduling policies for multiclass call centers with impatient customers," European Journal of Operational Research, Elsevier, vol. 207(1), pages 258-268, November.
    10. Tolga Tezcan & J. G. Dai, 2010. "Dynamic Control of N -Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic," Operations Research, INFORMS, vol. 58(1), pages 94-110, February.
    11. 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.
    12. Itai Gurvich & James Luedtke & Tolga Tezcan, 2010. "Staffing Call Centers with Uncertain Demand Forecasts: A Chance-Constrained Optimization Approach," Management Science, INFORMS, vol. 56(7), pages 1093-1115, July.
    13. Itai Gurvich & Ward Whitt, 2010. "Service-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing," Operations Research, INFORMS, vol. 58(2), pages 316-328, April.
    14. Vijay Mehrotra & Kevin Ross & Geoff Ryder & Yong-Pin Zhou, 2012. "Routing to Manage Resolution and Waiting Time in Call Centers with Heterogeneous Servers," Manufacturing & Service Operations Management, INFORMS, vol. 14(1), pages 66-81, January.
    15. repec:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2924-x is not listed on IDEAS
    16. Z. Justin Ren & Yong-Pin Zhou, 2008. "Call Center Outsourcing: Coordinating Staffing Level and Service Quality," Management Science, INFORMS, vol. 54(2), pages 369-383, February.
    17. Itay Gurvich & Ward Whitt, 2009. "Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 237-253, June.
    18. Mor Armony & Amy R. Ward, 2010. "Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems," Operations Research, INFORMS, vol. 58(3), pages 624-637, June.
    19. 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.
    20. Achal Bassamboo & Assaf Zeevi, 2009. "On a Data-Driven Method for Staffing Large Call Centers," Operations Research, INFORMS, vol. 57(3), pages 714-726, June.
    21. Mor Armony & Itai Gurvich, 2010. "When Promotions Meet Operations: Cross-Selling and Its Effect on Call Center Performance," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 470-488, April.


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