On the feasibility of solutions to the split delivery vehicle routing problem represented as edge variables

Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We show that this recognition problem depends on the formulation's constraints and prove that it's strongly NP-hard for a recent formulation. With subtour elimination constraints, we provide an O(n log n)-time recognition algorithm. This challenges assumptions about edge-based formulations and provides new insights into SDVRP solution verification complexity.