Graph-model Based Optimization of Shelter Hospitals: Integrating MILP for Efficient Layout and Deployment

This paper introduces a novel approach to optimizing the layout and deployment of mobile shelter hospitals, a concept that has gained prominence due to the increasing need for rapid medical response in diverse scenarios, including natural disasters and pandemics. Our approach integrates Mixed Integer Linear Programming (MILP) and the genetic algorithms to develop a graph model that represents the different functional areas of a shelter hospital as vertices. In this model, network edges are defined by capacity and transit time, employing a discrete time approach for patient movement and queuing. We establish a Nash equilibrium for the model to ensure optimal patient flow and treatment efficiency. Utilizing the genetic algorithms, the model's hyperparameters are refined, and we demonstrate its practical application through a case study. The results from our experiments indicate a significant improvement in layout planning and deployment strategies. In one specific instance, by optimizing the graph model parameters, the total time for all patients to receive services was reduced from 190 minutes to 170 minutes, a 10.5% reduction. This approach addresses the challenges of diverse and complex medical scenarios in shelter hospitals, enhancing their emergency response capabilities and operational efficiency.