A Continuous Districting Model Applied to Logistics Distribution Problems

The aim of districting problems is to get an optimized partition of a territory into smaller units, called districts or zones, subject to some side constraints such as balance, contiguity, and compactness. Logistics districting problems usuually involve additional optimization criteria and constraints. Districting problems are called continuous when the underlying space, both for facility sites and demand points, are determined by variables that will vary continuously. Voronoi diagrams can be successfully used in association with continuous approximation models to solve location-districting problems. We discuss in the paper the application of non-ordinary Voronoi diagrams in logistics districting problems, particularly the Power Voronoi diagram, associated with a continuous demand approach, which allows for the introduction of physical barriers into the vehicle displacement representation, such as rivers, reservoirs, hills, etc.