Two-echelon time-dependent vehicle routing problem with simultaneous pickup and delivery and satellite synchronization

Abstract

The multi-echelon distribution strategy has been widely applied in city logistics systems. This study develops a mixed-integer linear programming model for a new variant of vehicle routing problem, namely, a two-echelon time-dependent vehicle routing problem with simultaneous pickup and delivery and satellite synchronization, in which customers are divided into multiple customer regions according to different geographical characteristics. The pickup and delivery activities with hard time windows are performed simultaneously by the same vehicles from depots to satellites in the first echelon and from satellites to customers in different customer regions in the second echelon. A vehicle speed function is developed for each echelon based on traffic conditions. The function depends on commuter traffic and urbanization level. Satellites with storage buffer capacities for split and consolidation are allowed. Thus, demand unloading, storage, and reloading are synchronized. Costs of transportation, loading/unloading, inventory, and environment during one complete distribution process are considered. A memetic algorithm (MA) is proposed including a split algorithm for chromosome decoding and a three-phase construction heuristic for initial population generation. Self-adaptive operators of crossover, mutation, and local search are designed, and a neighborhood route improvement strategy is devised that includes distance-related destroy, route-based destroy, distance-based greedy repair, and time-distance cluster repair operators. Results of different scales of numerical experiments and sensitivity analysis show the effectiveness of the model and MA by comparing it with an exact algorithm, CPLEX, and adaptive large neighborhood search.