Service system planning in the presence of a random arrival rate

Abstract

A fundamental workforce management challenge for inbound call center managers is to determine the number of agents to be scheduled to answer calls during each time period. These decisions are typically based on the desire to minimize cost while achieving some pre-determined service objectives. These service objectives are typically functionals of the customer queue time distributions, which in turn are highly dependent on the distribution of customer arrivals. The traditional call center modeling approach is to divide a given planning horizon into a series of time periods, and to assume a deterministic fixed-rate Poisson arrival process for each period. These arrival processes then determine the performance measures that drive the selection of staffing levels. The arrival rate is very often not known with certainty, as we show in this paper through the analysis of historical data from several call centers. This type of uncertainty arises either because the arrival rate varies randomly over time or because the rate is simply unknown due to lack of information. In either case, the uncertainty in the arrival rate has major implications for the validity of traditional performance measures and consequently on the quality of staffing decisions. In this paper, we consider two potential forms of uncertainty in the arrival rates, and in each case address the question of what performance measures to use in order to support staffing decisions. We also explore ways to compute appropriate estimates for these performance measures. We clarify when the analytical approximations can be expected to be accurate and describe when and how simulation should be used to provide better estimates. 1

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