Multi-Class Advance Patient Scheduling
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Date
2021-09-29
Authors
Shirani Faradonbeh, Mohamad Sadegh
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
The problem of advance scheduling of service appointments for patients arriving to a healthcare facility received a lot of attentions in the literature of operations management. Broadly speaking, the main goal is on the efficient assignment of patients entering the system to the next operating days, advance in time and in a dynamic manner. In particular, the problem of multi-class advance patient scheduling, that aims to incorporate differences in the priority levels of patient classes, is of interest in many situations. In this setting, one needs to address important challenges to efficiently utilize the limited and costly resources of the underlying healthcare facilities. Furthermore, a reliable scheduling policy needs to reserve sufficient capacity for high-priority patients, in order to avoid long waiting-times for urgent cases in the future. Accordingly, at every time instant, the policy needs to consider all outstanding appointments, as well as uncertainties in the future demand.
This work presents the first theoretically tractable framework for design and analysis of efficient advance scheduling policies in a multi-class setting. First, we provide a realistic formulation of the problem that reflects both the transient as well as the long-term behavior of scheduling policies. Then, we study optimal policies that efficiently schedule patients of different classes and characterize the resulting coarse-grained fluid dynamics, as well as the finer dynamics of diffusion approximation. In fact, the former yields to a simple policy that schedules all patients on the day of their arrival, and also sets the stage for the analysis of the latter stochastic dynamical model. Then, we proceed towards considering diffusion processes based on which the study of scheduling policies becomes a Brownian control problem. Finally, by leveraging a dynamic programming approach, we characterize the optimal policy and validate it through numerical implementations.