Introducing radiality constraints in capacitated location-routing problems

In this paper, we introduce a unified mathematical formulation for the Capacitated Vehicle Routing Problem (CVRP) and for the Capacitated Location Routing Problem (CLRP), adopting radiality constraints in order to guarantee valid routes and eliminate subtours. This idea is inspired by formulations already employed in electric power distribution networks, which requires a radial topology in its operation. The results show that the proposed formulation greatly improves the convergence of the solver.