Daily traffic congestions form major problems for businesses such as logistical service providers and distribution firms. They cause late arrivals at customers and additional hiring costs for the truck drivers. The additional costs of traffic congestions can be reduced by taking into account and avoid well-predictable traffic congestions within off-line vehicle route plans. In the literature, various strategies are proposed to avoid traffic congestions, such as selecting alternative routes, changing the customer visit sequences, and changing the vehicle-customer assignments. We investigate the impact of these and other congestion avoidance strategies in off-line vehicle route plans on the performance of these plans in reality. For this purpose, we develop a set of VRP instances on real road networks, and a speed model that inhabits the main characteristics of peak hour congestion. The instances are solved for different levels of congestion avoidance using a modified Dijkstra algorithm and a restricted dynamic programming heuristic. Computational experiments show that 99% of late arrivals at customers can be eliminated if traffic congestions are accounted for off-line. On top of that, almost 70% of the extra duty times caused by the traffic congestions can be eliminated by clever avoidance strategies.

In practice, apart from the problem of vehicle routing, schedulers also face the problem of finding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose a restricted dynamic programming heuristic for the vehicle routing problem with time windows and the full European social legislation on drivers' driving and working hours. The problem we consider includes all rules in this legislation, whereas 1 in the literature only a basic set of rules has been addressed. In addition to this basic set of rules, the legislation contains a set of modifications that allow for more flexibility. To include the legislation in the restricted dynamic programming heuristic, we propose a break scheduling heuristic. Computational results show that our method finds solutions to benchmark instances -which only consider the basic set of rules -with 18% less vehicles and 5% less travel distance than state of the art approaches. Moreover, our results are obtained with significant less computational effort. Furthermore, the results show that including a set of rules on drivers' working hours -which has been generally ignored in the literature -has a significant impact on the resulting vehicle schedules: 3.9% more vehicle routes and 1.0% more travel distance are needed. Finally, using the modified rules of the legislation leads to an additional reduction of 4% in the number of vehicles and of 1.5% regarding the travel distance. Therefore, the modified rules should be exploited in practice.

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 Computational experiments demonstrate the trade-off between travel distance minimization and duty time minimization, and illustrate the cost savings of extending the depot opening hours such that traveling before the morning peak and after the evening peak becomes possible.

a b s t r a c tMost solution methods for the vehicle routing problem with time windows (VRPTW) develop routes from the earliest feasible departure time. In practice, however, temporary traffic congestion make such solutions non-optimal with respect to minimizing the total duty time. Furthermore, the VRPTW does not account for driving hours regulations, which restrict the available travel time for truck drivers. To deal with these problems, we consider the vehicle departure time optimization (VDO) problem as a postprocessing of a VRPTW. We propose an ILP formulation that minimizes the total duty time. The results of a case study indicate that duty time reductions of 15% can be achieved. Furthermore, computational experiments on VRPTW benchmarks indicate that ignoring traffic congestion or driving hours regulations leads to practically infeasible solutions. Therefore, new vehicle routing methods should be developed that account for these common restrictions. We propose an integrated approach based on classical insertion heuristics.

Most solution methods for solving large vehicle routing and scheduling problems are based on local search. A drawback of these approaches is that they are designed and optimized for specific types of vehicle routing problems (VRPs). As a consequence, it is hard to adapt these solution methods to handle new restrictions, without losing solution quality. We present a new framework for solving VRPs that can handle a wide range of different types of VRPs. Within this framework, restricted dynamic programming is applied to the VRP through the giant-tour representation. This algorithm is a construction heuristic which finds provably optimal solutions when unrestricted. We demonstrate the flexibility of the framework for a wide variety of different types of VRPs. The quality of solutions found by the framework is demonstrated by solving a set of benchmark instances for the capacitated VRP. The computational experiments show that restricted dynamic programming, which is a construction heuristic, develops routes of high quality. Therefore, this new framework for solving VRPs is highly valuable in practice.