IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v32y2024i3d10.1007_s10100-023-00883-z.html
   My bibliography  Save this article

A fast staffing algorithm for multistage call centers with impatient customers and time-dependent overflow

Author

Listed:
  • Michael Manitz

    (Mercator School of Management, University of Duisburg/Essen)

  • Marc-Philip Piehl

    (Mercator School of Management, University of Duisburg/Essen)

Abstract

Ensuring customer satisfaction is one of the main objectives of a call center. We focus on the question of how many agents are necessary and how they should be allocated to maintain a service level threshold and reduce the expected waiting time of the customers. In this paper, we consider a multistage call center that consists of a front and a back office, impatient customers, and an overflow mechanism. Based on the performance evaluation of such a system using a continuous-time Markov chain, a configuration of agents is determined using a binary search algorithm. We focus on structural insights, e.g., convexity conditions, to obtain a quick solution for the staffing problem. Since monotonicity does not always hold, the approach is heuristic. The numerical results show the performance of the algorithm. The influence of the fraction requiring second-level service in the back office and the impatience rate for the minimum number of agents is shown.

Suggested Citation

  • Michael Manitz & Marc-Philip Piehl, 2024. "A fast staffing algorithm for multistage call centers with impatient customers and time-dependent overflow," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 763-791, September.
    • Handle: RePEc:spr:cejnor:v:32:y:2024:i:3:d:10.1007_s10100-023-00883-z
    DOI: 10.1007/s10100-023-00883-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-023-00883-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10100-023-00883-z?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Linda V. Green & Peter J. Kolesar & João Soares, 2001. "Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands," Operations Research, INFORMS, vol. 49(4), pages 549-564, August.
    2. 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.
    3. Stolletz, Raik & Manitz, Michael, 2013. "The impact of a waiting-time threshold in overflow systems with impatient customers," Omega, Elsevier, vol. 41(2), pages 280-286.
    4. Auke Pot & Sandjai Bhulai & Ger Koole, 2008. "A Simple Staffing Method for Multiskill Call Centers," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 421-428, December.
    5. Stolletz, Raik, 2008. "Approximation of the non-stationary M(t)/M(t)/c(t)-queue using stationary queueing models: The stationary backlog-carryover approach," European Journal of Operational Research, Elsevier, vol. 190(2), pages 478-493, October.
    6. G. M. Koole & B. F. Nielsen & T. B. Nielsen, 2012. "First in Line Waiting Times as a Tool for Analysing Queueing Systems," Operations Research, INFORMS, vol. 60(5), pages 1258-1266, October.
    Full references (including those not matched with items on IDEAS)

    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. Ta, Thuy Anh & Chan, Wyean & Bastin, Fabian & L’Ecuyer, Pierre, 2021. "A simulation-based decomposition approach for two-stage staffing optimization in call centers under arrival rate uncertainty," European Journal of Operational Research, Elsevier, vol. 293(3), pages 966-979.
    2. Alex Roubos & Ger Koole & Raik Stolletz, 2012. "Service-Level Variability of Inbound Call Centers," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 402-413, July.
    3. Merve Bodur & James R. Luedtke, 2017. "Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty," Management Science, INFORMS, vol. 63(7), pages 2073-2091, July.
    4. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    5. Izady, Navid & Worthington, Dave, 2012. "Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments," European Journal of Operational Research, Elsevier, vol. 219(3), pages 531-540.
    6. Barth, Wolfgang & Manitz, Michael & Stolletz, Raik, 2008. "Analysis of Two-Level Support Systems with Time-Dependent Overflow - A Banking Application," Hannover Economic Papers (HEP) dp-399, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    7. Örmeci, E. Lerzan & Salman, F. Sibel & Yücel, Eda, 2014. "Staff rostering in call centers providing employee transportation," Omega, Elsevier, vol. 43(C), pages 41-53.
    8. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    9. Van den Bergh, Jorne & Beliën, Jeroen & De Bruecker, Philippe & Demeulemeester, Erik & De Boeck, Liesje, 2013. "Personnel scheduling: A literature review," European Journal of Operational Research, Elsevier, vol. 226(3), pages 367-385.
    10. Narayanan C. Viswanath, 2022. "Transient study of Markov models with time-dependent transition rates," Operational Research, Springer, vol. 22(3), pages 2209-2243, July.
    11. Elvin Coban & Aliza Heching & Alan Scheller‐Wolf, 2019. "Service Center Staffing with Cross‐Trained Agents and Heterogeneous Customers," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 788-809, April.
    12. Yiting Xing & Ling Li & Zhuming Bi & Marzena Wilamowska‐Korsak & Li Zhang, 2013. "Operations Research (OR) in Service Industries: A Comprehensive Review," Systems Research and Behavioral Science, Wiley Blackwell, vol. 30(3), pages 300-353, May.
    13. Achal Bassamboo & J. Michael Harrison & Assaf Zeevi, 2006. "Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method," Operations Research, INFORMS, vol. 54(3), pages 419-435, June.
    14. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    15. Benjamin Legros & Sihan Ding & Rob Mei & Oualid Jouini, 2017. "Call centers with a postponed callback offer," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1097-1125, October.
    16. Rodríguez-Sanz, à lvaro & Fernández de Marcos, Alberto & Pérez-Castán, Javier A. & Comendador, Fernando Gómez & Arnaldo Valdés, Rosa & París Loreiro, à ngel, 2021. "Queue behavioural patterns for passengers at airport terminals: A machine learning approach," Journal of Air Transport Management, Elsevier, vol. 90(C).
    17. Legros, Benjamin & Fransoo, Jan C., 2023. "Admission and pricing optimization of on-street parking with delivery bays," Other publications TiSEM 6d41ee5c-27dc-4d34-aff1-4, Tilburg University, School of Economics and Management.
    18. 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.
    19. Castillo, Ignacio & Joro, Tarja & Li, Yong Yue, 2009. "Workforce scheduling with multiple objectives," European Journal of Operational Research, Elsevier, vol. 196(1), pages 162-170, July.
    20. Dietz, Dennis C., 2011. "Practical scheduling for call center operations," Omega, Elsevier, vol. 39(5), pages 550-557, October.

    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:spr:cejnor:v:32:y:2024:i:3:d:10.1007_s10100-023-00883-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.