Joint Patient Selection and Scheduling under No-Shows: Theory and Application in Proton Therapy

Motivated by operational challenges facing adopters of new technologies in the service industry, we study how to admit and schedule customers from a pool of heterogeneous potential users when capacity is scarce. We model schedule-dependent no-show behavior and overtime costs as two important features that can significantly affect operational performance. We start by formulating the problem as a nonlinear integer optimization problem. However, since the solution to this formulation lacks both tractability and interpretability, to be relevant to practice, we limit our study to simple and interpretable policies that can be implemented in practice. In particular, we propose a simple index-based rule and derive analytical performance guarantees for it, which reveal its strong performance compared to the optimal solution. Our analytical performance analysis also demonstrates the robustness of the proposed policy to potential misspecification of no-show probabilities which are hard to accurately estimate in practice. Importantly, we test the validating of our approach through partnership with the proton therapy center of Massachusetts General Hospital (MGH), which offers a new radiation technology for cancer patients. We 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. Put together, these experiments 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.