IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v67y2019i6p1738-1751.html
   My bibliography  Save this article

Staffing, Routing, and Payment to Trade off Speed and Quality in Large Service Systems

Author

Listed:
  • Dongyuan Zhan

    (School of Management, University College London, London WC1E 6BT, United Kingdom)

  • Amy R. Ward

    (Booth School of Business, The University of Chicago, Chicago, Illinois 60637)

Abstract

Most common queueing models used for service-system design assume that the servers work at fixed (possibly heterogeneous) rates. However, real-life service systems are staffed by people, and people may change their service speed in response to incentives. The delicacy is that the resulting service speed is jointly affected by staffing, routing, and payment decisions. Our objective in this paper is to find a joint staffing, routing, and payment policy that induces optimal service-system performance. We do this under the assumption that there is a trade-off between service speed and quality and that employees are paid based on both. The employees selfishly choose their own service speed to maximize their own expected utility (which depends on the staffing through their busy time). The endogenous service-rate assumption leads to a centralized control problem in which the system manager jointly optimizes over the staffing, routing, and service rate. By solving the centralized control problem under fluid scaling, we find four different economically optimal operating regimes: critically loaded, efficiency driven, quality driven, and intentional idling (in which there is simultaneous customer abandonment and server idling). Then we show that a simple piece-rate payment scheme can be used to solve the associated decentralized control problem under fluid scaling.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:6:p:1738-1751
    DOI: 10.1287/opre.2018.1838
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/opre.2018.1838
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2018.1838?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. Rouba Ibrahim, 2018. "Managing Queueing Systems Where Capacity is Random and Customers are Impatient," Production and Operations Management, Production and Operations Management Society, vol. 27(2), pages 234-250, February.
    2. 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.
    3. 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.
    4. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    5. 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.
    6. Philipp Afèche, 2013. "Incentive-Compatible Revenue Management in Queueing Systems: Optimal Strategic Delay," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 423-443, July.
    7. Constantinos Maglaras & Assaf Zeevi, 2003. "Pricing and Capacity Sizing for Systems with Shared Resources: Approximate Solutions and Scaling Relations," Management Science, INFORMS, vol. 49(8), pages 1018-1038, August.
    8. Carri W. Chan & Galit Yom-Tov & Gabriel Escobar, 2014. "When to Use Speedup: An Examination of Service Systems with Returns," Operations Research, INFORMS, vol. 62(2), pages 462-482, April.
    9. 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.
    10. Vasiliki Kostami & Sampath Rajagopalan, 2014. "Speed–Quality Trade-Offs in a Dynamic Model," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 104-118, February.
    11. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    12. 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.
    13. Saed Alizamir & Francis de Véricourt & Peng Sun, 2013. "Diagnostic Accuracy Under Congestion," Management Science, INFORMS, vol. 59(1), pages 157-171, December.
    14. 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.
    15. HOLMSTROM, Bengt, 1979. "Moral hazard and observability," LIDAM Reprints CORE 379, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Amy R. Ward & Sunil Kumar, 2008. "Asymptotically Optimal Admission Control of a Queue with Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 167-202, February.
    17. 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.
    18. Ryan W. Buell & Tami Kim & Chia-Jung Tsay, 2017. "Creating Reciprocal Value Through Operational Transparency," Management Science, INFORMS, vol. 63(6), pages 1673-1695, June.
    19. 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.
    20. Gérard P. Cachon & Patrick T. Harker, 2002. "Competition and Outsourcing with Scale Economies," Management Science, INFORMS, vol. 48(10), pages 1314-1333, October.
    21. Xin Geng & Woonghee Tim Huh & Mahesh Nagarajan, 2015. "Fairness Among Servers When Capacity Decisions Are Endogenous," Production and Operations Management, Production and Operations Management Society, vol. 24(6), pages 961-974, June.
    22. 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.
    23. William S. Lovejoy & Kannan Sethuraman, 2000. "Congestion and Complexity Costs in a Plant with Fixed Resources that Strives to Make Schedule," Manufacturing & Service Operations Management, INFORMS, vol. 2(3), pages 221-239, February.
    24. Masha Shunko & Julie Niederhoff & Yaroslav Rosokha, 2018. "Humans Are Not Machines: The Behavioral Impact of Queueing Design on Service Time," Management Science, INFORMS, vol. 64(1), pages 453-473, January.
    25. Constantinos Maglaras & Assaf Zeevi, 2005. "Pricing and Design of Differentiated Services: Approximate Analysis and Structural Insights," Operations Research, INFORMS, vol. 53(2), pages 242-262, April.
    26. 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.
    27. Bengt Holmstrom, 1979. "Moral Hazard and Observability," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 74-91, Spring.
    28. Philipp Afèche & J. Michael Pavlin, 2016. "Optimal Price/Lead-Time Menus for Queues with Customer Choice: Segmentation, Pooling, and Strategic Delay," Management Science, INFORMS, vol. 62(8), pages 2412-2436, August.
    29. Laurens G. Debo & L. Beril Toktay & Luk N. Van Wassenhove, 2008. "Queuing for Expert Services," Management Science, INFORMS, vol. 54(8), pages 1497-1512, August.
    30. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(3), pages 488-500.
    31. Sameer Hasija & Edieal Pinker & Robert A. Shumsky, 2010. "OM Practice--Work Expands to Fill the Time Available: Capacity Estimation and Staffing Under Parkinson's Law," Manufacturing & Service Operations Management, INFORMS, vol. 12(1), pages 1-18, September.
    32. Achal Bassamboo & Ramandeep S. Randhawa, 2010. "On the Accuracy of Fluid Models for Capacity Sizing in Queueing Systems with Impatient Customers," Operations Research, INFORMS, vol. 58(5), pages 1398-1413, October.
    33. 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.
    34. Mor Armony & Constantinos Maglaras, 2004. "Contact Centers with a Call-Back Option and Real-Time Delay Information," Operations Research, INFORMS, vol. 52(4), pages 527-545, August.
    35. Xu Sun & Ward Whitt, 2018. "Creating Work Breaks from Available Idleness," Manufacturing & Service Operations Management, INFORMS, vol. 20(4), pages 721-736, October.
    36. 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.
    37. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    38. Costis Maglaras & John Yao & Assaf Zeevi, 2018. "Optimal Price and Delay Differentiation in Large-Scale Queueing Systems," Management Science, INFORMS, vol. 64(5), pages 2427-2444, May.
    39. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    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. Legros, Benjamin, 2022. "The principal-agent problem for service rate event-dependency," European Journal of Operational Research, Elsevier, vol. 297(3), pages 949-963.
    2. Xu, Shuling & Hall, Nicholas G., 2021. "Fatigue, personnel scheduling and operations: Review and research opportunities," European Journal of Operational Research, Elsevier, vol. 295(3), pages 807-822.
    3. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    4. 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.

    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. Terry A. Taylor, 2018. "On-Demand Service Platforms," Manufacturing & Service Operations Management, INFORMS, vol. 20(4), pages 704-720, October.
    2. 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.
    3. Masha Shunko & Julie Niederhoff & Yaroslav Rosokha, 2018. "Humans Are Not Machines: The Behavioral Impact of Queueing Design on Service Time," Management Science, INFORMS, vol. 64(1), pages 453-473, January.
    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. Benjamin Legros, 2022. "The principal-agent problem for service rate event-dependency," Post-Print hal-03605421, HAL.
    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. 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.
    8. 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.
    9. Vasiliki Kostami & Sampath Rajagopalan, 2014. "Speed–Quality Trade-Offs in a Dynamic Model," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 104-118, February.
    10. Delasay, Mohammad & Ingolfsson, Armann & Kolfal, Bora & Schultz, Kenneth, 2019. "Load effect on service times," European Journal of Operational Research, Elsevier, vol. 279(3), pages 673-686.
    11. Lily Jiang & Hsi-Cheng Yu, 2014. "Compensation systems and earnings inequality," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(1), pages 99-116, March.
    12. 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.
    13. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    14. Bartsch, Elga, 1996. "Enforcement of environmental liability in the case of uncertain causality and asymmetric information," Kiel Working Papers 755, Kiel Institute for the World Economy (IfW Kiel).
    15. Alexander, Corinne & Ivanic, Rasto & Rosch, Stephanie & Tyner, Wallace & Wu, Steven Y. & Yoder, Joshua R., 2012. "Contract theory and implications for perennial energy crop contracting," Energy Economics, Elsevier, vol. 34(4), pages 970-979.
    16. 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.
    17. Giorgio Coricelli & Luigi Luini, 1999. "Double Moral Hazard: an Experiment on Warranties," CEEL Working Papers 9901, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
    18. Jose A. Guajardo & Morris A. Cohen, 2018. "Service Differentiation and Operating Segments: A Framework and an Application to After-Sales Services," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 440-454, July.
    19. Henri Loubergé, 1998. "Risk and Insurance Economics 25 Years After," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 23(4), pages 540-567, October.
    20. Ying Xu & Alan Scheller-Wolf & Katia Sycara, 2015. "The Benefit of Introducing Variability in Single-Server Queues with Application to Quality-Based Service Domains," Operations Research, INFORMS, vol. 63(1), pages 233-246, February.

    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:67:y:2019:i:6:p:1738-1751. 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.