The two-echelon vehicle routing problem (2E-VRP) consists in making deliveries to a set of customers using two distinct fleets of vehicles. First-level vehicles pick up requests at a distribution center and bring them to intermediate sites. At these locations, the requests are transferred to second-level vehicles, which deliver them. This paper addresses a variant of the 2E-VRP that integrates constraints arising in city logistics such as time window constraints, synchronization constraints, and multiple trips at the second level. The corresponding problem is called the two-echelon multiple-trip vehicle routing problem with satellite synchronization (2E-MTVRP-SS). We propose an adaptive large neighborhood search to solve this problem. Custom destruction and repair heuristics and an efficient feasibility check for moves have been designed and evaluated on modified benchmarks for the VRP with time windows. 
An adaptive large neighborhood search for the two-echelon multiple-trip vehicle routing problem with satellite synchronization