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

• Published in: European journal of operational research Vol. 207; no. 3; pp. 1608 - 1619
• Main Authors: Robbins, Thomas R., Harrison, Terry P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.12.2010; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Arrivals; Call centers; Decisions; Exact sciences and technology; Firm modelling; Integer programming; Mathematical models; Mathematical programming; Operational research and scientific management; Operational research. Management science; Optimization; OR in manpower planning; Queuing theory. Traffic theory; Risk management; Schedules; Scheduling; Scheduling, sequencing; Service level agreements; Stochastic models; Stochastic programming; Stochastic programming Scheduling OR in manpower planning Call centers; Stochasticity; Studies; Uncertainty; Call centers; Scheduling; Stochastic programming; OR in manpower planning; Manpower; Stochastic model; Costs; Program optimization; Variability; Subcontracting; Modeling; Uncertain system; Arrival process; Reduced order systems; Call centres; Probabilistic approach; Decision making; One step method; Mixed integer programming; Staff management; Constrained optimization; Dimensioning; Integer programming; Mixed problem; Outsourcing; Risk management; Contract; Service quality
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2010.06.013

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.