PASA: A Priori Adaptive Splitting Algorithm for the Split Delivery Vehicle Routing Problem

The split delivery vehicle routing problem (SDVRP) is a relaxed variant of the capacitated vehicle routing problem (CVRP) where the restriction that each customer is visited precisely once is removed. Compared with CVRP, the SDVRP allows a reduction in the cost of the routes traveled by vehicles. The exact methods to solve the SDVRP are computationally expensive. Moreover, the complexity and difficult implementation of the state-of-the-art heuristic approaches hinder their application in real-life scenarios of the SDVRP. In this paper, we propose an easily understandable and effective approach to solve the SDVPR based on an a priori adaptive splitting algorithm (PASA). The idea of a priori split strategy was first introduced in Chen et al. (2017). In this approach, the demand of the customers is split into smaller values using a fixed splitting rule in advance. Consequently, the original SDVRP instance is converted to a CVRP instance which is solved using an existing CVRP solver. While the proposed a priori splitting rule in Chen et al. (2017) is fixed for all customers regardless of their demand and location, we suggest an adaptive splitting rule that takes into account the distance of the customers to the depot and their demand values. Our experiments show that PASA can generate solutions comparable to the state-of-the-art but much faster. Furthermore, our algorithm outperforms the fixed a priori splitting rule proposed by Chen et al. (2017)

A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups

The Vehicle Routing Problem with Discrete Split Deliveries and Pickups is a variant of the Vehicle Routing Problem with Split Deliveries and Pickups, in which customers’ demands are discrete in terms of batches (or orders). It exists in the practice of logistics distribution and consists of designing a least cost set of routes to serve a given set of customers while respecting constraints on the vehicles’ capacities. In this paper, its features are analyzed. A mathematical model and Tabu Search algorithm with specially designed batch combination and item creation operation are proposed. The batch combination operation is designed to avoid unnecessary travel costs, while the item creation operation effectively speeds up the search and enhances the algorithmic search ability. Computational results are provided and compared with other methods in the literature, which indicate that in most cases the proposed algorithm can find better solutions than those in the literature

A Matheuristic Approach for the Split Delivery Vehicle Routing Problem: An Efficient Set Covering-Based Model with Guided Route Generation Schemes

The Split Delivery Vehicle Routing Problem (SDVRP) is a relaxed version of the classical VRP where customers can be visited more than once. The SDVRP is also applicable for problems where one or more of the customers require a demand larger than the vehicle capacity. Constructive heuristics adapted from the parallel savings and the sweep methods are first proposed to generate a set of solutions which is then used in the new and more efficient set covering-based formulation which we put forward. An effective repair mechanism to remedy any infeasibility due to the set covering problem is presented. A reduced set of promising routes is used in our model, instead of the original set of routes, proposing and using well defined reduction schemes. This set covering-based approach is tested on large data sets from the literature with encouraging results. In brief, 7 best solutions including ties are found among the 137 SDVRP instances

Otimização da distribuição de mercadorias para as lojas Makro

Mestrado em Métodos Quantitativos para a Decisão Económica e EmpresarialEste relatório foi desenvolvido no âmbito de um estágio na empresa Transportes Florêncio & Silva. Durante o estágio foi proposto o desenvolvimento de uma aplicação que automatizasse e otimizasse a elaboração de rotas de distribuição que a empresa faz diariamente para as lojas Makro em Portugal. Este trabalho encontra-se dividido em duas partes. Numa primeira são estudados vários problemas de roteamento de veículos e é elaborado um modelo matemático que se ajusta ao problema em estudo. Na segunda, é apresentada a aplicação desenvolvida em linguagem VBA para Excel, baseada no algoritmo de savings, e procede-se à comparação entre os resultados obtidos pelo software e pela empresa. Após a obtenção de rotas através do programa, conclui-se que a diferença entre os dois métodos é pouco significativa, no entanto, este permite obter resultados de forma rápida e eficiente e possibilita a adaptação do código criado às necessidades futuras da empresa, nomeadamente a introdução de novas lojas.This report was developed as part of an internship at Transportes Florêncio & Silva. During the internship it was proposed the development of an application that would automate and optimize the elaboration of daily distribution routes that the company makes for Makro stores in Portugal. This work is divided into two parts. In the first one, several vehicle routing problems are studied and a mathematical model that fits the problem under study is elaborated. In the second one, the application developed in Excel?s VBA language, based on the savings algorithm, is presented and then comparisons between the results obtained by the software and the company are made. After using the program to determine routes, it is concluded that the difference between the two methods is not very significant, however the application allows results to be obtained quickly and efficiently and allows the adaptation of the created code to the future needs of the company, such as the introduction of new stores as variables.info:eu-repo/semantics/publishedVersio

A heuristic with a performance guarantee for the Commodity constrained Split Delivery Vehicle Routing Problem

The Commodity constrained Split Delivery Vehicle Routing Problem (C-SDVRP) is a routing problem where customer demands are composed of multiple commodities. A fleet of capacitated vehicles must serve customer demands in a way that minimizes the total routing costs. Vehicles can transport any set of commodities and customers are allowed to be visited multiple times. However, the demand for a single commodity must be delivered by one vehicle only. In this work, we developed a heuristic with a performance guarantee to solve the C-SDVRP. The proposed heuristic is based on a set covering formulation, where the exponentially-many variables correspond to routes. First, a subset of the variables is obtained by solving the linear relaxation of the formulation by means of a column generation approach which embeds a new pricing heuristic aimed to reduce the computational time. Solving the linear relaxation gives a valid lower bound used as a performance guarantee for the heuristic. Then, we devise a restricted master heuristic to provide good upper bounds: the formulation is restricted to the subset of variables found so far and solved as an integer program with a commercial solver. A local search based on a mathematical programming operator is applied to improve the solution. We test the heuristic algorithm on benchmark instances from the literature. Several new (best-known) solutions are found in reasonable computational time. The comparison with the state of the art heuristics for solving C-SDVRP shows that our approach significantly improves the solution time, while keeping a comparable solution quality

VRP dinâmico e de janelas de tempo aplicado ao planeamento de transportes

Na sociedade moderna, com os avanços tecnológicos e a ambição e necessidade das empresas de se tornarem cada vez mais competitivas, todos os setores são afetados. O setor correspondente aos transportes nada se afasta dos demais, havendo, progressivamente, uma maior procura por transportes mais baratos e mais rápidos, aumentando assim a procura de soluções mais eficazes por parte das empresas que tratam dos mesmos. Por sua vez, este trabalho tem como objetivo estudar e explicar os problemas de rotas de veículos (VRP), analisando duas das suas vertentes. A vertente dinâmica (DVRP) estuda a possibilidade do surgimento de clientes dinâmicos, bem como a necessidade da alteração de rotas. A vertente com a aplicação de janelas de tempo (VRPTW), estuda a realização das entregas, por parte dos fornecedores aos clientes, dentro de janelas de tempo anteriormente definidas (normalmente aquando da aquisição do produto ou pedido de entrega). Para a recolha da informação necessária para a melhor compreensão destes temas foram utilizadas várias plataformas online de partilha e publicação de documentos. Através da análise dos mesmos foram retiradas as ideias e conclusões apresentadas ao longo do documento. A vertente da aplicação das janelas de tempo é mais bem analisada, uma vez que se analisa um caso de estudo encontrado num artigo e, posteriormente, desenvolve-se uma possível solução para os problemas de rotas de veículos com janelas de tempo. O caso de estudo explorado teve como intuito perceber a relação existente entre a utilização de janelas de tempo com diferentes intervalos e os custos de encargo, a satisfação dos clientes e o tempo de viagem. A solução apresentada, à semelhança do caso de estudo analisado, estuda a influência que as janelas de tempo têm nos custos das entregas. Através do mesmo é possível variar o número de veículos com os quais se trabalha, bem como as suas capacidades, o número de clientes servidos, o horário e procura dos mesmos e ainda o tamanho das janelas de tempo nas quais as entregas são realizadas. Por fim, conclui-se que deve haver um equilíbrio das janelas de tempo, uma vez que as mesmas não devem ser muito pequenas, porque podem traduzir-se em custos mais elevados, nem muito grandes, uma vez que podem diminuir a satisfação dos clientes e aumentar o tempo de processamento. O tamanho e capacidade da frota utilizada deve ser de acordo com a quantidade e procura dos clientes, aos quais a empresa costuma atenderIn the modern society, with all the advances in technology and with the ambition and need from the companies to become more and more competitive, all the sectors are affected. The transport’s sector is no different, once there is, more and more, a demand for cheaper and faster transports, increasing, this way, the search for more effective solutions from the companies that deal with deliveries. In turn, the purpose of this paper is to study and explain the vehicle routing problem (VRP), analyzing two of its strands. The dynamic strand (DVRP) studies the possibility to arise new dynamic clients, as well as the need to change the routes initially planned. The strand that studies the application of time windows, analyzes the deliveries that are done within the time windows previously defined (normally when the product is bought, or the delivery is requested). To recall all the information needed to a better understanding of these topics were used multiple online platforms for sharing and publishing documents. Through their analysis, the ideas and conclusions presented along this document were withdrawn. The time windows strand was better analyzed, once it was found and examined a case study and, posteriorly, a possible solution was developed to solve the VRPTW vehicle routing problems with time windows. The case study was explored with the aim of understanding the relationship between the use of time windows with different intervals and the cost of charges, customer satisfaction and travel time. The solution presented, similar to the case study investigated, studies the influence that time windows have on delivery costs. In it, it is possible to vary the number of vehicles with which to work, as well as their capacities, the number of customers served, their schedule and demand and the size of the time windows in which deliveries are made. In conclusion, there should be a balance in the time windows, once they should not be either too small, because they can translate in higher costs, neither too long, once they can decrease customer satisfaction or increase process time. The size and the capacity of the vehicle fleet should be according to the amount of clientes and their deman