A Semi-Parametric Bayesian Model for Call Center Arrivals

Abstract

Nonhomogeneous Poisson process models have commonly been used to analyze and forecast arrivals. Such processes require specification of intensity (arrival rate) functions, which are typically defined in parametric form. The accuracy of the parametric models is highly sensitive to the choice of the specific intensity function for the arrival process. We use a Bayesian framework by proposing a nonparametric form for the intensity function and introduce a robust semi-parametric model. The model is suitable for analyzing both interval censored count data and time of arrival data, and can capture both monotonic and non-monotonic arrival intensity. The intensity function in the model can be modulated to incorporate auxiliary information as well as seasonal and random effect components. We develop the Bayesian analysis of the proposed model and implement it on two real call center data sets with different characteristics. We also consider several extensions to our model and develop their Bayesian analyses. Our random effects model with cumulative baseline intensity changing on the days of the week and interday correlation with Markov evolution extension models provide high predictive accuracy. We also show that our proposed semi-parametric model has robust performance for out-of-sample predictions. Accurate predictions of arrivals will assist managers in determining appropriate staffing levels and effective workforce scheduling, resulting in more efficient operations.

Keywords: call center; advertising; Bayesian nonparametric; gamma process; doubly stochastic

JEL Classification: C11, C14, C15, C44, C53, C55