Staffing Call Centers with Uncertain Demand Forecasts: A Chance-Constrained Optimization Approach

Itai Gurvich (), James Luedtke () and Tolga Tezcan ()
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Itai Gurvich: Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
James Luedtke: Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706
Tolga Tezcan: Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

Management Science, 2010, vol. 56, issue 7, 1093-1115

Abstract: We consider the problem of staffing call centers with multiple customer classes and agent types operating under quality-of-service (QoS) constraints and demand rate uncertainty. We introduce a formulation of the staffing problem that requires that the QoS constraints are met with high probability with respect to the uncertainty in the demand rate. We contrast this chance-constrained formulation with the average-performance constraints that have been used so far in the literature. We then propose a two-step solution for the staffing problem under chance constraints. In the first step, we introduce a random static planning problem (RSPP) and discuss how it can be solved using two different methods. The RSPP provides us with a first-order (or fluid) approximation for the true optimal staffing levels and a staffing frontier. In the second step, we solve a finite number of staffing problems with known arrival rates--the arrival rates on the optimal staffing frontier. Hence, our formulation and solution approach has the important property that it translates the problem with uncertain demand rates to one with known arrival rates. The output of our procedure is a solution that is feasible with respect to the chance constraint and nearly optimal for large call centers.

Keywords: call centers; chance-constrained optimization; queueing (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (29)

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