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Mathematical Problems in Engineering
Volume 2014, Article ID 517467, 11 pages
Research Article

A Hybrid GRASP+VND Heuristic for the Two-Echelon Vehicle Routing Problem Arising in City Logistics

School of Electronics and Information Engineering, Tongji University, Shanghai 201804, China

Received 29 November 2013; Accepted 30 March 2014; Published 23 April 2014

Academic Editor: Baozhen Yao

Copyright © 2014 Zheng-yang Zeng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The two-echelon vehicle routing problem (2E-VRP) is a variant of the classical vehicle routing problem (VRP) arising in two-level transportation systems such as those encountered in the context of city logistics. In the 2E-VRP, freight from a depot is compulsorily delivered through intermediate depots, named satellites. The first echelons are routes that distribute freight from depot to satellites, and the second are those from satellites to customers. This problem is solved by a hybrid heuristic which is composed of a greedy randomized adaptive search procedure (GRASP) with a route-first cluster-second procedure embedded and a variable neighborhood descent (VND), called GRASP+VND hereafter. Firstly, an extended split algorithm in the GRASP continuously splits randomly generated permutations of all customers and assigns customers to satellites reasonably until a feasible assignment appears, and a complete 2E-VRP feasible solution is obtained by solving the first echelon problem subsequently and, secondly, a VND phase attempts to improve this solution until no more improvements can be found. The process above is iterated until the maximum number of iterations is reached. Computational tests conducted on three sets of benchmark instances from the literature show that our algorithm is both effective and efficient and outperforms the best existing heuristics for the 2E-VRP.