A Lagrangian relaxation approach for resource allocation problem with capacity constraints

Abstract

AbstractThis study evaluates a capacitated facility location model enhanced with distance constraints for an emergency response problem, ensuring certain neighborhoods remain within an accessible range from facilities following a hurricane. The proposed model takes into account the capacity constraints for drones and vehicles. The model determines optimal locations for facilities and the distribution of supplies across the city. It also specifies which facilities should support the needs of each neighborhood and decides on the appropriate mode of transportation—ground vehicles if possible, or drones if roadways are obstructed. To solve the problem, a Lagrangian relaxation technique is employed, relaxing the constraints related to facility capacity and distance. The numerical results confirm the quality and efficiency of the solutions. The findings indicate that ground transportation is more frequently utilized than drones at each operational facility. A comprehensive set of sensitivity analyses is conducted to examine the impact of various variables and parameters on the solution.