The two-echelon distribution system considering the real-time transshipment capacity varying

As one of the most necessary infrastructures for two-echelon distribution with cross-docking systems, satellites enable transshipment and consolidation for cargo deliveries. Considering specially satellites' real-time transshipment capacity (RTC) varying with transshipment and consolidation operations, we introduce the two-echelon distribution system considering the real-time transshipment capacity varying (called the 2E-DS-RTC). The 2E-DS-RTC adopts RTC constraints and time constraints to make routings of the two echelons interacting. Of each satellite, the RTC is constrained by the maximal transshipment capacity (MTC) and the occupied transshipment capacity. A mixed integer linear programming model for the 2E-DS-RTC is proposed. The savings-based algorithm followed by the variable neighborhood search phase is provided. The mathematical formulation and the two-stage heuristic are tested by using 20 randomly-generated small-scale instances and 99 realistic instances with up to 30 satellites and 900 customers. Some small-scale instances can be solved directly by CPLEX to find exact solutions. The computational results of realistic instances indicate that the heuristic can solve various scale instances of the 2E-DS-RTC such that the solution quality and the computation time are acceptable.