Hongqi Li a *, Yinying Liua, Xiaorong Jiana, Yingrong Lua, b
aSchool of Transportation Science and Engineering, BeiHang University. No. 37 Xueyuan Road, Haidian District, Beijing, 100191, China
bBeijing Key Laboratory for Cooperative Vehicle Infrastructure System and Safety Control, BeiHang University. No. 37 Xueyuan Road, Haidian District, Beijing, 100191, China
* Corresponding author.E-mail addresses: lihongqi@buaa.edu.cn
Abstract
As one of the most necessary infrastructures for two-echelon distribution with cross-docking systems, satellites enable transshipment and consolidation for cargo deliveries. Considering speciallysatellites’ 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-RTCis proposed. The savings-based algorithmfollowed 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-RTCsuch that the solution quality and the computation time are acceptable.
Keywords: Two-echelon distribution system; Satellite transshipment capacity; Mixed integer linear programming; Variable neighborhood search
1. Introduction
In city logistics two main transport strategies are identified: full truckload or less-than-truckload (Cattaruzza et al., 2017). Typical less-than-truckload examples include parcel delivery services, express services, supermarkets distribution, etc. Dense urban areas are characterized by a high concentration of commercial activities that are usually performed along with less-than-truckload cargo deliveries (Franceschetti et al., 2017). City distribution systems need to reduce the nuisances associated with cargo deliveries in dense urban areas while supporting commercial activities (Crainic et al., 2009). In recent years logistics enterprises have changed their distribution and inventory strategies for better adapting them to the growing delivery demand and legal restrictionson truck traffic in dense urban areas. The multi-echelon distribution system has emerged as a popular alternative to perform urban deliveries (Gonzalez-Feliu, 2012, 2013; Cuda et al., 2015). The most representative examples are seen in grocery distribution, parcel and postal distribution, etc.
Fundamentally, the multi-echelon distribution system implies to use different types of vehicles on different echelons, and to use satellites (i.e., intermediate platforms) to consolidate and transship cargoes. Such system allows enterprises to leverage economies of scale from larger shipments on upper echelons, and to comply with regulations that aim to reduce the environmental footprints of distribution operations on lower echelons of dense urban areas (Merchán Dueñas, 2015). In multi-echelon distribution systems, two shipping strategies are predominant. In the multi-echelon distribution with warehousing system that includes factories, warehouses and the final destination of cargoes, cargo requests are made to warehouses. The warehouses command cargoes in large quantities to factories. The multi-echelon distribution with cross-docking system differs from the warehousing strategy. Cross-docking platforms don’t have the possibility to stock for a long time, but have the consent to cargo consolidation and transshipment. (Gonzalez-Feliu, 2010; Dondo et al., 2011)