A dynamic programming heuristic for vehicle routing with time-dependent travel times and required breaks

For the intensively studied vehicle routing problem (VRP), two real-life restrictions have received only minor attention in the VRP-literature: traffic congestion and driving hours regulations. Traffic congestion causes late arrivals at customers and long travel times resulting in large transport costs. To account for traffic congestion, time-dependent travel times should be considered when constructing vehicle routes. Next, driving hours regulations, which restrict the available driving and working times for truck drivers, must be respected. Since violations are severely fined, also driving hours regulations should be considered when constructing vehicle routes, even more in combination with congestion problems. The objective of this paper is to develop a solution method for the VRP with time windows (VRPTW), time-dependent travel times, and driving hours regulations. The major difficulty of this VRPTW extension is to optimize each vehicle’s departure times to minimize the duty time of each driver. Having compact duty times leads to cost savings. However, obtaining compact duty times is much harder when time-dependent travel times and driving hours regulations are considered. We propose a restricted dynamic programming (DP) heuristic for constructing the vehicle routes, and an efficient heuristic for optimizing the vehicle’s departure times for each (partial) vehicle route, such that the complete solution algorithm runs in A. L. Kok (&) Algorithmic R&D, ORTEC, P.O. Box 490, 2800 AL Gouda, Netherlands e-mail: [email protected] E. W. Hans J. M. J. Schutten W. H. M. Zijm Operational Methods for Production and Logistics, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands e-mail: [email protected] J. M. J. Schutten e-mail: [email protected] W. H. M. Zijm e-mail: [email protected] 123 Flex Serv Manuf J (2010) 22:83–108 DOI 10.1007/s10696-011-9077-4