Iterated local search algorithm for the vehicle routing problem with backhauls and soft time windows

The vehicle routing problem with backhauls and soft time windows contains two disjoint sets of customers: those that receive goods from the depot, who are called linehauls, and those that send goods to the depot, named backhauls. To each customer is associated an interval of time (time window), during which each one should be served. If a time window can be violated it is called soft, but this violation implies an additional cost. In this paper, only the upper limit of the interval can be exceeded. For solving this problem we created deterministic iterated local search algorithm, which was tested using a large set of benchmark problems taken from the literature. These computational tests have proven that this algorithm competes with best known algorithms in terms of the quality of the solutions andcomputing time. So far as we know, there is no published paper for this problem dealing with soft time windows, and, therefore, this comparison is only with the algorithms that do not allow time windows violation.info:eu-repo/semantics/publishedVersio

The double traveling salesman problem with partial last-in-first-out loading constraints

In this paper, we introduce the double traveling salesman problem with partial last-in-first-out loading constraints (DTSPPL). It is a pickup-and-delivery single-vehicle routing problem, where all pickup operations must be performed before any delivery operation because the pickup-and-delivery areas are geographically separated. The vehicle collects items in the pickup area and loads them into its container, a horizontal stack. After performing all pickup operations, the vehicle begins delivering the items in the delivery area. Loading and unloading operations must obey a partial last-in-first-out (LIFO) policy, that is, a version of the LIFO policy that may be violated within a given reloading depth. The objective of the DTSPPL is to minimize the total cost, which involves the total distance traveled by the vehicle and the number of items that are unloaded and then reloaded due to violations of the standard LIFO policy. We formally describe the DTSPPL through two integer linear programming (ILP) formulations and propose a heuristic algorithm based on the biased random-key genetic algorithm (BRKGA) to find high-quality solutions. The performance of the proposed solution approaches is assessed over a broad set of instances. Computational results have shown that both ILP formulations have been able to solve only the smaller instances, whereas the BRKGA obtained good-quality solutions for almost all instances, requiring short computational times

Large neighbourhood search with adaptive guided ejection search for the pickup and delivery problem with time windows

An effective and fast hybrid metaheuristic is proposed for solving the pickup and delivery problem with time windows. The proposed approach combines local search, large neighbourhood search and guided ejection search in a novel way to exploit the benefits of each method. The local search component uses a novel neighbourhood operator. A streamlined implementation of large neighbourhood search is used to achieve an effective balance between intensification and diversification. The adaptive ejection chain component perturbs the solution and uses increased or decreased computation time according to the progress of the search. While the local search and large neighbourhood search focus on minimising travel distance, the adaptive ejection chain seeks to reduce the number of routes. The proposed algorithm design results in an effective and fast solution method that finds a large number of new best known solutions on a well-known benchmark data set. Experiments are also performed to analyse the benefits of the components and heuristics and their combined use in order to achieve a better understanding of how to better tackle the subject problem

Vehicle routing problems in rice-for-the-poor distribution

This paper characterizes the routing problems arising in distribution of rice-for-the-poor in a district and presents a generic mathematical formulation of vehicle routing problems (VRP) for solving the problems. The proposed generic model, framed as a mixed integer linear programming, is formulated in such a way to encompass three distinct features; namely multiple depots (MD) establishment, multiple trips (MT) transportation, and split delivery (SD) mechanism. This model is implemented for a real-world problem of rice-for-the-poor distribution in the Ponorogo district of Indonesia, involved for deliveries among 3 depots—8, 17, and 23 villages depended on the distribution period—using a fleet of 5 vehicles of homogeneous capacity. Three types of distribution model are identified as MD-MT-VRP, MD-VRP-SD and MD-MT-VRP-SD

Desenvolvimento de uma heurística para a determinação de rotas de recolha e distribuição de produtos considerando múltiplos veículos

Trabalho de projecto de mestrado, Matemática Aplicada à Economia e Gestão, Universidade de Lisboa, Faculdade de Ciências, 2019Neste projeto, apresenta-se um problema de determinação de rotas de recolha e distribuição com escolha seletiva de mercados. Existe uma frota homogénea de veículos e existem pontos onde se faz a recolha de determinados produtos e, posteriormente, faz-se a distribuição pelos clientes, tendo estes uma dada procura que tem que ser satisfeita. Não é obrigatório visitar todos os pontos de recolha disponíveis. O objetivo é construir rotas para os veículos que partam de um depósito, passem por certos mercados para comprar os produtos, entreguem os produtos aos clientes e regressem ao depósito, de modo a minimizar a soma dos custos de aquisição dos produtos e dos custos de deslocação. Neste trabalho, faz-se uma breve referência a alguns problemas de determinação de rotas para veículos e à sua aplicação a casos reais. Apresenta-se, ainda, um modelo matemático em programação linear inteira mista. Desenvolve-se, para obter soluções admissíveis para este problema, uma heurística que é constituída por duas fases. A primeira fase consiste em criar rotas com um único cliente e com os mercados que o servem, tendo como base uma heurística desenvolvida para resolver o Travelling Purchaser Problem. Nesta primeira fase, constrói-se uma solução inicial, a qual é melhorada através de dois procedimentos: Market drop e Market exchange. A segunda fase consiste na fusão das rotas obtidas, juntando vários clientes na mesma rota, de modo a diminuir os custos de viagem. Os resultados computacionais são obtidos para dados gerados aleatoriamente, considerando duas áreas onde estão os clientes, o depósito e os mercados, dois tipos de probabilidade associados à existência de determinado produto em cada mercado e à probabilidade de a procura de determinado produto por parte de um cliente ser superior a zero e diferentes valores para número de mercados e procura. Fazse uma análise dos resultados obtidos em termos de média das melhorias percentuais quando se faz a fusão de rotas e em termos de tempos computacionais, considerando duas capacidades diferentes para os veículos.In this project, a pickup and delivery problem with selective choice of markets is presented. There is a fleet of homogenous vehicles which travels through pickup points to get certain products and then delivers them to the customers who have a certain demand that must be satisfied. It is not necessary to visit every available pickup point. The goal is to find a good, next to optimal, route for the vehicles that leave the depot, stop at certain markets where products are bought, deliver those products to the customers and then return to the depot, in order to minimize the sum of the purchasing costs and the travelling costs. In this project, a brief reference to some vehicle routing problems and some of its applications to the real world is made. A mixed integer linear programming model is presented. A heuristic is built to find feasible solutions for this problem. The heuristic consists of two phases, the first of which, consists of creating routes with a single customer and the markets which satisfy the customer’s demand. This phase is based on a heuristic for the Travelling Purchaser Problem where an initial feasible solution is found and improved upon through two procedures: Market Drop and Market Exchange. The second phase consists of merging the routes obtained beforehand, joining multiple customers in the same route, in order to decrease travelling costs. Some computational results were obtained for randomly generated data, considering two different areas for the depot, customers and markets, two different probabilities for the existence of a certain product in a certain market, two different probabilities for the existence of demand of a certain product for each customer and, lastly, different numbers of customers and markets. The results were analysed in regards to the average percentage improvements for the route merging, as well as regarding the computational time, considering two different maximum vehicle capacities

Non-Elementary Formulations for Single Vehicle Routing Problems with Pickups and Deliveries

We study the class of one-to-many-to-one single vehicle routing problems with pickups and deliveries, in which a single capacitated vehicle is used to serve a set of customers requiring a delivery, a pickup, or both. These problems have many real-world applications, including beverage distribution, courier service transportation, and reverse logistics. We first concentrate on a well-studied problem in this class, known as the single vehicle routing problem with deliveries and selective pickups (SVRPDSP), in which deliveries are mandatory but pickups are optional and generate a revenue if performed, and customers requiring both a delivery and a pickup (combined demand) can be visited either once or twice. Most exact algorithms in the literature solve SVRPDSP by looking for Elementary tours on an extended network which is obtained by transforming each combined demand customer into two different customers, one requiring only the delivery and the other one only the pickup. Because this can result in a significant loss in performance, in this work we focus instead on the original problem network and present formulations that can yield non-Elementary tours. Through the use of Benders Decomposition, valid inequalities, and tailored optimization techniques based on branch-and-cut frameworks, we develop exact algorithms that outmatch previous results in the literature and obtain proven optimal solutions for all benchmark instances. We then generalize the algorithms to solve several other vehicle routing problems with pickups and deliveries, including the cases of split deliveries, intermediate dropoffs, mandatory pickups, and multiple vehicles

Planning the delivery of home social services: a mathematical programming-based approach to support routing and scheduling assignments

The increased average lifespan, together with low birth rates, are transforming the European Union's age pyramid. Currently, we are experiencing a transition towards a much older population structure. Given that the institutions that provide care to these population groups are limited by budgetary constraints, it is imperative to optimize several processes, among which route planning and staff scheduling stand out. This dissertation aims to develop a mathematical programming model to support the planning of routes and human resources for providers of Home Social Services. Beyond general Vehicle Routing Problems assumptions, the proposed model also considers the following features: i) working time regulations, ii) mandatory breaks, iii) users' autonomy, and iii) meals' distribution. The present model, implemented using GAMS software, focuses simultaneously on two objective functions: minimization of operating costs, and maximization of equity through the minimization of differences in teams' working times. Chebyshev's method was chosen to solve the developed multiobjective model. The model was built based on a Portuguese Private Institution of Social Solidarity. Through the application of the model, significant improvements are obtained when compared to the current planning of the partner institution, such as it is the case of an improved workload distribution between caregivers and routes that will result in lower costs for the institution. This model is fully enforceable to other institutions that provide services similar or equal to the institution used as a reference.O aumento da esperança média de vida, juntamente com baixas taxas de natalidade, estão a transformar a pirâmide etária da União Europeia. Atualmente, estamos a vivenciar uma transição direcionada para uma estrutura populacional muito mais envelhecida. Dado que as instituições que prestam cuidados a esta fração se encontram limitadas por restrições orçamentais, torna-se imperativo otimizar vários processos, dos quais se destacam planeamento de rotas e escalonamento de funcionárias. Esta dissertação visa introduzir um modelo de programação matemática com a finalidade de apoiar o planeamento de rotas e recursos humanos para prestadores de Serviços de Apoio Domiciliário. O modelo assenta, além dos pressupostos de um "Vehicle Routing Problem", nos seguintes: i) regulações de tempo de trabalho, ii) pausas obrigatórias, iii) autonomia dos utentes, e iv) distribuição de refeições. O modelo, desenvolvido através de software GAMS, foca-se em duas funções objetivo, simultaneamente: minimização dos custos operacionais, e maximização da equidade, através da minimização das diferenças nos tempos de trabalho das equipas. O método de Chebyshev foi o escolhido para desenvolver o modelo multiobjetivo. O modelo foi construído tendo por base uma Instituição Particular de Solidariedade Social em Portugal. Através da aplicação do modelo, obtêm-se melhorias significativas, quando comparado com o atual planeamento da instituição parceira, como é o caso de uma melhor distribuição da carga de trabalho entre as funcionárias e das rotas que resultam da redução dos custos operacionais da instituição. Este modelo é totalmente extensível a outras instituições que prestem serviços semelhantes ou iguais à instituição utilizada como referência