Appointment scheduling is essential for healthcare services to streamline patient flow and improve operational efficiency. This study focuses on patient appointment management in healthcare services involving multiple service stages and multiple service providers at each stage. Real-world multi-stage, multi-server systems often adopt a queue-like service flow, which is characterized by the First-Come, First-Served rule for fairness and the work-conserving rule that starts services immediately when patients and resources are available. To incorporate these operational practices into the appointment decision-making process, we adopt a simulation optimization approach. However, these practices introduce discontinuities in the sample path cost function, resulting in biased gradient estimators. To address this challenge, we apply the conditional Monte Carlo technique to smooth the cost function and develop a tailored stochastic gradient descent algorithm based on an unbiased gradient estimator for optimizing appointment decisions. Our numerical experiments demonstrate that the proposed approach consistently outperforms benchmark stochastic gradient descent algorithms across various settings. Based on these results, we further derive managerial insights into shift design and patient sequencing in healthcare operations.
To inhibit fare evasion in proof-of-payment bus transportation systems, the transit authority schedules unpredictable passenger inspections conducted by inspection teams. The heterogeneous operating conditions and workloads faced by fare inspectors can be addressed by partitioning the transportation network into districts that ensure the efficient allocation of inspection teams to/from their assignments, as well as the fair distribution of workload among inspection teams. In this paper, we address the design of compact and balanced districts under an on-board fare inspection system, where the workload is defined in terms of the number of buses. Since buses travel throughout the transportation network, the workload is shared among bus stops, defining a novel districting problem. The problem of districting a bus transportation network under shared workload is formulated as a mixed-integer programming model for which a cutting-plane based branch-and-cut solution approach is proposed. The computational results highlight the effectiveness of the solution approach for large-scale networks when a tessellation technique and a well-designed restricted set of candidate district centers are used. Furthermore, we observe that a more balanced network design in terms of the number of buses leads to unbalanced designs in terms of geographic size.
