To Wait or Not to Wait: Two-way Functional Hazards Model for Understanding Waiting in Call Centers

TL;DR

This paper introduces a two-way functional hazards model to analyze customer waiting behavior in call centers, capturing how patience and service quality vary with waiting time and time of day, aiding better staffing and management.

Contribution

The paper develops a novel two-way hazards model with low-rank and smoothness constraints, and applies an ADMM algorithm for efficient estimation, providing new insights into customer waiting patterns.

Findings

Customer patience varies with waiting duration and time of day.

Service quality patterns differ across times of day.

Model insights inform staffing and system protocol improvements.

Abstract

Telephone call centers offer a convenient communication channel between businesses and their customers. Efficient management of call centers needs accurate modeling of customer waiting behavior, which contains important information about customer patience (how long a customer is willing to wait) and service quality (how long a customer needs to wait to get served). Hazard functions offer dynamic characterization of customer waiting behavior, and provide critical inputs for agent scheduling. Motivated by this application, we develop a two-way functional hazards (tF-Hazards) model to study customer waiting behavior as a function of two timescales, waiting duration and the time of day that a customer calls in. The model stems from a two-way piecewise constant hazard function, and imposes low-rank structure and smoothness on the hazard rates to enhance interpretability. We exploit an alternating direction method of multipliers (ADMM) algorithm to optimize a penalized likelihood function of the model. We carefully analyze the data from a US bank call center, and provide informative insights about customer patience and service quality patterns along waiting time and across different times of a day. The findings provide primitive inputs for call center agent staffing and scheduling, as well as for call center practitioners to understand the effect of system protocols on customer waiting behavior.