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

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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https://hal-hec.archives-ouvertes.fr/hal-00713790
Contributor : Antoine Haldemann <>
Submitted on : Monday, July 2, 2012 - 4:11:22 PM
Last modification on : Friday, April 19, 2019 - 2:54:14 PM

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Shuang Qing Liao, Ger Koole, Christian Van Delft, Oualid Jouini. Staffing a call center with uncertain non-stationary arrival rate and flexibility. OR Spectrum, Springer Verlag, 2012, 34 (3), pp.691-721. ⟨10.1007/s00291-011-0257-0⟩. ⟨hal-00713790⟩

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