Appointment scheduling and real-time sequencing strategies for patient unpunctuality

Patient unpunctuality causes perturbations in healthcare operations, compromising productivity and service quality. In this paper, we propose an approach that mitigates the negative impacts of unpunctuality using both appointment scheduling and real-time sequencing taking into account patient unpunctuality, no-shows, random service durations, and multiple providers. The objective is to minimize the total cost incurred by patient waiting and provider overtime. An optimal real-time sequencing strategy is established to serve the waiting patient with the smallest “LAR” index, which is defined as the Larger of Appointment time and Real arrival time for a patient. The optimal appointment schedule is determined by a simulation optimization approach with unbiased gradient estimators. Sample path discontinuities are smoothed by smoothed perturbation analysis. Properties of the optimal real-time sequencing strategies are used for the efficient sample path gradient estimation. Extensive experiments demonstrate the effectiveness of the proposed algorithm. Using real data, numerical experiments illustrate that the optimal appointment schedule depends on the system parameters and differs significantly from those of the existing literature. Specifically, the pattern of the appointment schedule is determined by the number of providers and the real-time sequencing strategy. The length of the appointment intervals is sensitive to the degree of unpunctuality and no-shows. Compared with the schedules in the previous studies, our schedule can achieve a significant cost reduction. Further, the optimal real-time sequencing strategy outperforms the commonly-used strategies in practice (e.g., appointment order, arrival order). Managerial insights are also provided for hospital managers to schedule unpunctual patients.