Staffing to Maximize Profit for Call Centers with Impatient and Repeat-Calling Customers

Motivated by call center practice, we study the optimal staffing of many-server queues with impatient and repeat-calling customers. A call center is modeled as an M/M/s+M queue, which is developed to a behavioral queuing model in which customers come and go based on their satisfaction with waiting time. We explicitly take into account customer repeat behavior, which implies that satisfied customers might return and have an impact on the arrival rate. Optimality is defined as the number of agents that maximize revenues net of staffing costs, and we account for the characteristic that revenues are a direct function of staffing. Finally, we use numerical experiments to make certain comparisons with traditional models that do not consider customer repeat behavior. Furthermore, we indicate how managers might allocate staffing optimally with various customer behavior mechanisms.