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

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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.

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Authors and Affiliations

  1. Laboratoire Génie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92290, Châtenay-Malabry, France

    Shuangqing Liao & Oualid Jouini

  2. Department of Mathematics, VU University Amsterdam, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Ger Koole

  3. Département Management des Opérations et des Systèmes d’Information, Groupe HEC, Rue de la Libération, 78351, Jouy-en-Josas, France

    Christian van Delft

  4. Rouen Business School, Boulevard André Siegfried, 76130, Mont-Saint-Aignan, France

    Oualid Jouini

Authors
  1. Shuangqing Liao
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  2. Ger Koole
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  3. Christian van Delft
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  4. Oualid Jouini
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Correspondence to Shuangqing Liao.

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Liao, S., Koole, G., van Delft, C. et al. Staffing a call center with uncertain non-stationary arrival rate and flexibility. OR Spectrum 34, 691–721 (2012). https://doi.org/10.1007/s00291-011-0257-0

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