Modelling and Analysis of Hub-and-Spoke Networks under Stochastic Demand and Congestion

Motivated by the strategic importance of congestion management, in this paper we present a model to design hub-and-spoke networks under stochastic demand and congestion. The proposed model determines the location and capacity of the hub nodes and allocate non-hub nodes to these hubs while minimizing the sum of the ?xed cost, transportation cost and the congestion cost. In our approach, hubs are modelled as spatially distributed M/G/1 queues and congestion is captured using the expected queue lengths at hub facilities. A simple transformation and a piecewise linear approximation technique are used to linearize the resulting nonlinear model. We present two solution approaches: an exact method that uses a cutting plane approach and a novel genetic algorithm based heuristic. The numerical experiments are conducted using CAB and TR datasets. Analysing the results obtained from a number of problem instances, we illustrate the impact of congestion cost on the network topology and show that substantial reduction in congestion can be achieved with a small increase in total cost if congestion at hub facilities is considered at the design stage. The computational results further confirm the stability and e?ciency of both exact and heuristic approaches

Benders Decomposition for Profit Maximizing Hub Location Problems with Capacity Allocation

This paper models capacity allocation decisions within profit maximizing hub location problems to satisfy demand of commodities from different market segments. A strong deterministic formulation of the problem is presented and two exact algorithms based on a Benders reformulation are described to solve large-size instances of the problem. A new methodology is developed to strengthen the Benders optimality cuts by decomposing the subproblem in a two-phase fashion. The algorithms are enhanced by the integration of improved variable fixing techniques. The deterministic model is further extended by considering uncertainty associated with the demand to develop a two-stage stochastic program. To solve the stochastic version, a Monte-Carlo simulation-based algorithm is developed that integrates a sample average approximation scheme with the proposed Benders decomposition algorithms. Novel acceleration techniques are presented to improve the convergence of the algorithms proposed for the stochastic version. The efficiency and robustness of the algorithms are evaluated through extensive computational experiments. Computational results show that large-scale instances with up to 500 nodes and three demand segments can be solved to optimality, and that the proposed algorithms generate cuts that provide significant speedups compared to using Pareto-optimal cuts. The proposed two-phase methodology for solving the Benders subproblem as well as the variable fixing and acceleration techniques can be used to solve other discrete location and network design problems

Large-scale analytics and optimization in urban transportation : improving public transit and its integration with vehicle-sharing services

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 143-154).Public transportation is undeniably an effective way to move a large number of people in a city. Its ineffectiveness, such as long travel times, poor coverage, and lack of direct services, however, makes it unappealing to many commuters. In this thesis, we address some of the shortcomings and propose solutions for making public transportation more preferable. The first part of this thesis is focused on improving existing bus services to provide higher levels of service. We propose an optimization model to determine limited-stop service to be operated in parallel with local service to maximize total user welfare. Theoretical properties of the model are established and used to develop an efficient solution approach. We present numerical results obtained using real-world data and demonstrate the benefits of limited-stop services. The second part of this thesis concerns the design of integrated vehicle-sharing and public transportation services. One-way vehicle-sharing services can provide better access to existing public transportation and additional options for trips beyond those provided by public transit. The contributions of this part are twofold. First, we present a framework for evaluating the impacts of integrating one-way vehicles haring service with existing public transportation. Using publicly available data, we construct a graph representing a multi-modal transportation service. Various evaluation metrics based on centrality indices are proposed. Additionally, we introduce the notion of a transfer tree and develop a visualization tool that enables us to easily compare commuting patterns from different origins. The framework is applied to assess the impact of Hubway (a bike-sharing service) on public transportation service in the Boston metropolitan area. Second, we present an optimization model to select a subset of locations at which installing vehicle-sharing stations minimizes overall travel time over the integrated network. Benders decomposition is used to tackle large instances. While a tight formulation generally generates stronger Benders cuts, it requires a large number of variables and constraints, and hence, more computational effort. We propose new algorithms that produce strong Benders cuts quickly by aggregating various variables and constraints. Using data from the Boston metropolitan area, we present computational experiments that confirm the effectiveness of our solution approach.by Virot Chiraphadhanakul.Ph.D

Hub Location Problems with Profit Considerations

This thesis studies profit maximizing hub location problems. These problems seek to find the optimal number and locations of hubs, allocations of demand nodes to these hubs, and routes of flows through the network to serve a given set of demands between origin-destination pairs while maximizing total profit. Taking revenue into consideration, it is assumed that a portion of the demand can remain unserved when it is not profitable to be served. Potential applications of these problems arise in the design of airline passenger and freight transportation networks, truckload and less-than-truckload transportation, and express shipment and postal delivery. Firstly, mathematical formulations for different versions of profit maximizing hub location problems are developed. Alternative allocation strategies are modeled including multiple allocation, single allocation, and $r$-allocation, as well as allowing for the possibility of direct connections between non-hub nodes. Extensive computational analyses are performed to compare the resulting hub networks under different models, and also to evaluate the solution potential of the proposed models on commercial solvers with emphasis on the effect of the choice of parameters. Secondly, revenue management decisions are incorporated into the profit maximizing hub location problems by considering capacities of hubs. In this setting, the demand of commodities are segmented into different classes and there is available capacity at hubs which is to be allocated to these different demand segments. The decision maker needs to determine the proportion of each class of demand to serve between origin-destination pairs based on the profit to be obtained from satisfying this demand. A strong mixed-integer programming formulation of the problem is presented and Benders-based algorithms are proposed to optimally solve large-scale instances of the problem. A new methodology is developed to strengthen the Benders optimality cuts by decomposing the subproblem in a two-phase fashion. The algorithms are enhanced by the integration of improved variable fixing techniques. Computational results show that large-scale instances with up to 500 nodes and 750,000 commodities of different demand segments can be solved to optimality, and that the proposed algorithms generate cuts that provide significant speedups compared to using Pareto-optimal cuts. As precise information on demand may not be known in advance, demand uncertainty is then incorporated into the profit maximizing hub location problems with capacity allocation, and a two-stage stochastic program is developed. The first stage decision is the locations of hubs, while the assignment of demand nodes to hubs, optimal routes of flows, and capacity allocation decisions are made in the second stage. A Monte-Carlo simulation-based algorithm is developed that integrates a sample average approximation scheme with the proposed Benders decomposition algorithm. Novel acceleration techniques are presented to improve the convergence of the algorithm. The efficiency and robustness of the algorithm are evaluated through extensive computational experiments. Instances with up to 75 nodes and 16,875 commodities are optimally solved, which is the largest set of instances that have been solved exactly to date for any type of stochastic hub location problems. Lastly, robust-stochastic models are developed in which two different types of uncertainty including stochastic demand and uncertain revenue are simultaneously incorporated into the capacitated problem. To embed uncertain revenues into the problem, robust optimization techniques are employed and two particular cases are investigated: interval uncertainty with a max-min criterion and discrete scenarios with a min-max regret objective. Mixed integer programming formulations for each of these cases are presented and Benders-based algorithms coupled with sample average approximation scheme are developed. Inspired by the repetitive nature of sample average approximation scheme, general techniques for accelerating the algorithms are proposed and instances involving up to 75 nodes and 16,875 commodities are solved to optimality. The effects of uncertainty on optimal hub network designs are investigated and the quality of the solutions obtained from different modeling approaches are compared under various parameter settings. Computational results justify the need for embedding both sources of uncertainty in decision making to provide robust solutions

Design network model applied to brazilian soybeans exportation

Orientadores: Takaaki Ohishi, Anibal Tavares de AzevedoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: A cadeia de exportação da soja tem alta participação no desempenho econômico do país. No entanto, as principais áreas produtoras são expostas a diversos problemas logísticos decorrentes da falta de planejamento e de investimentos em infraestrutura. Como resultado, os produtores são onerados pelos custos diminuindo seu capital disponível para investimentos, o que compromete as safras futuras e a projeção econômica do país. Diante desta realidade o governo brasileiro tem tomado medidas e realizando investimentos para sanar estes problemas. Os investimentos realizados em infraestrutura devem ser planejados para o longo prazo. Deste modo, este trabalho propõe a análise de um modelo capacitado de design de rede de hubs e, posteriormente, com base no mesmo, desenvolve três de modelos matemáticos que descrevem a cadeia exportação da soja e suas especificidades a fim de, criar uma ferramenta de análise para definir a localização de facilidades, armazenadoras/ consolidadoras/ redirecionadoras de fluxo, as rotas a serem utilizadas e a utilização dos portos para otimizar esta cadeia. Para aplicar os modelos, o Estado do Mato Grosso foi selecionado como foco do estudo., e com base no qual, foi realizado um extenso levantamento de dados da soja. Considerando que o Estado do Mato Grosso é dividido em 22 microrregiões foram esti-madas a quantidade de soja produzida, identificada a quantidade de soja exportada e a capacidade estática de cada microrregião. Também foram identificados os principais países importadores da soja brasileira e os principais portos de exportação, além das quantidades de soja exportada para cada país, a utilização atual dos portos e identificação das rotas terrestres e marítimas utilizadas no transporteAbstract: The soybean exporter chain has high participation in the economic performance of the country. However, the main producing areas are exposed to several logistical problems arising from lack of planning and investment in infrastructure. As a result, producers are burdened by the costs and have an available capital decrease to future investments, which reduce futures crops and future economic potential of the country. Faced with this reality, the Brazilian government has taken measures and investing to solve these problems. Investments in infrastructure should be planned for the long term. Thus, this paper proposes the analysis of a capacitated model design of network hubs and then, based on it, develops three mathematical models that describe the soybeans exporter chain, in order to create an analysis tool to define the location of facilities, as storage / switching / transshipment facilities, define routes and ports that should be utilized to optimize the use of the chain. In order to apply the model, the state of Mato Grosso was selected as the focus of this study and, based on which, an extensive survey data of soybeans was realized. Whereas that the State of Mato Grosso is divided into 22 micro regions it was estimated their soybeans production, identified the amount of soybeans exported and the static capacity to each one. The main importer¿s countries of Brazilian soybeans and the major export ports it was also identified, in addition, the amounts of soybeans exported by each country and ports, and identification of routes and sea routes used to transportDoutoradoAutomaçãoDoutora em Engenharia Elétric

Algorithms for vehicle routing problems with heterogeneous fleet, flexible time windows and stochastic travel times

Orientador: Vinícius Amaral ArmentanoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Este trabalho aborda três variantes multiatributo do problema de roteamento de veículos. A primeira apresenta frota heterogênea, janelas de tempo invioláveis e tempos de viagem determinísticos. Para resolvê-la, são propostos algoritmos ótimos baseados na decomposição de Benders. Estes algoritmos exploram a estrutura do problema em uma formulação de programação inteira mista, e três diferentes técnicas são desenvolvidas para acelerá-los. A segunda variante contempla os atributos de frota heterogênea, janelas de tempo flexíveis e tempos de viagem determinísticos. As janelas de tempo flexíveis permitem o início do serviço nos clientes com antecipação ou atraso limitados em relação às janelas de tempo invioláveis, com custos de penalidade. Este problema é resolvido por extensões dos algoritmos de Benders, que incluem novos algoritmos de programação dinâmica para a resolução de subproblemas com a estrutura do problema do caixeiro viajante com janelas de tempo flexíveis. A terceira variante apresenta frota heterogênea, janelas de tempo flexíveis e tempos de viagem estocásticos, sendo representada por uma formulação de programação estocástica inteira mista de dois estágios com recurso. Os tempos de viagem estocásticos são aproximados por um conjunto finito de cenários, gerados por um algoritmo que os descreve por meio da distribuição de probabilidade Burr tipo XII, e uma matheurística de busca local granular é sugerida para a resolução do problema. Extensivos testes computacionais são realizados em instâncias da literatura, e as vantagens das janelas de tempo flexíveis e dos tempos de viagem estocásticos são enfatizadasAbstract: This work addresses three multi-attribute variants of the vehicle routing problem. The first one presents a heterogeneous fleet, hard time windows and deterministic travel times. To solve this problem, optimal algorithms based on the Benders decomposition are proposed. Such algorithms exploit the structure of the problem in a mixed-integer programming formulation, and three algorithmic enhancements are developed to accelerate them. The second variant comprises a heterogeneous fleet, flexible time windows and deterministic travel times. The flexible time windows allow limited early and late servicing at customers with respect to their hard time windows, at the expense of penalty costs. This problem is solved by extensions of the Benders algorithms, which include novel dynamic programming algorithms for the subproblems with the special structure of the traveling salesman problem with flexible time windows. The third variant presents a heterogeneous fleet, flexible time windows and stochastic travel times, and is represented by a two-stage stochastic mixed-integer programming formulation with recourse. The stochastic travel times are approximated by a finite set of scenarios generated by an algorithm which describes them using the Burr type XII distribution, and a granular local search matheuristic is suggested to solve the problem. Extensive computational tests are performed on instances from the literature, and the advantages of flexible windows and stochastic travel times are stressed.DoutoradoAutomaçãoDoutor em Engenharia Elétrica141064/2015-3CNP