More Capacity, More Demand: MRI Planning with Fluid Models and Reinforcement Learning

Abstract: Long waiting times for MRI examinations pose a persistent challenge in healthcare systems worldwide. Using data from the UK National Health Service (NHS), we show that increasing MRI capacity does not necessarily reduce congestion; instead, it may induce additional demand and worsen waiting times. This endogenous interaction between capacity and demand makes MRI acquisition a challenging decision problem. We model this setting using a fluid approximation and formulate an optimization problem that captures time- and capacity-dependent arrival rates, as well as acquisition, maintenance, and waiting costs. The model is validated against the NHS data and accurately captures the observed dynamics of demand and congestion. While it enables performance evaluation for a given policy, the dependence between capacity and demand renders the optimal acquisition policy analytically intractable. To address this challenge, we develop an AI-driven decision system based on reinforcement learning (RL). Specifically, we employ a Deep Q-Network (DQN) agent that learns adaptive MRI acquisition policies through interaction with the modeled environment. This hybrid framework combines the analytical structure of fluid models with data-driven learning to support dynamic capacity planning. Numerical results show that the learned policy substantially outperforms standard acquisition strategies, reducing total cost by more than 91% relative to all baseline policies and highlighting the value of adaptive, state-dependent capacity planning when demand responds endogenously to service availability.