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Routing and Staffing When Servers Are Strategic

Author

Listed:
  • Ragavendran Gopalakrishnan

    (Xerox Research Centre India, Bangalore, Karnataka 560103, India)

  • Sherwin Doroudi

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Amy R. Ward

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

  • Adam Wierman

    (Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125)

Abstract

Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by the system’s routing and staffing policies. This observation has consequences when modeling service system performance, and our objective in this paper is to investigate those consequences.We do this in the context of the M / M / N queue, which is the canonical model for large service systems. First, we present a model for “strategic” servers that choose their service rate to maximize a trade-off between an “effort cost,” which captures the idea that servers exert more effort when working at a faster rate, and a “value of idleness,” which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time (such as the longest idle server first policy). We find that the system must operate in a quality-driven regime, in which servers have idle time, for an equilibrium to exist. The implication is that to have an equilibrium solution the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:4:p:1033-1050
    DOI: 10.1287/opre.2016.1506
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    References listed on IDEAS

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    Cited by:

    1. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    2. Terry A. Taylor, 2018. "On-Demand Service Platforms," Manufacturing & Service Operations Management, INFORMS, vol. 20(4), pages 704-720, October.
    3. Debjit Roy & Eirini Spiliotopoulou & Jelle de Vries, 2022. "Restaurant analytics: Emerging practice and research opportunities," Production and Operations Management, Production and Operations Management Society, vol. 31(10), pages 3687-3709, October.
    4. Leon Yang Chu & Zhixi Wan & Dongyuan Zhan, 2018. "Harnessing the Double-edged Sword via Routing: Information Provision on Ride-hailing Platforms," Working Papers 18-04, NET Institute.
    5. Karen Donohue & Özalp Özer, 2020. "Behavioral Operations: Past, Present, and Future," Manufacturing & Service Operations Management, INFORMS, vol. 22(1), pages 191-202, January.
    6. Mor Armony & Guillaume Roels & Hummy Song, 2021. "Pooling Queues with Strategic Servers: The Effects of Customer Ownership," Operations Research, INFORMS, vol. 69(1), pages 13-29, January.
    7. Haji, Babak & Ross, Sheldon, 2020. "Minimizing expected discounted cost in a queueing loss model with discriminating arrivals," European Journal of Operational Research, Elsevier, vol. 282(2), pages 593-601.
    8. Benjamin Legros, 2021. "Agents’ Self‐Routing for Blended Operations to Balance Inbound and Outbound Services," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3599-3614, October.
    9. Jim G. Dai & Pengyi Shi, 2021. "Recent Modeling and Analytical Advances in Hospital Inpatient Flow Management," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1838-1862, June.
    10. 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.
    11. Legros, Benjamin, 2022. "The principal-agent problem for service rate event-dependency," European Journal of Operational Research, Elsevier, vol. 297(3), pages 949-963.
    12. Dongyuan Zhan & Amy R. Ward, 2019. "Staffing, Routing, and Payment to Trade off Speed and Quality in Large Service Systems," Operations Research, INFORMS, vol. 67(6), pages 1738-1751, November.
    13. Jacob, Jagan & Roet-Green, Ricky, 2021. "Ride solo or pool: Designing price-service menus for a ride-sharing platform," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1008-1024.
    14. Rami Atar & Subhamay Saha, 2017. "An ɛ -Nash Equilibrium with High Probability for Strategic Customers in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 626-647, August.

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