Customer Acquisition and Retention: A Fluid Approach for Staffing

Abstract

We investigate the trade-off between acquisition and retention efforts when customers are sensitive to the quality of service they receive, i.e., whether they get timely access to a company's resources when requested. We model the problem as a multi-class queueing network with new and returning customers, time-dependent arrivals, and abandonment. We derive its fluid approximation; a system of ordinary linear differential equations with continuous, piecewise smooth, right-hand sides. Based on the fluid model, we propose a novel approach to determine optimal stationary staffing levels for new and returning customer queues in anticipation of future time-varying dynamics. Using system accessibility as a proxy for service quality and staffing levels as a proxy for investment, we demonstrate how to apply our approach to two families of time-varying arrival functions motivated by real-world applications: an advertising campaign and a clinical setting. In a numerical study, we demonstrate that our approach creates staffing policies that maximize throughput while balancing acquisition and retention efforts more effectively (i.e., equitable abandonment from each customer class) than commonly used near-stationary methods such as segmentation-based square-root staffing policies. Our model confirms that acquisition and retention efforts are intimately linked; this has been found in empirical studies but not captured in the operations literature. We suggest that in time-varying environments, focusing on either alone is not sufficient to maintain high levels of throughput and service quality.