Pollution routing problem with time window and split delivery

In most classic vehicle routing problems, the main goal is to minimise the total travel time or distance while, the green vehicle routing problem, in addition to the stated objectives, also focuses on minimising fuel costs and greenhouse gas emissions, including carbon dioxide emissions. In this research, a new approach in Pollution Routing Problem (PRP) is proposed to minimise the CO2 emission by investigating vehicle weight fill level in length of each route. The PRP with a homogeneous fleet of vehicles, time windows, considering the possibility of split delivery and constraint of minimum shipment weight that must be on the vehicle in each route is investigated simultaneously. The mathematical model is developed and implemented using a simulated annealing algorithm which is programmed in MATLAB software. The generated results from all experiments demonstrated that the application of the proposed mathematical model led to the reduction in CO2 emission

Decomposition strategies for large scale multi depot vehicle routing problems

Das Umfeld in der heutigen Wirtschaft verlangt nach immer bessern Ansätzen, um Transportprobleme möglichst effizient zu lösen. Die Klasse der ”Vehicle Routing Problems” (VRP) beschäftigt sich speziell mit der Optimierung von Tourenplanungsproblemen in dem ein Service-Leister seine Kunden möglichst effizient beliefern muss. Eine der VRP-Varianten ist das ”Multi Depot Vehicle Routing Problem with Time Windows” (MDVRPTW), in dem Kunden von verschiedenen Depots in einem fix vorgegebenen Zeitintervall beliefert beliefert werden müssen. Das MDVRPTW ist im realen Leben dank seiner realitätsnahen Restriktionen sehr oft vertreten. Typische Transportprobleme, wie sie in der Wirklichkeit auftreten, sind jedoch oftmals so groß, dass sie von optimalen Lösungsansätzen nicht zufriedenstellend gelöst werden können. In der vorliegenden Dissertation werden zwei Lösungsansätze präsentiert, wie diese riesigen, realitätsnahen Probleme zufriedenstellend bewältigt werden können. Beide Ansätze benutzen die POPMUSIC Grundstruktur, um das Problem möglichst intelligent zu dekomponieren. Die Dekomponierten und damit kleineren Subprobleme können dann von speziell entwickelten Algorithmen effizienter bearbeitet und letztendlich gelöst werden. Mit dem ersten Ansatz präsentieren wir eine Möglichkeit Transportprobleme zu dekomponieren, wenn populationsbasierte Algorithmen als Problemlöser eingesetzt werden. Dazu wurde ein maßgeschneiderter Memetischer Algorithmus (MA) entwickelt und in das Dekompositionsgerüst eingebaut um ein reales Problem eines österreichischen Transportunternehmens zu lösen. Wir zeigen, dass die Dekomponierung und Optimierung der resultierenden Subprobleme, im Vergleich zu den Ergebnissen des MA ohne Dekomposition, eine Verbesserung der Zielfunktion von rund 20% ermöglicht. Der zweite Ansatz beschäftigt sich mit der Entwicklung einer Dekomponierungsmethode für Lösungsalgorithmen, die nur an einer einzigen Lösung arbeiten. Es wurde ein ”Variable Neigborhood Search” (VNS) als Optimierer in das POPMUSIC Grundgerüst implementiert, um an das vorhandene Echtwelt-Problem heranzugehen. Wir zeigen, dass dieser Ansatz rund 7% bessere Ergebnisse liefert als der pure VNS Lösungsansatz. Außerdem präsentieren wir Ergebnisse des VNS Dekompositionsansatzes die um rund 6% besser sind als die des MA Dekompositionsansatzes. Ein weiterer Beitrag dieser Arbeit ist das Vorstellen von zwei komplett verschiedenen Ansätzen um das Problem in kleinere Sub-Probleme zu zerteilen. Dazu wurden acht verschiedene Nähe-Maße definiert und betrachtet. Es wurde der 2,3 und 4 Depot Fall getestet und im Detail analysiert. Die Ergebnisse werden präsentiert und wir stellen einen eindeutigen Gewinner vor, der alle Testinstanzen am Besten lösen konnte. Wir weisen auch darauf hin, wie einfach die POPMUSIC Dekomponierung an reale Bedürfnisse, wie zum Beispiel eine möglichst schnelle Ergebnisgenerierung, angepasst werden kann. Wir zeigen damit, dass die vorgestellten Dekomponierungsstrategien sehr effizient und flexibel sind, wenn Transportprobleme, wie sie in der realen Welt vorkommen gelöst werden müssen.The optimization of transportation activities is of high importance for companies in today’s economy. The Vehicle Routing Problem (VRP) class is dealing with the routing of vehicles so that the customer base of a company can be served in the most efficient way. One of the many variants in the VRP class is the Multi Depot Vehicle Routing Problem with Time Windows (MDVRPTW) which extends the VRP by additional depots from which customers can be served, as well as an individual time window for each customer in which he is allowed to be served. Modern carrier fleet operators often encounter these MDVRPTW in the real world, and usually they are of very large size so that exact approaches cannot solve them efficiently. This thesis presents two different approaches how this real world large scale MDVRPTWs can be solved. Both approaches are based on the POPMUSIC framework, which intelligently tries to decompose the large scale problem into much smaller sub-problems. The resulting sub-problems can then be solved more efficiently by specialized optimizers. The first approach in this thesis was developed for population based optimizers. A Memetic Algorithm (MA) was developed and used as an optimizer in the framework to solve a real world MDVPRTW from an Austrian carrier fleet operator. We show that decomposing the complete problem and solving the resulting sub-problems improves the solution quality by around 20% compared to using the MA without any decomposition. The second approach specially focuses on decomposition strategies for single solution methods. More precisely, a Variable Neighborhood Search (VNS) was implemented in the POPMUSIC framework to solve the real world instances. We show that decomposing the problem can yield improvements of around 7% compared to using the pure VNS method. Compared to the POPMUSIC MA approach the second approach can further improve the solution quality by around 6%. Another contribution in this thesis is the development of two generally different ways to measure proximity when creating sub-problems. In detail we tested eight different proximity measures and analyzed how good they decompose the problem in different environments. We tested the two, three and four depot case and present a clear winner that can outperform all other measures. Further we demonstrate that the POPMUSIC approach can flexibly be adjusted to real world demands, like a faster solution finding process, while at the same time maintaining high quality solutions. We show that a decomposition strategies combined with state of the art metaheuristic solvers are a very efficient and flexible tool to tackle real world problems with regards to solution quality as well as runtime

Uma nova abordagem heurística para a resolução do problema do roteamento de veículos capacitados com restrições tridimensionais de carregamento

Orientadora : Profa. Dra. Maria Teresinha Arns SteinerDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas e Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 11/02/2011Bibliografia: fls. 91-95Área de concentração: Programação matemáticaResumo: O Problema do Roteamento de Veículos Capacitados com Restrições Tridimensionais de Carregamento (3L – CVRP) é um recente avanço da pesquisa operacional para a resolução de problemas logísticos de alta complexidade. O interesse prático reside no transporte e distribuição de mercadorias de baixa densidade, cujo carregamento dos itens deve atender a restrições espaciais, como, eletrodomésticos, componentes mecânicos, móveis, entre outros. O 3L – CVRP também apresenta um grande desafio teórico na medida em que generaliza dois dos mais conhecidos problemas de otimização combinatória: O Problema do Roteamento de Veículos Capacitados e o Problema do Bin Packing Tridimensional. A solução do 3L – CVRP requer a determinação de rotas de menor custo para uma frota de veículos de mesma capacidade, de forma que se atenda a demanda de clientes dispersos em uma região. Tal demanda consiste em caixas retangulares que precisam ser carregadas atendendo a restrições operacionais. A resolução integrada implica na evocação iterativa de um método que resolve o problema do carregamento na medida em que o problema do roteamento vai sendo resolvido. Este trabalho apresenta uma nova abordagem para a resolução do 3L – CVRP. O método proposto resolve de forma heurística o problema do roteamento em dois estágios: o primeiro deles consiste em agrupar os clientes conforme sua demanda volumétrica enquanto que o segundo estágio constrói uma rota inicial refinando-a sequencialmente. O problema do carregamento é resolvido por um software comercial com licença trial. Foi desenvolvida uma nova estratégia para a integração entre os dois problemas baseada em limites de ocupação volumétrica do veículo. Os testes computacionais foram realizados em três etapas: Primeiramente avaliou-se o desempenho da heurística para o problema do roteamento de veículos capacitados. Testes foram realizados com instâncias clássicas da literatura e comparados com outras abordagens existentes (exatas e heurísticas), produzindo resultados satisfatórios tanto em termos de eficácia, quanto de eficiência. O segundo estágio de estes avaliou o software de carregamento para instâncias referentes ao problema de carregamento de contêineres e o problema do Bin Packing tridimensional. A comparação com outras abordagens existentes aponta um desempenho satisfatório do software. O terceiro e último estágio foi feito sobre instâncias do 3L – CVRP e comparadas com outros trabalhos existentes, produzindo resultados superiores em termos de eficácia para algumas instâncias, dependendo das configurações de restrição de carregamento, com melhorias em termos de eficiência para a grande maioria das instâncias testadas.Abstract: The Three Dimensional Loading Capacitated Vehicle Routing Problem (3L – CVRP) is a recent advance in operational research to solve logistical problems of high complexity. The practical interest is in transportation and distribution of low-density goods, whose shipment of the items must meet the spatial constraints, for example, mechanical components, furniture, household appliances, among other. The problem is also a great theoretical challenge because it generalizes two of the most well known problems in combinatorial optimization: the Capacitated Vehicle Routing Problem and the Three-dimensional Bin Packing Problem. The solution of the 3L - CVRP requires the determination of routes of minimum cost for a fleet of vehicles of the same capacity, so that it meets the demand of customers scattered across a region. This demand consists of rectangular boxes that need to be loaded given a set of operational constraints. The integrated resolution implies the evocation of an iterative method that solves the loading problem while the routing problem is solving. This work presents a new approach to solve the 3L – CVRP. The method employs heuristics procedures to solve the Capacitated Vehicle Routing Problem, in a strategy divided in two stages. The first grouping customers according to their demand based on volume, and the second builds an initial route and improve this route sequentially. The loading problem is solved by commercial software with a trial license. It was developed a new strategy for the integration of the two problems based on occupancy limits of the vehicle volume. The computational experiments were made in three stages: First was evaluated the performance of the heuristic to the Capacitated Vehicle Routing Problem. Tests were performed with instances of classical literature and compared with other existing approaches (heuristic and exact), producing satisfactory results in terms of effectiveness and efficiency. The second stage of tests evaluated the performance of software loading. For this, we use instances for the Container Loading Problem and the problem of Three- Dimensional Bin Packing. A comparison with other existing approaches shows a satisfactory performance of the software. The third and final stage was made on instances of 3L - CVRP and compared with other existing works, producing superior results in terms of effectiveness in some instances, depending on the load restriction settings, with improvements in efficiency for the most of instances tested

Heurística de dos fases para reducir el tiempo de recorrido en la distribución de material electoral al distrito de Puente Piedra en las elecciones generales 2021

Se plantea un modelo del problema de ruteo de vehículos, con la finalidad de minimizar el tiempo de recorrido en la distribución de material electoral al distrito de Puente Piedra en las Elecciones Generales 2021, otorgando 96 locales de votación a rutas definidas de entrega, teniendo en cuenta una flota de vehículos con capacidad homogénea. Se propone la heurística de dos fases (asignar primero-rutear despues) para encontrar la solución a la problemática actual de distribución, programándose el algoritmo de Clarke and Wright y el algoritmo de Búsqueda Tabú de la fase I y fase II, respectivamente, en el lenguaje de programación Visual Basic, utilizándose el software Visual Studio. Se realizó la corrida del programa y se evidenció que la fase I reduce en 23 minutos el tiempo de recorrido actual y luego con la fase II logra reducir 87 minutos más. obteniéndose un ahorro total de 110 minutos entre la situación actual y encontrada. Esta disminución representa el 7,83% del tiempo de recorrido y costo en combustible. El estudio aspira ilustrar como la optimización de rutas a través de la heurística de dos fases, puede reducir el costo de la logística de distribución de una empresa

Vehicle routing with multi-dimensional loading constraints

Zwei der wichtigsten Problemstellungen in der Transportlogistik behandeln einerseits das Verladen von Produkten auf LKWs und andererseits die ressourceneffiziente Belieferung der Kunden auf dem gegebenen Straßennetz. Bis dato wurden diese zwei Probleme mit Hilfe von kombinatorischer Optimierung getrennt von einander behandelt und es existieren zahlreiche Publikationen zu beiden Themen in den einschlägigen Fachzeitschriften. Erst in den letzten drei Jahren wurde einem integrierten Ansatz, der beide Problemstellungen zu einem Optimierungsproblem vereint betrachtet. Somit werden die Bestellungen einzelner Kunden nicht bloß über ihre Gewichte, sondern auch über ihre Abmessungen definiert. Der klare Vorteil dieses Ansatzes liegt darin, dass die einzelnen LKW Routen auch tatsächlich so gefahren werden können, da die tatsächliche Beladung auch berücksichtigt wurde. Andererseits steigt die kombinatorische Komplexität drastisch, weil das kapazitierte Vehicle Routing Problem (CVRP) mit Bin Packing Problemen (BPP) kombiniert wird und beide Probleme für sich alleine NP schwer sind. Diese Dissertation präsentiert drei verschiedene Probleme, die sich neben der Frage welches Fahrzeug beliefert welchen Kunden auch der Frage widmet, wie die bestellten Produkte auf den LKW geladen werden können. - Das Multi-Pile Vehicle Routing Problem (MP-VRP) bindet in das klassische CVRP eine Beladekomponente ein, die zwischen eindimensionalem und zweidimensionalem Bin Packing Problem angesiedelt ist. Die Problemstellungen wurden durch einen österreichischen Holzzulieferer motiviert. - Beim kapazitierten Vehicle Routing Problem mit zweidimensionalen Beladenebenbedingungen (2L-CVRP) bestellt jeder Kunden rechteckige Objekte, welche auf der rechteckigen Beladefläche des LKWs untergebracht werden müssen. - Das allgemeinste Beladeproblem stellt das dreidimensionale Bin Packing Problem dar. Hier bestellt jeder Kunde dreidimensionale Objekte, welche auf dem dreidimensionalen Laderaum des LKWs untergebracht werden müssen. Das klassische dreidimensionale Bin Packing Problem wird durch zusätzliche Beladenebenbedingungen erweitert. Momentan gibt es zu diesen kombinierten Problemen nur wenige Publikationen. Exakte Ansätze gibt es momentan nur zwei, einen für das MP-VRP (hier können Probleme bis zu 50 Kunden gelöst werden) und für das 2L-CVRP (hier können Probleme bis zu 30 Kunden exakt gelöst werden). Für Realweltanwendungen müssen jedoch Heuristiken gefunden werden, welche größere Probleminstanzen lösen können. In dieser Arbeit wird für alle drei Problemstellungen ein Ameisenalgorithmus verwendet und mit bestehenden Lösungsansätzen aus dem Bereich der Tabu-Suche (TS) verglichen. Es wird gezeigt, dass der präsentierte Ameisenansatz für die zur Verfügung stehenden Benchmarkinstanzen die besten Ergebnisse liefert. Darüber hinaus wird der Einfluss verschiedener Beladenebenbedingungen auf die Lösungsgüte untersucht, was eine wichtige Entscheidungsgrundlage für Unternehmen darstellt.Two of the most important problems in distribution logistics concern the loading of the freight into the vehicles, and the successive routing of the vehicles along the road network, with the aim of satisfying the demands of the clients. In the combinatorial optimization field, these two loading and routing problems have been studied intensively but separately yielding a large number of publications either for routing or packing problems. Only in recent years some attention has been brought to their combined optimization. The obvious advantage is that, by considering the information on the freight to be loaded, one can construct more appropriate routes for the vehicles. The counterpart is that the combinatorial difficulty of the problem increases consistently. One must not forget that both the vehicle routing problem and the bin packing problem are NP hard problems! This thesis presents three different problems concerning the combination of routing and loading (packing) problems. - The Multi-Pile Vehicle Routing Problem (MP-VRP) incorporates an interesting loading problem situated between one dimensional and two dimensional bin packing. This problem has been inspired by a real world application of an Austrian wood distributing company. - The Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints (2L-CVRP) augments the classical Capacitated Vehicle Routing Problem by requiring the satisfaction of general two dimensional loading constraints. This means that customers order items represented by rectangles that have to be feasibly placed on the rectangular shaped loading surface of the used vehicles. - The most general packing problem to be integrated is the Three Dimensional Bin Packing Problem (3DBPP) resulting in the Capacitated Vehicle Routing Problem with Three-Dimensional Loading Constraints (3L-CVRP). Here the order of each customer consists of cuboid shaped items that have to be feasibly placed on the loading space of the vehicle. A feasible placement is influenced by additional constraints that extend the classical 3DBPP. Concerning the literature solving these problems with exact methods it becomes clear that this is only possible to some very limited extent (e.g.: the MP-VRP can be solved up to 50, the 2L-CVRP can be solved exact up to 30 customers, for the 3L-CVRP no exact approach exists). Nevertheless for real world applications the problem instances are much larger which justifies the use of (meta-)heuristics. The rank-based Ant System was modified and extended to solve the combined problem by integrating different packing routines. The designed methods outperform the existing techniques for the three different problem classes. The influence of different loading constraints on the objective value is investigated/is intensively studied to support the decision makers of companies facing similar problems

Meta-heurísticas de optimização por colónias de formigas em problemas periódicos de estabelecimento de rotas

Nesta tese são apresentados procedimentos inovadores na classe das meta-heurísticas de optimização por colónias de formigas e técnicas de pós-optimização que se revelaram promissores na resolução de problemas periódicos de estabelecimento de rotas de grandes dimensões. Um sistema de recolha de resíduos sólidos urbanos de um concelho do centro de Portugal é usado como caso de estudo, sendo objectivo dos modelos desenvolvidos a optimização dos circuitos dos veículos de recolha. Os problemas periódicos de estabelecimento de rotas (PVRP) constituem uma extensão do problema clássico de estabelecimento de rotas no qual os clientes têm que ser visitados um número diferenciado de vezes num dado horizonte temporal. Deste modo, é necessário elaborar um planeamento, definindo a calendarização das visitas aos clientes, e desenhar o conjunto de rotas para o horizonte temporal. São comparadas duas abordagens para a resolução deste tipo de problemas: uma formulação em que a calendarização e o estabelecimento de rotas são abordados em duas fases distintas e sequenciais, e outra formulação em que estas duas vertentes do problema são abordadas em simultâneo. Deste modo, são desenvolvidos dois modelos distintos que incorporam elementos inovadores e cujo desempenho se compara favoravelmente com outros modelos da mesma classe anteriormente desenvolvidos e publicados.This thesis presents innovative procedures in metaheuristics by ant colony optimisation and post-optimisation techniques which are shown to be promising in solving large periodic vehicle routing problems. A real-world solid waste collection system of a municipality in the center of Portugal is used as a case study, for which the optimisation of the routes of the collection vehicles constitutes the aim of the developed models. Periodic vehicle routing problems (PVRP) are an extension of the classical vehicle routing problem where customers are visited with different frequencies over a time horizon. Therefore it is necessary to create a plan defining the schedule of visits to customers and to design a set of routes for the time horizon. In this thesis, two approaches for solving this type of problems are compared. In the first one, scheduling and designing routes are approached in two stages; in the other, both of these problems are tackled simultaneously. Hence, two distinct models are developed, both based on ant colony metaheuristics, complemented by post-optimisation techniques, that incorporate innovative elements and have shown a performance that compares favorably with other models of the same class previously published.Bolseira do programa Concurso nº2/ 5.3/PRODEP/2001 de Financiamento à Formação Avançada de Docentes do Ensino Superior – Medida 5/ Acção 5.3, do Programa da Intervenção Operacional Educaçã

The dynamic vehicle routing problem: a metaheuristics based investigation

The desire to optimise problems is as prevalent in today's society as it has ever been. The demand for increases in speed and efficiency is relentless and has resulted in the need for mathematical models to bear greater resemblance to real-life situations. This focus on increased realism has paved the way for new dynamic variants to classic optimisation problems. This thesis begins by considering the Dynamic Vehicle Routing Problem. The basic premise of this routing problem is as follows a percentage of customers are known a priori, for which routes are constructed, further customers then arrive during the course of the working day and need to be incorporated into an evolving schedule. Literature has proposed a timeslot approach, whereby one partitions the working day into a series of smaller problems, that one is then required to solve in succession. This technique is used to produce a variety of metaheuristics based implementations, most noticeably Ant Colony Optimisation and Tabu Search. Consideration is then given to the Dynamic Vehicle Routing Problem with Time Windows. This problem is similar to the Dynamic Vehicle Routing Problem, but requires each customer to be serviced within a predefined period of the day. A metaheuristic approach adapted from the most successful algorithm implemented on the Dynamic Vehicle Routing Problem is presented. Finally consideration is given to a time-based decomposition technique for the Vehicle Routing Problems with Time Windows (Large-Scale instances). This work makes use of the dynamic solution technique developed in the preceding work, and is used in conjunction with an Ant Colony Optimisation algorithm and a descent algorithm