Treffer: Route Optimization in Home Physiotherapy: A Traveling Salesman Problem-based Framework for Health Care Logistics Efficiency.

The expansion of home health care services poses important logistical challenges, especially for physiotherapists who serve multiple geographically dispersed patients. This study proposes an optimization model based on the Traveling Salesman Problem (TSP) to rationalize physiotherapist routes in urban contexts. Using Graph Theory, an exact mathematical model implemented in Python was developed with the NetworkX and Matplotlib libraries. The methodology included: (1) construction of a 7×7 distance matrix based on simulated geographic coordinates; (2) implementation of a brute-force algorithm for analysis of all 720 possible permutations and (3) comparison with non-optimized empirical route. The results showed a 23.9% reduction in the distance covered (25.2 km versus 33.1 km), with positive impacts on operational efficiency and care availability. The main contribution of this study consists of the practical adaptation of the Traveling Salesman Problem (TSP) to the context of home physiotherapy, incorporating relevant clinical and operational variables, and demonstrating, through computer modeling, the feasibility of exact solutions to optimize routes in urban health networks, with concrete gains in logistical efficiency and quality of care. It is concluded that the mathematical optimization of routes represents a viable strategy to qualify the management of functional rehabilitation in extra-hospital environments, with potential application in other care contexts. [ABSTRACT FROM AUTHOR]