Edge-Based Contiguous p-Median Problem for Logistics Districting

A new paper on arXiv introduces the edge-based contiguous p-median (ECpM) problem, which partitions road networks into compact and contiguous territories for logistics districting. The study proposes two binary programming models that incorporate network distance. The first model uses an exponential number of cut set-based constraints to enforce contiguity and is paired with a branch-and-cut (B&C) algorithm that generates only a small number of these constraints. The second model employs a polynomial number of shortest-path constraints (SPC) and can be solved with off-the-shelf solvers. The approaches were tested on road networks with over 2,700 nodes and nearly 3,400 edges, resulting in models with over 9.6 million binary variables. Solving the SPC-based model via standard branch and bound achieved significant computational speedups. The paper is available on arXiv with the identifier 2608.11230.