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

S. Liao, C. van Delft, O. Jouini, G.M. Koole

Research output: Contribution to JournalArticleAcademicpeer-review

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. © 2011 Springer-Verlag.
Original languageEnglish
Pages (from-to)691-721
JournalOR Spectrum: Quantitative Approaches in Management
Volume34
Issue number3
Early online date23 May 2011
DOIs
Publication statusPublished - 2012

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