Tackling Dynamic Vehicle Routing Problem with Time Windows by means of Ant Colony System

The Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the well-known Vehicle Routing Problem (VRP), which takes into account the dynamic nature of the problem. This aspect requires the vehicle routes to be updated in an ongoing manner as new customer requests arrive in the system and must be incorporated into an evolving schedule during the working day. Besides the vehicle capacity constraint involved in the classical VRP, DVRPTW considers in addition time windows, which are able to better capture real-world situations. Despite this, so far, few studies have focused on tackling this problem of greater practical importance. To this end, this study devises for the resolution of DVRPTW, an ant colony optimization based algorithm, which resorts to a joint solution construction mechanism, able to construct in parallel the vehicle routes. This method is coupled with a local search procedure, aimed to further improve the solutions built by ants, and with an insertion heuristics, which tries to reduce the number of vehicles used to service the available customers. The experiments indicate that the proposed algorithm is competitive and effective, and on DVRPTW instances with a higher dynamicity level, it is able to yield better results compared to existing ant-based approaches.Comment: 10 pages, 2 figure

Transporte de doentes não urgentes : elementos de modelação estatística e melhorias potenciais de eficiência via otimização de roteamento

Com este trabalho pretende-se averiguar, de acordo com a realidade de um caso real em transportes de ambulâncias, quais as variáveis que têm maior importância no funcionamento dos Transporte de Doentes Não Urgentes (TDNU) na ilha da Madeira e no Porto Santo, bem como, a formulação de um modelo matemático no roteamento de viaturas. O estudo recorre à base de dados criada com a consulta de triagem dos transportes em 2014, tornando-se percetível avaliar Elementos de Modelação Estatística nesse ano, testando a normalidade da amostra através do teste Kolmogorov-Smirnov, calculando as medidas de tendência central nas variáveis e aplicando os testes não paramétricos, Qui-Quadrado de Pearson, Wilcoxon-Mann-Whitney e Kruskal-Wallis. Para alguns cálculos, utilizou-se os softwares Excel e SPSS. Ao longo do trabalho abordar-se-á o clássico Problema de Roteamento de Veículos e os diferentes modelos de VRPs, um dos mais estudados problemas na área da otimização combinatória. Neste sentido surge esta dissertação, que pretende estudar como o Serviço de Saúde da Região Autónoma da Madeira, Empresas Públicas Empresariais (E.P.E), pode beneficiar da aplicação de um Modelo Matemático para o problema Dial-a-Ride Problem (DARP), no Roteamento de Transporte de Doentes Não Urgentes. Deste modo, explora-se a aplicação do DARP para um dia de trabalho, a 02/01/2014, combinando as variáveis de interesse, com uma descrição exploratória de dados e parâmetros, cujo futuro permitirá aplicar um algoritmo baseado num modelo, apoiado por um software, permitindo minimizar a distância total percorrida pelas ambulâncias e totalizando um custo mínimo para a empresa. Para simplificar o problema real, incidimos o estudo no cálculo de alguns parâmetros do Modelo Matemático, apenas aos doentes que utilizaram transporte de ambulância pertencentes à Zona I e II do Concelho do Funchal.This paper intends to investigate, according to the reality of a real case in ambulance transport, which variables are most important in the operation of Non-Urgent Patient Transport (TDNU) on the island of Madeira and Porto Santo, and like, the formulation of a mathematical model in the routing of vehicles. The study uses the database created with the transportation screening consultation in 2014, making it possible to evaluate Elements of Statistical Modeling in that year, testing the normality of the sample through the Kolmogorov-Smirnov test, calculating the measures of central tendency in the variables and applying the non-parametric tests, Pearson's Chi-Square, Wilcoxon-Mann-Whitney, and Kruskal-Wallis. For some calculations, Excel and SPSS software were used. Throughout the work the classic Vehicle Routing Problem and the different models of VRPs will be addressed, one of the most studied problems in the area of combinatorial optimization. In this sense, this dissertation aims to study how the Health Service of the Autonomous Region of Madeira, Public Business Enterprises (E.P.E), can benefit from the application of a Mathematical Model for the problem of Dial-a-Ride Problem (DARP) in Routing of Non-Urgent Patients. In this way, the application of the DARP for a working day, on 02/01/2014, is explored, combining the variables of interest, with an exploratory description of data and parameters, whose future will allow to apply an algorithm based on a model, supported by a software, allowing to minimize the total distance traveled by the ambulances and totaling a minimum cost for the company. In order to simplify the real problem, we applied the study in the calculation of some parameters of the Mathematical Model, only to the patients who used ambulance transport belonging to Zone I and II of the Municipality of Funchal