Rescue Vehicle Distribution Using Geographic Information and Uncapacitated P-Median Combinatorial Optimization

Objective: This study investigates the optimization of rescue vehicle distribution in Curitiba, Paraná, using historical data and combinatorial optimization models based on the p-median approach. The primary goal is to minimize travel distances and service costs. Theoretical Framework: The study is grounded in classical facility location theories, including the p-median model. References include Weber (1909), Arakaki and Lorena (2006), and Laporte et al. (2005), which explore location-allocation methods for spatial optimization. Methodology: The methodology involves formulating a mathematical model to designate support points (SP) and call points (CP), considering travel costs, installation costs, and demand. The model was implemented in C# using the Gurobi solver and validated through scenarios generated from data on 29,732 historical rescue service calls. Results and Discussion: The results show that in 75% of the tested instances, the model provided better solutions than the current scenario, reducing travel distances and costs. The model allows for the inclusion of budget constraints and installation costs, offering flexibility to meet different operational demands. Research Implications: This study contributes by presenting a practical application of combinatorial optimization in emergency services, providing insights to improve operations and reduce costs in the sector. Originality/Value: The research stands out for integrating geolocation, mathematical modeling, and computational tools to address a real-world logistical optimization problem, with direct impacts on the operational and financial efficiency of rescue services.