Fairness over time in dynamic resource allocation with an application in Healthcare

TL;DR

This paper develops a mathematical framework for ensuring fairness over time in dynamic resource allocation problems, with a focus on healthcare applications like ambulance allocation, balancing efficiency and fairness among stakeholders.

Contribution

It introduces novel formulations and algorithms to optimize and improve fairness over multiple decision rounds in complex, constrained healthcare resource allocation scenarios.

Findings

Efficient algorithms significantly outperform naive approaches in solving fairness optimization problems.

Structural results help identify fair allocation policies under constraints.

Application to ambulance allocation demonstrates practical effectiveness.

Abstract

Decision making problems are typically concerned with maximizing efficiency. In contrast, we address problems where there are multiple stakeholders and a centralized decision maker who is obliged to decide in a fair manner. Different decisions give different utility to each stakeholder. In cases where these decisions are made repeatedly, we provide efficient mathematical programming formulations to identify both the maximum fairness possible and the decisions that improve fairness over time, for reasonable metrics of fairness. We apply this framework to the problem of ambulance allocation, where decisions in consecutive rounds are constrained. With this additional complexity, we prove structural results on identifying fair feasible allocation policies and provide a hybrid algorithm with column generation and constraint programming-based solution techniques for this class of problems. Computational experiments show that our method can solve these problems orders of magnitude faster than a naive approach.