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Journal of Applied Mathematics
Volume 2013, Article ID 127156, 10 pages
Research Article

A Simulation-Based Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Travel Times

School of Software, Dalian University of Technology, Dalian, Liaoning 116620, China

Received 17 March 2013; Revised 24 September 2013; Accepted 25 September 2013

Academic Editor: Song Cen

Copyright © 2013 Zheng Wang and Lin Lin. 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.


This paper presents a flexible solution methodology for the capacitated vehicle routing problem with stochastic travel times (CVRPSTT). One of the basic ideas of the methodology is to consider a vehicle working time lower than the actual maximum vehicle working time when designing CVRPSTT solutions. In this way, the working time surplus can be used to cope with unexpected congestions when necessary. Another important idea is to transform the CVRPSTT instance to a limited set of capacitated vehicle routing problems (CVRP), each of which is defined by a given percentage of the maximum vehicle working time. Thus, our approach can take advantage of any efficient heuristic that already exists for the CVRP. Based on the two key ideas, this paper presents a simulation-based algorithm, in which Monte Carlo simulation is used to obtain estimates of the cost and the reliability of each solution, and the Clarke and Wright heuristic is improved to generate more reliable solutions. Finally, a number of numerical experiments are done in the paper with the purpose of analyzing the efficiency of the described methodology under different uncertainty scenarios.