Joint patient selection and scheduling under no‐shows: Theory and application in proton therapy

We study how to admit and schedule heterogeneous patients by using simple, interpretable, yet effective policies when capacity is scarce, no‐show behavior is patient‐ and time‐dependent, service duration and reward are deterministic but patient‐dependent, and overtime is costly. Our work is motivated by the aforementioned operational challenges that typically face adopters of new technologies in the healthcare sector. We anchor our study on a partnership with the proton therapy center of Massachusetts General Hospital (MGH), which offers a new radiation technology for cancer patients. We formulate the problem as a nonlinear integer optimization problem. However, as the solution to this formulation lacks both tractability and interpretability, to be relevant to practice, we limit our study to simple and interpretable policies. In particular, we propose a simple index‐based rule and derive analytical performance guarantees for it. We also calibrate our model using empirical data from our partner hospital, and conduct a series of experiments to evaluate the performance of our proposed policy under practical circumstances. The analytical performance guarantees and our numerical experiments demonstrate (a) the strong performance of the proposed policies, and (b) their robustness to various practical considerations (e.g., to potential misspecification of no‐show probabilities). Our results show that our proposed policy, despite being a simple and interpretable index‐based rule, is capable of improving performance by about 20% at an organization such as MGH, and of delivering results that are not far from being optimal across a wide range of parameters that might vary between organizations. This suggests that the proposed policy can be viewed as an effective “one‐fits‐all” capacity allocation rule that can be used in a variety of environments in which operational challenges such as no‐shows and overtime costs need to be navigated using simple and interpretable rules.