Intraday Scheduling with Patient Re-Entries and Variability in Behaviours

Problem definition: We consider the intraday scheduling problem in a group of Orthopaedic clinics where the planner schedules appointment times given a sequence of appointments. We consider patient re-entry - where patients may be required to go for an X-ray examination, returning to the same doctor they have seen - and variability in patient behaviours such as walk-ins, lateness, and no-shows, which leads to inefficiency such as long patient waiting time and physician overtime. Academic/Practical relevance: In our dataset, 25% of the patients are required to go for X-ray examination. We also found significant variability in patient behaviours. Hence patient re-entry and variability in behaviours are common, but we found little in the literature that could handle them. Our model has potential wider applications, e.g. in machine scheduling and ride-sharing. Methodology: We formulate the problem as a two-stage optimization problem, where scheduling decisions are made in the first stage. Queue dynamics in the second stage is modeled under a P-Queue (Bandi and Loke, 2018) paradigm which minimizes a risk index, representing the chance of violating performance targets such as patient waiting times. The model reduces to a sequence of mixed-integer linear optimization problems. Results: Simulations shows that our model can achieve as much as 15% reduction on various metrics including patient waiting time and server overtime over the benchmark policy. Managerial insights: We present an optimization model that is easy to implement in practice and tractable to compute. Our simulation indicates that not accounting for patient re-entry or variability in patient behaviours will lead to sub-optimal policies, especially when X-ray rate is high and lateness has a large spread.