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A Logarithmic Safety Staffing Rule for Contact Centers with Call Blending

Author

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  • Guodong Pang

    (The Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, Pennsylvania State University, University Park, Pennsylvania 16802)

  • Ohad Perry

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

We consider large contact centers that handle two types of jobs—inbound and outbound—simultaneously, a process commonly referred to as call blending . Inbound work arrives to the system according to an exogenous arrival process, whereas outbound work is generated by the contact center. We assume that there is an infinite supply of outbound work to process, and that inbound calls are prioritized over the outbound calls. We propose a logarithmic safety staffing rule, combined with a threshold control policy, ensuring that agents' utilization is very close to one at all times, but that there are practically always idle agents present. Specifically, we prove that it is possible to have almost all inbound calls answered immediately upon their arrival, in addition to satisfying a target long-run throughput rate of outbound calls, with at most a negligible proportion of those calls dropped. Simulation experiments demonstrate the effectiveness and accuracy of our analysis. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Suggested Citation

  • Guodong Pang & Ohad Perry, 2015. "A Logarithmic Safety Staffing Rule for Contact Centers with Call Blending," Management Science, INFORMS, vol. 61(1), pages 73-91, January.
    • Handle: RePEc:inm:ormnsc:v:61:y:2015:i:1:p:73-91
    DOI: 10.1287/mnsc.2014.2019
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    References listed on IDEAS

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    1. Ohad Perry & Ward Whitt, 2013. "A Fluid Limit for an Overloaded X Model via a Stochastic Averaging Principle," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 294-349, 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. Itai Gurvich & Ohad Perry, 2012. "Overflow Networks: Approximations and Implications to Call Center Outsourcing," Operations Research, INFORMS, vol. 60(4), pages 996-1009, August.
    4. Douglas A. Samuelson, 1999. "Predictive Dialing for Outbound Telephone Call Centers," Interfaces, INFORMS, vol. 29(5), pages 66-81, October.
    5. 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.
    6. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    7. Achal Bassamboo & Ramandeep S. Randhawa & Jan A. Van Mieghem, 2012. "A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems," Operations Research, INFORMS, vol. 60(6), pages 1423-1435, December.
    8. Ohad Perry & Ward Whitt, 2011. "A Fluid Approximation for Service Systems Responding to Unexpected Overloads," Operations Research, INFORMS, vol. 59(5), pages 1159-1170, October.
    9. Noah Gans & Yong-Pin Zhou, 2003. "A Call-Routing Problem with Service-Level Constraints," Operations Research, INFORMS, vol. 51(2), pages 255-271, April.
    10. 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.
    11. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
    12. 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.
    13. 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.
    14. 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.
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    Cited by:

    1. Li Xiao & Susan H. Xu & David D. Yao & Hanqin Zhang, 2022. "Optimal staffing for ticket queues," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 309-351, October.
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    3. Vianney Bœuf & Philippe Robert, 2019. "A stochastic analysis of a network with two levels of service," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 203-232, August.

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