Dynamic multi-priority admission scheduling for multimorbid patients: an MDP approach incorporating balking penalties

Efficient admission scheduling for multimorbid patients remains a critical challenge in hospital operations, particularly in mitigating patient balking behavior caused by bed shortages. This study investigates the multi-priority admission problem across Endocrinology (ED), Cardiology (CR), and Nephrology (NP) departments. We propose a finite-horizon Markov Decision Process (MDP) model that optimizes dynamic admission decisions by incorporating balking penalties, quantifying the implicit cost of rejecting patients. Unlike static allocation, our model supports a dynamic multi-priority assignment​ mechanism (first, second, and third attempts) to maximize the total expected net benefit. Using a value iteration algorithm, we derive the optimal Priority Cutoff (Policy-PC). Computational experiments based on real-world hospital data demonstrate that Policy-PC significantly reduces patient balking rates and improves bed utilization compared to four benchmark policies. The results confirm that integrating balking penalties into dynamic scheduling provides hospital managers with a robust tool for balancing resource loads and enhancing patient satisfaction.