Data-driven Models for Inferring the Patient Scheduling Policies via Inverse Reinforcement Learning

Abstract

In this work, we study multi-class patient scheduling with stochastic daily patient arrivals. Different classes of patients are characterized by different service times, waiting cost parameters, and rejection cost parameters. Our primary objective is to infer the policy used by the decision-makers, who schedule patients over a finite time horizon, based on their historical decisions. To achieve this, we first develop a mathematical model that captures the complexities of patient scheduling and is representative of the problem that decision-makers may consider to scheduling patients. Then, we utilize the Riccati and Hamiltonian approaches to estimate the cost parameters that have influenced the scheduling decisions made by the decision-maker. The Riccati approach begins by estimating the expert's policy, which is then used to determine the cost parameters. Conversely, the Hamiltonian approach derives the cost parameters through the optimality conditions of a path trajectory without needing to estimate the expert's policy. Using a simulation model, we demonstrate the efficiency and robustness of the proposed methods. Furthermore, we apply Riccati and Hamiltonian approaches to MRI data from two hospitals to estimate the cost parameters used in their scheduling decisions. Utilizing the estimated cost parameters, we analyze the root causes of the observed outcomes and examine the impact of these underlying factors on the scheduling process. Finally, through counterfactual analysis, we propose two alternative scheduling policies that reduce the total cost, even with the original cost parameters used by the decision-makers.