A two-echelon location-routing problem with synchronisation

Motivated by an actual problem of a national postal service company, we introduce and define a new two-echelon location-routing problem (2E-LRP). The 2E-LRP is defined in a two-echelon distribution system where products are transported from origins to destinations through intermediate facilities. A major question that arises in a two-echelon distribution system is how to synchronise the flows of the two echelons at intermediate facilities. The synchronisation is important due to limited storage space or waiting times for transshipments at the intermediate facilities. In our new 2E-LRP, the activities in the two echelons are organised into two waves; a delivery wave, where products are sent from the primary facility to the customers through the intermediate facilities, and a following pickup wave, where the flow of products is reversed. The model only considers temporal constraints, assuming that capacities are never binding; the vehicles are always large enough given the constraints on time. As a solution approach, we propose a decomposition-based heuristic. Besides the solution approach, we propose data-driven schemes for use in combination with the model and we provide the computational results for different sets of instances.