Column generation for a real world vehicle routing problem

We present an optimization algorithm we developed for a software provider of planning tools for distribution logistics companies. The algorithm computes a daily plan for a heterogeneous fleet of vehicles, that can depart from different depots and must visit a set of customers for delivery operations. Besides multiple capacities and time windows associated with depots and customers, the problem also considers incompatibility constraints between goods, depots, vehicles and customers, maximum route length and durations, upper limits on the number of consecutive driving hours and compulsory drivers' rest periods, the possibility to skip some customers and to use express courier services instead of the given fleet to fulfill some orders, the option of splitting up the orders, the possible existence of pick-up operations to be performed by empty vehicles traveling back to their depots and the possibility of ``open" routes that do not terminate at depots. Moreover, the cost of each vehicle route is computed through a system of fares, depending on the locations visited by the vehicle, the distance traveled, the vehicle load and the number of stops along the route. We developed a column generation algorithm, where the pricing problem is a particular resource constrained elementary shortest path problem, solved through a bounded bi-directional dynamic programming algorithm. We describe how to encode the cost function and the complicating constraints by an appropriate use of resources and we present computational results on real instances obtained from the software company

A Metaheuristic for the Pickup and Delivery Problem with Split-Loads and its Extension

In this dissertation, we study improvements in the Pickup and Delivery Problem that can be achieved by allowing multiple vehicle trips to serve a common load. We explore how costs can be reduced through the elimination of the constraint that a load must be served by only one vehicle trip. Specifically, we investigate the problem of routing vehicles to serve loads that have distinct origins and destinations, with no constraint on the amount of a load that a vehicle may serve at a time. We develop a metaheuristic to solve large scale practical size problems in this form and apply the metaheuristic to randomly generated data sets. The metaheuristic is based on a predetermined fixed number of restarts of annealing-like procedure with tabu-lists to avoid cycling in the search process and the annealing-like procedure is to guide the local search in three neighborhoods defined to solve the problem. We test the algorithm on several sets of problem instances generated with different transportation requests and over different load size ranges. The experimental results on these problem sets have shown that benefits are common if split loads are adopted in designing practical sized transportation network for different load size configurations, and the most benefit is achieved when all the loads are just a little above half of the vehicle capacity and have small variations, and this most benefit is around 33% for all the three 75-, 100-, and 125-request problem sets, which overtakes the one reported in previous literature. In a more general setting when some load sizes are greater than the vehicle capacity and have to be split, there are also certain cost reduction if split loads are applied. We also generate numeral tests on different load size ranges and split the loads that are greater than the vehicle capacity using different ”splitting” strategy, in term of how much amount to split from the original load to form a new load, and find that there seem to be no optimal ”splitting” strategy, which can assure the best quality of solutions using the metaheuristic developed in the dissertation

Supply chain complexity and robustness analysis

Imperial Users onl

Metodología de algoritmos meméticos para el problema de ruteo de vehículos con entregas parciales y tiempos de viaje dependientes con ventanas de tiempo

El problema de ruteo de vehículos VRP es uno de los problemas más estudiados en investigación de operaciones, dada su relevancia en los campos del transporte y la logística. En los últimos años ha aumentado el interés en minimizar la contaminación por la emisión de gases efecto invernadero a causa del consumo de combustibles fósiles. El sector transporte representa una parte importante en esas emisiones. En el transporte, situaciones como los embotellamientos en las horas pico, por ejemplo, conducen a una red vial dinámica en la que varían los tiempos de viaje y consecuentemente el consumo de combustible. Por lo anterior el problema de enrutamiento de vehículos con tiempos dependientes TDVRP es una representación más cercana la vida real que los modelos tradicionales de enrutamientos de vehículos, VRP. Por otro lado, el problema de enrutamiento de vehículos con partición de entregas, SDVRP permite asignar múltiples rutas a un mismo cliente, propiciando ahorros en las mismas. El objetivo de esta tesis es desarrollar un método para el uso de los recursos de transporte, con el fin de atender a los clientes de manera eficiente respecto al costo total de la distancia recorrida y al tiempo total de viaje requerido. El problema consiste en programar un recorrido durante un día dividido en intervalos o zonas horarias, con ventanas de tiempo para atender a cada cliente, vehículos homogéneos con capacidad fija Q y un depósito único. Para ello se propone en este trabajo un Algoritmo Memético (MA) capaz de encontrar soluciones que respetan las restricciones del problema, teniendo en cuenta la posibilidad de hacer particiones en las entregas. Mediante el Diseño de Experimentos se evaluó la calidad de las soluciones generadas respecto a un Algoritmo Genético (GA) desarrollado también para el propósito, teniendo como criterio de evaluación el porcentaje de mejores soluciones alcanzado por cada algoritmo. Los experimentos permiten afirmar que el Algoritmo Memético propuesto supera el Algoritmo Genético, resultando más robusto ante cambios en los parámetros de ambos métodos. La solución propuesta representa un modelo más cercano a la realidad de las redes viales y genera rutas tendientes a disminuir la cantidad, recorrido y tiempo de permanencia de los vehículos en la red vial, conllevando a la disminución de las emisiones de gases efecto invernadero.Abstract: The vehicle routing problem VRP is one of the most studied problems in operations research, given its relevance in the fields of transport and logistics. In recent years, interest in minimizing pollution due to the emission of greenhouse gases, as a result of the consumption of fossil fuels, has increased. The transport sector represents an important part of those emissions. In transport, situations such as traffic jams during peak hours, for example, lead to a dynamic road network in which travel times and consequently fuel consumption vary. Therefore, the time dependent vehicle routing problem, TDVRP, is a closer representation of real life than the traditional vehicle routing models, VRP. On the other hand, the split delivery vehicle routing problem, SDVRP, allows assigning multiple routes to the same client, promoting savings in them. The objective of this thesis is to develop a method for the use of transportation resources, in order to serve customers efficiently with regard to the total cost of the distance traveled and the total traveled time required. The problem consists of scheduling a trip for a day which is divided into intervals or time zones, with time windows to serve each customer, homogeneous vehicles with fixed capacity Q and a single deposit. In order to do so, a Memetic Algorithm (MA) is proposed in this work, capable of finding solutions that respect the constraints of the problem, taking into account the possibility of splitting the deliveries. By using Design of Experiments, the quality of the solutions generated by the Memetic Algorithm was evaluated with respect to a Genetic Algorithm (GA) also developed for the purpose, having as the evaluation criterion the percentage of best solutions reached by each algorithm. The experiments show that the proposed memetic algorithm surpasses the genetic algorithm, being more robust to changes in the parameters of both methods The proposed solution represents a model that is closer to the reality of road networks and generates routes that tend to reduce quantity, travel length and time spent by vehicles on the road network, leading to a reduction in greenhouse gas emissions.Maestrí

Trucks in movement

Beton erzeugende Unternehmen sehen sich täglich vor die Aufgabe gestellt, für die Belieferung der Baustellen eine möglichst effiziente Tourenplanung - unter Berücksichtigung ihrer heterogenen Fahrzeugflotte - zu erstellen. Da der Betonbedarf einer Baustelle die Kapazität eines einzelnen Fahrzeuges übersteigt, muss in der Regel jede Baustelle mehrmals hintereinander mit Beton beliefert werden. Das Planungsproblem ergibt sich nun insbesondere daraus, dass sich aufeinander folgenden Lieferungen nicht überschneiden dürfen, da nicht mehrere Fahrzeuge gleichzeitig entladen werden können. Eventuell entstehenden Lücken zwischen aufeinanderfolgenden Lieferungen jedoch sollten möglichst kurz gehalten werden. Im Rahmen dieser Dissertation werden mehrere Methoden besprochen, mit Hilfe derer eingangs erwähntes Tourenplanungsproblem gelöst werden kann. Die angewendeten Konzepte basieren auf exakten Verfahren, Heuristiken, Metaheuristiken, sowie hybriden Ansätzen. Ein exaktes Modell, beruhend auf einer Erweiterung des klassischen Vehicle Routing Problems (VRP, Tourenplanungsproblem) wurde entwickelt. Allerdings lässt sich die daraus resultierende Formulierung nur für äußerst kleine Instanzen exakt lösen. In der Praxis hingegen, ist dieser Ansatz aufgrund der zu langen Rechenzeiten und des enormen Rechenaufwandes nicht sinnvoll anwendbar. Daher wurde ein von Local Branching (LB) inspiriertes Verfahren konzipiert. Dieser integrativ hybride Ansatz wendet zusätzlich Nachbarschaftstrukturen, wie sie auch bei Variable Neighborhood Search (VNS) angewendet werden, kombiniert an. Darüber hinaus wurden valid inequalities für eine Verbesserung der unteren Schranken herangezogen. Ein weiterer Ansatz beruht auf einer Formulierung für multi-commodity network flow Problemen (MCNF). Anstatt einer globalen Sicht auf das Problem an sich, werden in diesem Zusammenhang nur ausgewählte Subbereiche näher betrachtet. So genannte Muster werden für alle BestellungenCompanies in the concrete industry are facing the following scheduling problem on a daily basis: concrete produced at several plants has to be delivered at customers' construction sites using a heterogeneous fleet of vehicles in a timely, but cost-effective manner. As the ordered quantity of concrete typically exceeds the capacity of a single vehicle several deliveries need to be scheduled to fulfill an order. The deliveries cannot overlap and the time between consecutive deliveries has to be small. This thesis presents a broad range of different ways on how to solve the problem stated above. Various solution methods based on exact, heuristic, meta-heuristic and hybrid approaches have been developed. Exact methods based on a formulation the so called VRP° (a Split Delivery Multi Depot Heterogeneous Vehicle Routing Problem with Time Windows) have been implemented. The resulting problem formulation can be solved to optimality for very small instances. For real-world-sized instances however, even with a steady increase in computational power, just to ``to MIP'' is not the way to success. Hence an algorithm, which controls the solution process of the embedded MIP-formulation, has been developed in order to tackler larger problem instances. This \emph{integrative hybrid} approach is based on Local Branching (LB) which itself is guided by means of Variable Neighborhood Search (VNS). Attention has also been paid to the development of valid inequalities and cuts in order to improve the quality of lower bounds. Another approach has been developed, which is based on a multi-commodity network flow model (MCNF) formulation. Rather than having a comprehensive view on the problem only subparts are considered and solved to optimality. So called \emph{patterns} (options on how orders could be satisfied) are generated heuristically and serve as an input for the MCNF. Given on a set of input pattern it is possible to solve the problem to optimality. Moreover the entir