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In cities, the "last mile" is not only a logistical issue, but also a significant urban planning challenge. The final mile in the supply chain involves highfrequency, low-volume, and short-haul distribution of products to end consumers. The last leg of the supply chain is the most crucial, but also the least efficient. Transportation planning is one of the major contributors to the severity of last-mile delivery (LMD) issues in cities. The scope of our thesis is on the transportation planning for perishable food supply chains. In recent years, the global food market has shown substantial growth. Therefore, posing new challenges, and initiating a drastic change in the last mile logistics. These challenges are mainly related to the high perishability of food product that require specific management approaches to maintain their quality. Additionally, we mention the growing demand from customers for deliveries to be made on time, at a lower cost, and in an environmentally friendly manner. Customers search other alternatives, if the service doesn’t meet their expectations. Last mile logistics is essential in developing brand loyalty in this competitive environment, as it allows transporters to deliver fresh and high quality products to consumers, faster and cost-effectively. The aim of this thesis is to propose models and solving approaches that can support decision-making process in food supply chain through addressing concerns about transportation costs, carbon emissions, product quality, service level, etc. Specifically, different decision problems that can be regarded as routing problems, are considered. We start by modelling a delivery problem with specific temporal customer’s requirements as a capacitated vehicle routing problem with soft time windows. The problem is formulated as a Mixed 0-1 non-Linear Program (MINLP). The objective is to minimize the total cost, consisting of transportation costs, food quality degradation costs, and time-windows violation costs. To model the temporal preference of the customers in a most realistic way, we provide another model that represent this preference information as a fuzzy number with respect to the satisfaction of service time. This problem is a Capacitated Vehicle Routing Problem with Fuzzy TimeWindows (CVPFTW) and formulated as a fuzzy mixed-integer linear programming model. Both problems are addressed on real road networks where arcs are labelled with multiple attributes, and solved using CPLEX solver. The performance of the proposed models is assessed through computational analyses on several test instances. Some instances are derived from real-life applications, others are randomly generated. The results proved that our approach can help reduce the operational costs of delivery while improving customer service. To improve customer satisfaction, we propose a many-objective Customer- Centric Perishable Food Distribution Problem. The proposed model focuses on the cost, the quality of the product, and the service level improvement by considering not only time windows but also the customers’ target time and their priority. Owing the difficulty of solving such model, we propose a General Variable Neighbourhood Search (GVNS) metaheuristic. By solving a mono-objective sub-problem, such approach enables to generate a set of diverse solutions. These solutions are evaluated over some non-optimized criteria and then ranked using an a posteriori approach that requires minimal information about decision maker preferences. The computational results show: (a) GVNS achieved the same quality solutions as an exact solver (CPLEX) in the sub-problem; (b) GVNS can generate a wide number of candidate solutions, and (c) the use of the a posteriori approach makes easy to generate different decision maker profiles which in turn allows obtaining different rankings of the solutions. Solving a perishable food distribution problem in a real world setting is a very complex task. This is due to products characteristics, and the requirements of customers.To ensure a safe, quality product with a desired service level, a bunch of specifications should be included during the decision/optimization process. Many times, the computational models necessarily leave out of consideration several characteristics and features of the real world. Thus, trying to obtain the optimum solution can not be enough for a problemsolving point of view. To address this problem, we propose a modelling to generate Alternatives- metaheuristic based approach to generate a set of alternative solutions. The aim is to allow the decision maker to consider different perspectives, and non-modelled criteria., En las ciudades, la "última milla" no es sólo una cuestión logística, sino también un importante reto de planificación urbana. La última milla de la cadena de suministro implica la distribución de alta frecuencia, bajo volumen y corta distancia de los productos a los consumidores finales. El último tramo de la cadena de suministro es el más crucial, pero también el menos eficiente. La planificación del transporte es uno de los principales factores que contribuyen a la gravedad de los problemas de la última milla (LMD) en las ciudades. En los últimos años, el mercado mundial de la alimentación ha experimentado un crecimiento considerable, lo que ha planteado nuevos retos y ha provocado un cambio drástico en la logística de la última milla. Estos retos están relacionados principalmente con el alto grado de perecederos de los productos alimentarios, que requieren enfoques de gestión específicos para mantener su calidad. Y la creciente demanda de los clientes de que las entregas se realicen a tiempo, con un coste menor y de forma respetuosa con el medio ambiente. La logística de última milla es esencial para desarrollar la lealtad a la marca en este entorno competitivo, ya que permite a los transportistas entregar productos frescos y de alta calidad a los consumidores, de forma más rápida y rentable. El objetivo de esta tesis es proponer modelos y enfoques de resolución que puedan apoyar el proceso de toma de decisiones en la cadena de suministro de alimentos, abordando las preocupaciones sobre los costes de transporte, las emisiones de carbono, la calidad del producto y el nivel de servicio. Comenzamos modelando el problema de las necesidades del cliente para una entrega en un rango de tiempo específico como un problema de enrutamiento de vehículos capacitados con una ventana de tiempo suave, para el que se formula un programa no lineal mixto 0-1 (MINLP). El objetivo es minimizar los costes totales, que consisten en los costes de transporte, los costes de degradación de la calidad de los alimentos y los costes de violación de la ventana de tiempo. Para modelar la preferencia de los clientes en términos de ventana de tiempo muy bien, proporcionamos otro modelo que representa esta información de preferencia como un número difuso con respecto a la satisfacción del tiempo de servicio. Este problema se considera como un problema de enrutamiento de vehículos capacitados con ventanas de tiempo difusas CVPFTW y se formula como un modelo de programación lineal de enteros mixtos. Ambos problemas se abordan en redes de carreteras reales en las que los arcos están etiquetados con múltiples atributos, y se resuelven utilizando algoritmos exactos. El rendimiento de los modelos propuestos se evalúa mediante análisis computacionales adecuados que tienen en cuenta varios conjuntos de instancias de prueba, algunas derivadas de una aplicación real y otras generadas aleatoriamente. Para aumentar la satisfacción del cliente, proponemos un problema de distribución de alimentos perecederos centrado en el cliente que se centra en el coste, la calidad del producto y la mejora del nivel de servicio teniendo en cuenta no sólo las ventanas de tiempo, sino también el tiempo objetivo de los clientes y su prioridad. Reconociendo la dificultad de resolver este modelo, proponemos un enfoque metaheurístico basado en la Búsqueda de Vecindario General (GVNS) que permite resolver eficientemente un subproblema y obtener un conjunto de soluciones. Estas soluciones se evalúan sobre algunos criterios no optimizados xiy luego se clasifican utilizando un enfoque a posteriori que requiere una información mínima sobre las preferencias del decisor. Los resultados computacionales muestran (a) que GVNS logra soluciones de la misma calidad que un solucionador exacto (CPLEX) en el subproblema; (b) que GVNS puede generar un amplio número de soluciones candidatas, y (c) que el uso del enfoque a posteriori facilita la generación de diferentes perfiles de tomadores de decisiones, lo que a su vez permite obtener diferentes clasificaciones de las soluciones.La resolución de un problema de distribución de alimentos perecederos en un entorno real es una tarea muy compleja. Para garantizar un producto seguro y de calidad con el nivel de servicio deseado, es necesario incluir un conjunto de especificaciones durante el proceso de decisión y optimización de las operaciones. Muchas veces, los modelos computacionales no tienen en cuenta varias características y rasgos del mundo real, por lo que intentar obtener la solución óptima puede no ser suficiente desde el punto de vista de la resolución de problemas. Para abordar este problema, proponemos un enfoque basado en la metaheurística Modeling to Generate Alternatives para generar un conjunto de soluciones alternativas. El objetivo es permitir que el responsable de la toma de decisiones considere diferentes perspectivas y criterios no modelados., Tesis Univ. Granada.

In this research work, we applied some solving techniques on Travelling salesman problem (TSP) and Capaciated Vehicle routing problem (CVRP) which are some of the variants of vehicle routing problem. For each of the considered problem, Branch-and-cut was applied on TSP and Column generation technique was used on CVRP. We obtained optimal solution and tour. Hence, these methods can be used to solve similar problem for optimal solution.

International audience; Genetic Algorithms (GA) have long been used for ordering optimization problems with some considerable efforts to improve their exploration and exploitation abilities. A great number of GA implementations have been proposed varying from GAs applying simple or advanced variation operators to hybrid GAs combined with different heuristics. In this work, we propose a short review of genetic operators for ordering optimization with a classification according to the information used in the reproduction step. Crossover operators could be position ("blind") operators or heuristic operators. Mutation operators could be applied randomly or using local optimization. After studying the contribution of each class on solving two benchmark instances of the Capacitated Vehicle Routing Problem (CVRP), we explain how to combine the variation operators to allow simultaneously a better exploration of the search space with higher exploitation. We then propose the random and the balanced hybridization of the operators' classes. The hybridization strategies are applied to solve 24 CVRP benchmark instances. Results are analyzed and compared to demonstrate the role of each class of operators in the evolution process.

Cost of transportation of goods and services is an interesting topic in today’s society. The Capacitated vehicle routing problem, which is been consider in this research, is one of the variants of the vehicle routing problem. In this research we develop a reinforcement learning technique to find optimal paths from a depot to the set of customers while also considering the capacity of the vehicles, in order to reduce the cost of transportation of goods and services. Our basic assumptions are; each vehicle originates from a depot, service the customers and return to the depot, the vehicles are homogeneous. We solve the CVRP with an exact method; column generation, goole’s operation research tool and reinforcement learning and compare their solutions. Our objective is to solve a large-size of vehicle routing problem to optimality.

SyD Colombia S.A.S, es una organización que en los últimos años ha presentado un crecimiento en el número de operaciones, el cual ha venido acompañado de altos costos logísticos y problemas relacionados con el servicio al cliente debido al uso de empresas de mensajería externas para la distribución de sus productos. Para resolver esta problemática se diseñó un sistema de ruteo vehicular usando la metodología Cluster First-Route Second, en la que se realiza la formación de clústeres por medio de una adaptación del método de barrido, para luego elaborar una ruta dentro de cada uno de estos, usando un modelo matemático del Problema de Ruteo de Vehículos con Capacidad, con soporte del software de uso libre llamado “Grafos”. Finalmente, se validó el diseño propuesto con los datos de un día de operación en la empresa SyD Colombia S.A.S, donde se evalúan diferentes indicadores, los cuales son esenciales para medir la efectividad de la nueva metodología. Como resultado del diseño desarrollado, se logró una disminución del 25.08% en la distancia recorrida en comparación con la metodología actual de la empresa, acompañada de una reducción de 13.75% en los costos de fletes. Se espera que con la adaptación realizada en la etapa de clusterización, la empresa logre reducir el porcentaje de inconformidad presentado por los clientes preferenciales. SyD Colombia S.A.S, is an organization that in recent years has presented a growth in the number of its operations, which has been accompanied by high logistics costs and problems related to customer service due to the use of external courier companies for the distribution of their products. To solve this problem, a vehicle routing system was designed using the Cluster First - Route Second methodology, in which clusters are formed by adapting the Sweep Algorithm, and then a route is created within each of these, using a mathematical model of the capacitated vehicle routing problem with support from the free software called "Grafos". Finally, the proposed design was validated with data from one day of operation in the company SyD Colombia S.A.S, where different indicators are evaluated, which are essential to measure the effectiveness of the new methodology. As a result of the design developed, a 25.08% decrease in the distance traveled was achieved in comparison with the company's current methodology, accompanied by a 13.75% reduction in freight costs. It is expected that with the adaptation made in the clustering stage, the company will be able to reduce the percentage of dissatisfaction presented by preferential clients.

En la ciudad de Tunja no se cuenta con fuentes de información e indicadores exactos que establezcan la cantidad de llantas usadas y desechadas en tiraderos clandestinos, patios de casas y centros de acopio, las cuales generan impacto negativo en el medio ambiente y la salud de los habitantes, evidenciando la necesidad de generar una solución logística. Se presenta una investigación de enfoque cuantitativo de tipo estudio de caso; en esta se utilizó el método CVRP, que consiste en el diseño de un conjunto de rutas de menor coste, donde cada cliente se visite una única vez por un único vehículo y todas las rutas comienzan y finalizan en un centro de gravedad. Como resultados se logró la caracterización y diseño de un modelo logístico, que integró la ubicación de punto de acopio, demanda, rutas de recolección, capacidades, como herramienta sólida y actualizada que generara alternativas ambientales para la ciudad.

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that has been of great interest for decades for both, science and industry. The CVRP is a variant of the vehicle routing problem characterized by capacity constrained vehicles. The aim is to plan tours for vehicles to supply a given number of customers as efficiently as possible. The problem is the combinatorial explosion of possible solutions, which increases superexponentially with the number of customers. Classical solutions provide good approximations to the globally optimal solution. D-Wave's quantum annealer is a machine designed to solve optimization problems. This machine uses quantum effects to speed up computation time compared to classic computers. The problem on solving the CVRP on the quantum annealer is the particular formulation of the optimization problem. For this, it has to be mapped onto a quadratic unconstrained binary optimization (QUBO) problem. Complex optimization problems such as the CVRP can be translated to smaller subproblems and thus enable a sequential solution of the partitioned problem. This work presents a quantum-classic hybrid solution method for the CVRP. It clarifies whether the implementation of such a method pays off in comparison to existing classical solution methods regarding computation time and solution quality. Several approaches to solving the CVRP are elaborated, the arising problems are discussed, and the results are evaluated in terms of solution quality and computation time.

Submitted by admin tede (tede@pucgoias.edu.br) on 2019-09-24T23:42:57Z No. of bitstreams: 1 Dissertação - Edgar Marcos Ancioto Junior.pdf: 2404833 bytes, checksum: 6230e1f53a81bab2f71e8ab49512a675 (MD5) Made available in DSpace on 2019-09-24T23:42:57Z (GMT). No. of bitstreams: 1 Dissertação - Edgar Marcos Ancioto Junior.pdf: 2404833 bytes, checksum: 6230e1f53a81bab2f71e8ab49512a675 (MD5) Previous issue date: 2019-04-17 In optimization there are methods applicable to a variety of minimization problems. When defining the method to be applied to a real problem, it is based on the scientific production seeking similarity with the problem and the efficiency of its results. There is a gap in the challenge of extracting information from experiments in scientific works that make possible the reproduction of the study. This work aims to develop an online experimental environment focused on optimization, with the functionality of performing experimental tests with metaheuristic algorithms, with the possibility of hybridization, validating the concepts developed through the solution of benchmark problems and allowing the comparison with other methods developed in the literature. All codes are developed in the Python programming language and are open source. The environment will allow the configuration of the algorithm and will demonstrate the resolution of the problem, allowing the understanding of the application of methods, the evaluation of hybridizations and the comparison between all the methods. For metaheuristic methods, Genetic Algorithm (GA), Simulated Annealing (SA) and Ant Colony (ACO) were developed for routing problems. For non-linear optimization GA and SA methods were applied to the functions and benchmark instances to evaluate the efficiency of the methods. Hybridizations of the methods were evaluated using retransmitted collaborative work logic. The results demonstrated that the hybrid techniques have a superior capability to the conventional methods to solve the problems of instances for the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (CVRP). The ACO + GA hybridization was the combination which reached the best average efficiency values for the problems with values of 97.5% for the TSP and 96.66% for the CVRP, highlighting the executions involving the biggest problems among the selected ones. An environment was made available on the web, http://hybroo.hopto.org:5000/ to access the methods and the execution of the tests, allowing the data conference of this research Na otimização existem métodos aplicáveis a uma variedade de problemas de minimização. Ao definir o método a ser aplicado para um problema real, baseia-se na produção científica buscando similaridade com o problema e a eficiência de seus resultados. Surge uma lacuna no desafio de extrair informações de experimentos em trabalhos científicos que possibilitem a reprodução do estudo. Este trabalho tem como objetivo desenvolver um ambiente experimental online voltado à otimização, com a funcionalidade de realizar testes experimentais com algoritmos meta-heurísticos, com a possibilidade de hibridização, validando os conceitos desenvolvidos por meio da solução de problemas de benchmark e permitindo a comparação com outros métodos desenvolvidos na literatura. Todos os códigos são desenvolvidos na linguagem de programação Python e são de código aberto. O ambiente permitirá a configuração do algoritmo e demonstrará a resolução do problema, permitindo a compreensão da aplicação de métodos, a avaliação de hibridizações e a comparação entre todos os métodos. Para problemas de roteirização foram desenvolvidos os métodos metaheurísticos Algoritmo Genético (GA), Recozimento Simulado (SA) e Colônia de Formigas (ACO). Para otimização não linear os métodos GA e SA foram aplicados às funções e instâncias de benchmark para avaliação da eficiência dos métodos. Foram avaliadas as hibridizações dos métodos utilizando a lógica de trabalho colaborativo retransmitido. Os resultados demonstraram que as técnicas híbridas tem uma capacidade superior aos métodos convencionais para resolução dos problemas de instâncias para o Problema do Caixeiro Viajante (TSP) e Problema de Roteamento de Veículos Capacitado (CVRP), sendo que a hibridização ACO+GA foi a combinação que atingiu os melhores valores de eficiência média para os problemas com valores de 97,5% para o TSP e 96,66% para o CVRP, com destaque para as execuções que envolvem os maiores problemas entre as instâncias da biblioteca A-VRP. Um ambiente foi disponibilizado na web, http://hybroo.hopto.org:5000/ para acesso dos métodos e execução dos testes, permitindo a conferência dos dados desta pesquisa

Along this paper, we present a new multi agent-based system to gather waste on cities and villages. We have developed a low cost wireless sensor prototype to measure the volume level of the containers. Furthermore a route system is developed to optimize the routes of the trucks and a mobile application has been developed to help drivers in their working days. In order to evaluate and validate the proposed system a practical case study in a real city environment is modeled using open data available and with the purpose of identifying limitations of the system.

Ovaj rad obrađuje problem usmjeravanja vozila, te njegove instance s ograničenim kapacitetom, vremenskim prozorima i mogućnošću preuzimanja tereta i dostave. Dan je detaljan opis problema i korištenih metaheurističkih algoritama: genetskog algoritma turnirske eliminacije i algoritma evolucijske strategije. Implementirana su tri oblika zapisa rješenja, operatori mutacije i križanja i dva lokalna operatora. Istraživana je ovisnost kvalitete rješenja o obliku zapisa, korištenom algoritmu i korištenju lokalnih operatora. Dobiveni rezultati prikazani su grafički i analizirani. This paper deals with vehicle routing problem and its instances with limited capacity, time windows and pick-up and delivery. Detailed description of the problem is given, as well as of the two metaheuristic algorithms that were used: genetic algorithm with tournament selection and evolution strategy algorithm. Three forms of results, mutation and crossover operators and two local operators were implemented. The dependence of the quality of the solution on the form of result, used algorithm and the use of local operators was explored. The obtained results are shown graphically and analyzed.

U ovom radu opisan je i obrađen problem usmjeravanja vozila i rješavanje tri inačice tog problema metaheurističkim pristupom, konkretno genetskim algoritmom. Navedene su postojeće metode rješavanja problema i ostvarena je vlastita implementacija rješenja u tri oblika zapisa u statičkim uvjetima. Kao dinamička komponenta za različite genotipe i inačice problema ispitana je brzina konvergencije rješenja ka rješenjima dobivenim heurističkim pristupom kao i brzina pronalaska rješenja za fiksni broj evaluacija. Rezultati su uspoređeni međusobno te prikazani grafički. In this thesis, vehicle routing problem and solving three variants of it is described. Problem variants were solved using metaheuristic approach, specifically genetic algorithm. The existing methods of solving the VRP problem were mentioned as well as the solution implementation that was recorded in three forms in static conditions. As a dynamic component for different genotypes and variants of the problem, convergence speed to the solutions obtained by heuristic approach was examined as well as the speed of finding a solution for a fixed number of evaluations. The results were compared and presented graphically.

Background: The Capacitated Vehicle Routing Problem (CVRP) is one of the most important transportation problems in logistics and supply chain management. The standard CVRP considers a fleet of vehicles with homogeneous capacity that depart from a warehouse, collect products from (or deliver products to) a set of customer locations (points) and return to the same warehouse. However, the operation of carrier companies and third-party transportation providers may follow a different network flow for collection and delivery. This may lead to non-optimal route planning through the use of the standard CVRP. Objective: To propose a model for carrier companies to obtain optimal route planning. Method: A Capacitated Vehicle Routing Problem for Carriers (CVRPfC) model is used to consider the distribution scenario where a fleet of vehicles depart from a vehicle storage depot, collect products from a set of customer points and deliver them to a specific warehouse before returning to the vehicle storage depot. Validation of the model’s functionality was performed with adapted CVRP test problems from the Vehicle Routing Problem LIBrary. Following this, an assessment of the model’s economic impact was performed and validated with data from a real carrier (real instance) with the previously described distribution scenario. Results: The route planning obtained through the CVRPfC model accurately described the network flow of the real instance and significantly reduced its distribution costs. Conclusion: The CVRPfC model can thus improve the competitiveness of the carriers by providing better fares to their customers, reducing their distribution costs in the process.

The capacitated vehicle routing problem (CVRP) is one of the most challenging problems in the optimization of distribution. Most approaches can solve case studies involving less than 100 nodes to optimality, but time-consuming. To overcome the limitation, this paper presents a novel two-phase heuristic approach for the capacitated vehicle routing problem. Phase I aims to identifying sets of cost-effective feasible clusters through an improved density-based clustering algorithm. Phase II assigns clusters to vehicles and sequences them on each tour. Max-min ant system is used to order nodes within clusters. The simulation results indicate efficiency of the proposed algorithm.

Many optimization problems require heuristic methods to solve the problem. Variable Neighborhood Search (VNS) is a metaheuristic form that systematically changes its “neighborhood” in search of solutions. One method in VNS is Variable Neighborhood Descent (VND), which performs a deterministic neighborhood change. The change of the neighborhood in VND can be done in a random and sequential order. This paper compares sequential and random neighborhood selection methods in solving Capacitated Vehicle Routing Problem (CVRP) problems. There are 6 intra-route neighborhood structures and 4 inter-route structures used. CVRP problems are taken from several dataset providers. The initial solution is formed by Sequential Insertion method. The experimental results show that the random selection of neighborhood operators can provide a more optimal route length (in 10 of 13 datasets used) than that of sequential selection (only better in 3 dataset). However, the random selection takes more iterations to reach convergent state than the sequential one. For sequential selection, determination of the neighborhood structure’s order affects the speed to the convergent state. Hence, a random selection in VND method is more preferable than sequential selection.

Combinatorial optimization problems on graphs arise in many practical applications. One of the most studied practical combinatorial optimization problem is the Vehicle Routing Problem (VRP). When coupled with modern in-car navigation and fleet management software, real world applications of VRP optimization result in significant cost savings. In this paper novel multiple improvements pivoting rule for Capacitated VRP (CVRP) is proposed. Its application significantly reduces computational time needed for CVRP optimization. A novel pivoting rule is implemented as part of the search step selection mechanism in the iterated local search algorithm. Augmented iterated local search algorithm is tested on 4 large scale real- world problems in Croatia with up to 7065 customers and 236 vehicles and on standard CVRP benchmark sets. Real-world problem data was obtained from a large Croatian logistics company. Comparison of well known first and best pivoting rules with proposed novel multiple improvements pivoting rule regarding travel distance, number of search moves and computational time is given. Achieved computational speed-ups are up to 29 times compared to the first and 9 times compared to the best improvement pivoting rule, without any substantial degradation in quality of the obtained solution.

The proposed approach solves the Multi-Depot Open VRP.An uniform view of ejection chains is adopted for all neighborhoods.Multiple Neighborhood Search (MNS) and Tabu Search (TS) are combined.MNS-TS outperforms the state-of-the-art methods. In this paper, we address the Multi-Depot Open Vehicle Routing Problem (MDOVRP), which is a generalization of the Capacitated Vehicle Routing Problem (CVRP) where vehicles start from different depots, visit customers, deliver goods and are not required to return to the depot at the end of their routes. The goal of this paper is twofold. First, we have developed a general Multiple Neighborhood Search hybridized with a Tabu Search (MNS-TS) strategy which is proved to be efficient and second, we have settled an unified view of ejection chains to be able to handle several neighborhoods in a simple manner. The neighborhoods in the proposed MNS-TS are generated from path moves and ejection chains. The numerical and statistical tests carried out over OVRP and MDOVRP problem instances from the literature show that MNS-TS outperforms the state-of-the-art methods.

La logística para el transporte de mercancía en zonas urbanas cada vez tiene mayores exigencias referente a la reducción de emisiones al ambiente, ruido y tamaño de vehículos, por lo que los vehículos eléctricos se han convertido en una opción para las empresas dedicadas a esta actividad. Sin embargo aún existen grandes barreras para adoptar esta tecnología, principalmente el costo inicial, límite de autonomía de batería, tiempo de recarga y cantidad de estaciones existentes. En la actualidad se analiza este tipo de flota como una opción que en muchos casos se pone a prueba como programas pilotos. Sin embargo, de acuerdo a la tendencia de normativas ambientales, se cree que en poco tiempo será una obligación, por lo que conseguir las rutas optimas al menor costo posible es una necesidad imperiosa. Por lo tanto, se propone una metodología de solución planteando el problema como un CVRP clásico con restricciones de capacidad de batería e incluyendo el tiempo de recarga como parte del costo. La logística per al transport de mercaderia en zones urbanes cada vegada té més exigències en referència a la reducció d'emissions a l'ambient, soroll i mida de vehicles, de manera que els vehicles elèctrics s'han convertit en una opció per a les empreses dedicades a aquesta activitat. No obstant això encara hi ha grans barreres per adoptar aquesta tecnologia, principalment el cost inicial, límit d'autonomia de bateria, temps de recàrrega i quantitat d'estacions existents. En l'actualitat s'analitza aquest tipus de flota com una opció que en molts casos es posa a prova com programes pilots. No obstant això, d'acord amb la tendència de normatives ambientals, es creu que en poc temps serà una obligació, per la qual cosa aconseguir les rutes òptimes al menor cost possible és una necessitat imperiosa. Per tant, es proposa una metodologia de solució plantejant el problema com un CVRP clàssic amb restriccions de capacitat de bateria i incloent el temps de recàrrega com a part del cost. Logistics for the transport of merchandise in urban areas is increasingly higher demands regarding reducing emissions to the environment, noise and size of vehicles, so that electric vehicles have become an option for companies engaged in this activity, but there are still major barriers to adopting this technology mainly initial cost, limited battery life, recharge time and quantity of existing stations. At present this type of fleet is analyzed as an option in many cases is tested as pilot programs, however according to the trend of environmental regulations is believed that soon will be an obligation, so get optimum routes at the lowest possible cost is imperative, therefore a solution methodology is proposed raising the issue as a classic CVRP restricted battery capacity and including recharge time as part of the cost, the solution arises from the adaptation of the proposal made by Quintero-araujo et al., 2016 in planning routes in mountainous areas by the method of successive approximations, adding a local search to include visits to charging stations battery and iterating with time ranges in order to achieve the best possible solution with the objective of minimizing the total cost function.