Markov Decision Process and Approximate Dynamic Programming for a Patient Assignment Scheduling problem

TL;DR

This paper models the hospital patient assignment scheduling problem as a Markov Decision Process to optimize patient flow management, using Approximate Dynamic Programming for large instances, with real hospital data application.

Contribution

It introduces a novel MDP framework for PAS and develops approximate dynamic programming methods to solve large-scale, realistic hospital scheduling problems.

Findings

Numerical methods effectively optimize patient assignment policies.

Application to Australian hospital data demonstrates practical utility.

Method reduces long-term costs in patient flow management.

Abstract

We study the Patient Assignment Scheduling (PAS) problem in a random environment that arises in the management of patient flow in the hospital systems, due to the stochastic nature of the arrivals as well as the Length of Stay distribution. We develop a Markov Decision Process (MDP) which aims to assign the newly arrived patients in an optimal way so as to minimise the total expected long-run cost per unit time over an infinite horizon. We assume Poisson arrival rates that depend on patient types, and Length of Stay distributions that depend on whether patients stay in their primary wards or not. Since the instances of realistic size of this problem are not easy to solve, we develop numerical methods based on Approximate Dynamic Programming. We illustrate the theory with numerical examples with parameters obtained by fitting to data from a tertiary referral hospital in Australia, and demonstrate the application potential of our methodology under practical considerations.