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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 824961, 13 pages
Research Article

Column Generation for a Multitrip Vehicle Routing Problem with Time Windows, Driver Work Hours, and Heterogeneous Fleet

Department of Naval Architecture and Ocean Engineering, University of São Paulo, Avenida Professor Mello Moraes 2231, 05508-030 São Paulo, SP, Brazil

Received 3 December 2012; Revised 29 January 2013; Accepted 4 February 2013

Academic Editor: Rubén Ruiz García

Copyright © 2013 Michel Povlovitsch Seixas and André Bergsten Mendes. 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 study addresses a vehicle routing problem with time windows, accessibility restrictions on customers, and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can perform multiple routes per day, all starting and ending at a single depot, and it is assigned to a single driver whose total work hours are limited. A column generation algorithm is proposed. The column generation pricing subproblem requires a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performing multiple routes per day and to address the need to set the workday’s start time within the planning horizon. A constructive heuristic and a metaheuristic based on tabu search are also developed to find good solutions.