IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v64y2016i4p1033-1050.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2016.1506
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2016.1506?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gad Allon & Itai Gurvich, 2010. "Pricing and Dimensioning Competing Large-Scale Service Providers," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 449-469, August.
    2. B. Krishnamoorthi, 1963. "On Poisson Queue with Two Heterogeneous Servers," Operations Research, INFORMS, vol. 11(3), pages 321-330, June.
    3. Ehud Kalai & Morton I. Kamien & Michael Rubinovitch, 1992. "Optimal Service Speeds in a Competitive Environment," Management Science, INFORMS, vol. 38(8), pages 1154-1163, August.
    4. Tolga Tezcan, 2008. "Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 51-90, February.
    5. Francis de Véricourt & Yong-Pin Zhou, 2005. "Managing Response Time in a Call-Routing Problem with Service Failure," Operations Research, INFORMS, vol. 53(6), pages 968-981, December.
    6. Cohen-Charash, Yochi & Spector, Paul E., 2001. "The Role of Justice in Organizations: A Meta-Analysis," Organizational Behavior and Human Decision Processes, Elsevier, vol. 86(2), pages 278-321, November.
    7. 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.
    8. 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.
    9. Gérard P. Cachon & Fuqiang Zhang, 2007. "Obtaining Fast Service in a Queueing System via Performance-Based Allocation of Demand," Management Science, INFORMS, vol. 53(3), pages 408-420, March.
    10. 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.
    11. 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.
    12. Stephen M. Gilbert & Z. Kevin Weng, 1998. "Incentive Effects Favor Nonconsolidating Queues in a Service System: The Principal--Agent Perspective," Management Science, INFORMS, vol. 44(12-Part-1), pages 1662-1669, December.
    13. Gérard P. Cachon & Patrick T. Harker, 2002. "Competition and Outsourcing with Scale Economies," Management Science, INFORMS, vol. 48(10), pages 1314-1333, October.
    14. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    15. Diwas S. Kc & Christian Terwiesch, 2009. "Impact of Workload on Service Time and Patient Safety: An Econometric Analysis of Hospital Operations," Management Science, INFORMS, vol. 55(9), pages 1486-1498, September.
    16. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    17. 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.
    18. Yaşar Levent Koçağa & Mor Armony & Amy R. Ward, 2015. "Staffing Call Centers with Uncertain Arrival Rates and Co-sourcing," Production and Operations Management, Production and Operations Management Society, vol. 24(7), pages 1101-1117, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Legros, Benjamin, 2022. "The principal-agent problem for service rate event-dependency," European Journal of Operational Research, Elsevier, vol. 297(3), pages 949-963.
    5. 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.
    6. 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.
    7. Terry A. Taylor, 2018. "On-Demand Service Platforms," Manufacturing & Service Operations Management, INFORMS, vol. 20(4), pages 704-720, October.
    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. 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.
    10. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    11. 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.
    12. Karen Donohue & Özalp Özer, 2020. "Behavioral Operations: Past, Present, and Future," Manufacturing & Service Operations Management, INFORMS, vol. 22(1), pages 191-202, January.
    13. 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.
    14. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jinsheng Chen & Jing Dong & Pengyi Shi, 2020. "A survey on skill-based routing with applications to service operations management," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 53-82, October.
    2. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    3. 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.
    4. Dongyuan Zhan & Amy R. Ward, 2014. "Threshold Routing to Trade Off Waiting and Call Resolution in Call Centers," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 220-237, May.
    5. 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.
    6. Mor Armony & Avishai Mandelbaum, 2011. "Routing and Staffing in Large-Scale Service Systems: The Case of Homogeneous Impatient Customers and Heterogeneous Servers," Operations Research, INFORMS, vol. 59(1), pages 50-65, February.
    7. 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.
    8. Sarang Deo & Itai Gurvich, 2011. "Centralized vs. Decentralized Ambulance Diversion: A Network Perspective," Management Science, INFORMS, vol. 57(7), pages 1300-1319, July.
    9. Francis de Véricourt & Otis B. Jennings, 2008. "Dimensioning Large-Scale Membership Services," Operations Research, INFORMS, vol. 56(1), pages 173-187, February.
    10. Lauren Xiaoyuan Lu & Jan A. Van Mieghem & R. Canan Savaskan, 2009. "Incentives for Quality Through Endogenous Routing," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 254-273, July.
    11. J. G. Dai & Tolga Tezcan, 2011. "State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 271-320, May.
    12. 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.
    13. Adan, Ivo J.B.F. & Boon, Marko A.A. & Weiss, Gideon, 2019. "Design heuristic for parallel many server systems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 259-277.
    14. Sunil Kumar & Ramandeep S. Randhawa, 2010. "Exploiting Market Size in Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 511-526, September.
    15. Krishnan S. Anand & M. Faz{i}l Paç & Senthil Veeraraghavan, 2011. "Quality-Speed Conundrum: Trade-offs in Customer-Intensive Services," Management Science, INFORMS, vol. 57(1), pages 40-56, January.
    16. 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.
    17. 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.
    18. Avishai Mandelbaum & Petar Momčilović & Yulia Tseytlin, 2012. "On Fair Routing from Emergency Departments to Hospital Wards: QED Queues with Heterogeneous Servers," Management Science, INFORMS, vol. 58(7), pages 1273-1291, July.
    19. Gad Allon & Itai Gurvich, 2010. "Pricing and Dimensioning Competing Large-Scale Service Providers," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 449-469, August.
    20. Hummy Song & Anita L. Tucker & Karen L. Murrell, 2015. "The Diseconomies of Queue Pooling: An Empirical Investigation of Emergency Department Length of Stay," Management Science, INFORMS, vol. 61(12), pages 3032-3053, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:64:y:2016:i:4:p:1033-1050. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.