Two-Way Hazards Model for Call Center Waiting Times

Abstract

Big Data in Business Analytics. The research is motivated by the business analytics application of call center workforce management, in particular modeling hazard functions of call center customer waiting times. Such waiting times reveal important patterns of customer patience (how long a customer is willing to wait) and offered wait (how long a customer is required to wait) which are closely related to customer satisfaction and service quality. Existing approaches only model hazard rate as a function of waiting time, ignoring the important time-of-day aspect. We develop a nonparametric two-way hazards model that incorporates both timescales simultaneously. The method is formulated as a penalized likelihood problem with a low-rank constraint, where the likelihood is derived from a two-way piecewise constant hazards model and the roughness penalty ensures smoothness of the hazard function in both timescales. The estimated surface is highly interpretable and can capture continuous patterns over waiting time across different times of day. We demonstrate the advantage of our method using data from a US banking call center. Interesting findings provide insights for both call center managers and general customers.