A stochastic programming model for scheduling call centers with global Service Level Agreements

Thomas R. Robbins, Terry Paul Harrison

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


We consider the issue of call center scheduling in an environment where arrivals rates are highly variable, aggregate volumes are uncertain, and the call center is subject to a global service level constraint. This paper is motivated by work with a provider of outsourced technical support services where call volumes exhibit significant variability and uncertainty. The outsourcing contract specifies a Service Level Agreement that must be satisfied over an extended period of a week or month. We formulate the problem as a mixed-integer stochastic program. Our model has two distinctive features. Firstly, we combine the server sizing and staff scheduling steps into a single optimization program. Secondly, we explicitly recognize the uncertainty in period-by-period arrival rates. We show that the stochastic formulation, in general, calculates a higher cost optimal schedule than a model which ignores variability, but that the expected cost of this schedule is lower. We conduct extensive experimentation to compare the solutions of the stochastic program with the deterministic programs, based on mean valued arrivals. We find that, in general, the stochastic model provides a significant reduction in the expected cost of operation. The stochastic model also allows the manager to make informed risk management decisions by evaluating the probability that the Service Level Agreement will be achieved.

Original languageEnglish (US)
Pages (from-to)1608-1619
Number of pages12
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - Dec 16 2010

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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