Having an interpretable, dynamic length-of-stay model can help hospital administrators and clinicians make better decisions and improve the quality of care. The widespread implementation of electronic medical record (EMR) systems has enabled hospitals to collect massive amounts of health data. However, how to integrate this deluge of data into healthcare operations remains unclear. We propose a framework grounded in established clinical knowledge to model patients’ lengths of stay. In particular, we impose expert knowledge when grouping raw clinical data into medically meaningful variables that summarize patients’ health trajectories. We use dynamic, predictive models to output patients’ remaining lengths of stay, future discharges, and census probability distributions based on their health trajectories up to the current stay. Evaluated with large-scale EMR data, the dynamic model significantly improves predictive power over the performance of any model in previous literature and remains medically interpretable. Summary of Contribution: The widespread implementation of electronic health systems has created opportunities and challenges to best utilize mounting clinical data for healthcare operations. In this study, we propose a new approach that integrates clinical analysis in generating variables and implementations of computational methods. This approach allows our model to remain interpretable to the medical professionals while being accurate. We believe our study has broader relevance to researchers and practitioners of healthcare operations.

We provide a practical methodology for solving the generalized joint replenishment (GJR) problem, based on a mathematical programming approach to approximate dynamic programming. We show how to automatically generate a value function approximation basis built upon piecewise-linear ridge functions by developing and exploiting a theoretical connection with the problem of finding optimal cyclic schedules. We provide a variant of the algorithm that is effective in practice, and we exploit the special structure of the GJR problem to provide a coherent, implementable framework.