A branch-and-cut algorithm for the soft-clustered vehicle-routing problem

The soft-clustered vehicle-routing problem is a variant of the classical capacitated (CVRP) in which customers are partitioned into clusters and all same cluster must be served by vehicle. We introduce novel symmetric formulation clustering part modeled with an asymmetric sub-model. solve new model branch-and-cut algorithm exploiting some known valid inequalities for CVRP that can adapted. In addition, we derive problem-specific cutting planes heuristic exact separation procedures. For square grid instances Euclidean plane, provide lower-bounding techniques reduction scheme also applicable to respective traveling salesman problem. comprehensive computational test on standard benchmark instances, compare different formulations strategies order determine best performing algorithmic setup. results this show several previously open now solved proven optimality.