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Staffing a call center with uncertain non-stationary arrival rate and flexibility

Author

Listed:
  • Shuang Qing Liao

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

  • Ger Koole

    (VU - Vrije Universiteit Amsterdam [Amsterdam])

  • Christian van Delft

    (Département Management des Opérations et des Systèmes d'Information - HEC Paris - Ecole des Hautes Etudes Commerciales)

  • Oualid Jouini

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec, Pôle de Recherche - Rouen Business School - Rouen Business School)

Abstract

We consider a multi-period staffing problem in a single-shift call center. The call center handles inbound calls, as well as some alternative back-office jobs. The call arrival process is assumed to follow a doubly non-stationary stochastic process with a random mean arrival rate. The inbound calls have to be handled as quickly as possible, while the back-office jobs, such as answering emails, may be delayed to some extent. The staffing problem is modeled as a generalized newsboy-type model under an expected cost criterion. Two different solution approaches are considered. First, by discretization of the underlying probability distribution, we explicitly formulate the expected cost newsboy-type formulation as a stochastic program. Second, we develop a robust programming formulation. The characteristics of the two methods and the associated optimal solutions are illustrated through a numerical study based on real-life data. In particular we focus on the numerical tractability of each formulation. We also show that the alternative workload of back-office jobs offers an interesting flexibility allowing to decrease the total operating cost of the call center.

Suggested Citation

  • Shuang Qing Liao & Ger Koole & Christian van Delft & Oualid Jouini, 2012. "Staffing a call center with uncertain non-stationary arrival rate and flexibility," Post-Print hal-00713790, HAL.
    • Handle: RePEc:hal:journl:hal-00713790
    DOI: 10.1007/s00291-011-0257-0
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    Citations

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    Cited by:

    1. Ibrahim, Rouba & Ye, Han & L’Ecuyer, Pierre & Shen, Haipeng, 2016. "Modeling and forecasting call center arrivals: A literature survey and a case study," International Journal of Forecasting, Elsevier, vol. 32(3), pages 865-874.
    2. 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.
    3. 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.
    4. 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.
    5. Wang, Haiyan & Olsen, Tava Lennon & Liu, Guiqing, 2018. "Service capacity competition with peak arrivals and delay sensitive customers," Omega, Elsevier, vol. 77(C), pages 80-95.
    6. Andersen, Anders Reenberg & Nielsen, Bo Friis & Reinhardt, Line Blander & Stidsen, Thomas Riis, 2019. "Staff optimization for time-dependent acute patient flow," European Journal of Operational Research, Elsevier, vol. 272(1), pages 94-105.
    7. Raj, G. & Roy, D. & de Koster, R. & Bansal, V., 2024. "Stochastic modeling of integrated order fulfillment processes with delivery time promise: Order picking, batching, and last-mile delivery," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1114-1128.
    8. Mattia, Sara & Rossi, Fabrizio & Servilio, Mara & Smriglio, Stefano, 2017. "Staffing and scheduling flexible call centers by two-stage robust optimization," Omega, Elsevier, vol. 72(C), pages 25-37.

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