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, earliness, and no-shows, which leads to inefficiency such as long patient waiting time and physician overtime. Academic/practical relevance: in our data set, 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. 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 are modeled under a P-Queue 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: Our model achieves significant reductions, in comparative studies against a sample average approximation (SAA) model, on patient waiting times, while keeping server overtime constant. Our simulations further characterize the types of uncertainties under which SAA performs poorly. Managerial insights: We present an optimization model that is easy to implement in practice and tractable to compute. Our simulations indicate that not accounting for patient re-entry or variability in patient behaviours will lead to suboptimal policies, especially when they have specific structure that should be considered.

Automated summary

The study focused on the intraday scheduling problem in orthopaedic clinics, addressing patient re-entry and variability in patient behaviors. By formulating a two-stage optimization problem and modeling queue dynamics, the model achieved significant reductions in patient waiting times.