Solving the vehicle routing problem with lunch break arising in the furniture delivery industry

In this paper we solve the Vehicle Routing Problem with Lunch Break (VRPLB) which arises when drivers must take pauses during their shift, for example, for lunch breaks. Driver breaks have already been considered in long haul transportation when drivers must rest during their travel, but the underlying optimization problem remains difficult and few contributions can be found for less than truckload and last mile distribution contexts. This problem, which appears in the furniture delivery industry, includes rich features such as time windows and heterogeneous vehicles. In this paper we evaluate the performance of a new mathematical formulation for the VRPLB and of a fast and high performing heuristic. The mixed integer linear programming formulation has the disadvantage of roughly doubling the number of nodes, and thus significantly increasing the size of the distance matrix and the number of variables. Consequently, standard branch-and-bound algorithms are only capable of solving small-sized instances. In order to tackle large instances provided by an industrial partner, we propose a fast multi-start randomized local search heuristic tailored for the VRPLB, which is shown to be very efficient. Through a series of computational experiments, we show that solving the VRPLB without explicitly considering the pauses during the optimization process can lead to a number of infeasibilities. These results demonstrate the importance of integrating drivers pauses in the resolution process

Optimizing departure times in vehicle routes

Most 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 post-processing 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 heuristic

Roteirização e programação de veículos com carga completa em viagens de longa distância

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Produção, Florianópolis, 2015.O objetivo desta tese consiste em resolver o problema de roteamento e programação de caminhões, com restrições de horário de trabalho do motorista profissional impostas pela legislação (HOS), considerando carga completa e viagens de longa distância, de modo a minimizar os custos totais de operação. Diferentemente de outros trabalhos encontrados na literatura, nesta tese a rota e os locais de parada são determinados concomitantemente com a programação da operação. Este problema foi modelado através de um grafo, para o qual três algoritmos de busca foram aplicados. Testes realizados mostram que o método de solução proposto reage adequadamente às mudanças realizadas nos custos dos serviços oferecidos nos diversos locais de parada existentes, tanto no que se refere a escolha da rota, como dos locais em que as paradas deverão ser realizadas. Os resultados obtidos indicam, ainda, que soluções de mínimo custo podem ser encontradas com baixo tempo computacional.Abstract : The main goal of this thesis is to solve the problem of routing and scheduling of trucks, with professional driver working time restrictions imposed by legislation (HOS), considering fully loaded trucks and long-distance work journeys, in order to minimize the total costs of operation. Differently from other studies found in the literature, in this thesis the route and stopping points locations are determined concomitantly with the scheduling. This problem was modeled by a graph, for which three search algorithms were applied. Tests show that the proposed method reacts appropriately to changes made in the costs of services provided under the various stopping places, both as regards the choice of route, such as the locations where the stops will be performed. The results also indicate that low-cost solutions can be found with low computational time

A Quantitative Model for Truck Parking Utilization with Hours of Service Regulations

Continual growth in traffic volume on U.S. Highways and insufficient parking for commercial trucking vehicles has led to significant safety concerns for truck drivers. Hours of Service (HOS) regulations dictate driving and rest periods of truck drivers. When a truck driver must stop as designated by the HOS regulations and the nearest parking location is at capacity, the trucker must either continue driving past the HOS limit or park in an undesignated and possibly illegal or unsafe spot such as an off-ramp. The combination of these two variables play an important role in the safety of truck drivers on a daily basis. Previous research on truck parking shortages has followed a survey-based approach while research on HOS regulations in conjunction with truck routing and driver scheduling has not included the full suite of HOS regulations as well as restrictions on parking availability. Current research techniques do not take into account parking capacity on a driver’s route while following HOS regulations. Because there are limitations governing where along a route a driver can rest, including some customer locations and parking locations at capacity, these models do not prove to be an accurate measure of trip planning for truck drivers. This research aims to develop a mathematical model to link truck parking with hours of service regulations in order to determine feasible routes for truck drivers and optimal truck parking locations on the highway network

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 polynomial time. 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

Efficient neighborhood evaluations for the vehicle routing problem with multiple time windows

In the vehicle routing problem with multiple time windows (VRPMTW), a single time window must be selected for each customer from the multiple time windows provided. Compared with classical vehicle routing problems with only a single time window per customer, multiple time windows increase the complexity of the routing problem. To minimize the duration of any given route, we present an exact polynomial time algorithm to efficiently determine the optimal start time for servicing each customer. The proposed algorithm has a reduced worst-case and average complexity than existing exact algorithms. Furthermore, the proposed exact algorithm can be used to efficiently evaluate neighborhood operations during a local search resulting in significant acceleration. To examine the benefits of exact neighborhood evaluations and to solve the VRPMTW, the proposed algorithm is embedded in a simple metaheuristic framework generating numerous new best known solutions at competitive computation times

The Bi-objective Long-haul Transportation Problem on a Road Network

In this paper we study a long-haul truck scheduling problem where a path has to be determined for a vehicle traveling from a specified origin to a specified destination. We consider refueling decisions along the path, while accounting for heterogeneous fuel prices in a road network. Furthermore, the path has to comply with Hours of Service (HoS) regulations. Therefore, a path is defined by the actual road trajectory traveled by the vehicle, as well as the locations where the vehicle stops due to refueling, compliance with HoS regulations, or a combination of the two. This setting is cast in a bi-objective optimization problem, considering the minimization of fuel cost and the minimization of path duration. An algorithm is proposed to solve the problem on a road network. The algorithm builds a set of non-dominated paths with respect to the two objectives. Given the enormous theoretical size of the road network, the algorithm follows an interactive path construction mechanism. Specifically, the algorithm dynamically interacts with a geographic information system to identify the relevant potential paths and stop locations. Computational tests are made on real-sized instances where the distance covered ranges from 500 to 1500 km. The algorithm is compared with solutions obtained from a policy mimicking the current practice of a logistics company. The results show that the non-dominated solutions produced by the algorithm significantly dominate the ones generated by the current practice, in terms of fuel costs, while achieving similar path durations. The average number of non-dominated paths is 2.7, which allows decision makers to ultimately visually inspect the proposed alternatives