A matheuristic for a 2-echelon vehicle routing problem with capacitated satellites and reverse flows

• Two-echelon vehicle routing problem with three important real-world extensions. Simultaneous handling of reverse flows, satellite capacities, and timing aspects. Matheuristic solution approach combines different decomposition strategies. New for efficient feasibility testing local-search moves. Last-mile collection delivery services often rely on multi-echelon logistic systems many types practical spatial, temporal, resource constraints. We consider extensions the basic 2-echelon that are interest: First, second-echelon vehicles need to simultaneously deliver collect goods at customers within their specified time window. Second, first-echelon allowed perform multiple trips during planning horizon. Third, intermediate facilities, called satellites, allow temporary storage goods, but quantity can be stored a is limited. This paper integrates these complicating features in single mathematical model. To solve problem, we design decomposition-based matheuristic. It employs reduced refined mixed-integer programming formulation two echelon-specific large neighborhood searches (LNS) produce improving routes respective echelon. The most algorithmic component check LNS relies sequence constant-time low-complexity tests. final test allows re-scheduling operations taking place satellite. Extensive computational experiments systematically evaluate new components matheuristic benchmark it against recent exact method related problem. Moreover, impact main such as number capacity satellites well integration forward flows analyzed.