An Optimization-Based Scheduling Methodology for Appointment Systems with Heterogeneous Customers and Nonstationary Arrival Processes

In this paper, we analyze appointment systems involving heterogeneous customers, each requesting different services, with nonstationary arrival processes. The main goal is to identify server schedules that lead to good-performing systems, which we measure through the expected system time and the number of customer rejections. This decision problem arises in a number of applications and is especially relevant when certain service types dominate other service types. A key challenge in this analysis is the lack of closed-form analytical expressions that characterize the performance of the system. In this work, we construct a stylized optimization model based on a pointwise stationary approximation that emulates the original stochastic system. An analysis of the resulting stylized model comprised of a single customer type leads to key structural properties which we use to devise a globally convergent solution scheme that runs in polynomial time. This solution scheme is then generalized to the case of multiple customer types for two different formulations of the decision problem. To demonstrate the effectiveness of the proposed framework, we conduct a case study on Texas A&M University’s College and Psychological Services. Our results show that our optimal solutions substantially improve the performance of the system over current practices by reducing access time for critical mental health services by as much as 56%. Our analysis also identifies an easily implementable scheduling policy consisting of a single modification whose performance is within 10% of the more complex policies.