Multi-attribute two-echelon location routing: Formulation and dynamic discretization discovery approach

We study the two-echelon location-routing system under tight synchronization constraints, in addition to several other interacting attributes. Prompted, in particular, by city-logistics applications, the system we address concerns a two-echelon distribution layout composed of a set of platform facilities and a set of intermediate satellite facilities to deliver freight from supply zones outside the city to customers within. The problem setting includes time-dependent multicommodity demand, time windows, lack of storage capacity at intermediate facilities, and synchronization at these facilities of the fleets operating on different echelons. The problem requires the selection of facilities at both levels, the allocation of suppliers to platforms and of customers to satellites, and the routing and scheduling of vehicles at each echelon, in order to deliver the freight from platforms to customers, through the satellites. The lack of storage capacity of the shared facilities, the satellites, requires tight scheduling of the vehicle routes and demand itineraries, i.e., departure times from the platforms and satellites, and the synchronization of vehicle routes at satellites for efficient transshipment operations. We introduce the problem setting, present a mixed-integer programming formulation, and a dynamic discretization discovery-based exact solution method for the problem. We perform thorough analyses to assess the impact of the problem attributes and requirements on the system behaviour and algorithm performance.