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

Shuang Qing Liao (), Ger Koole, Christian van Delft and Oualid Jouini ()
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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

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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.

Keywords: Call centers; Uncertain arrival rate parameters; Staffing; Newsboy model; Stochastic programming; Robust programming (search for similar items in EconPapers)
Date: 2012-07
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Citations: View citations in EconPapers (8)

Published in OR Spectrum, 2012, 34 (3), pp.691-721. ⟨10.1007/s00291-011-0257-0⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00713790

DOI: 10.1007/s00291-011-0257-0

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