The planning process of public transit systems have for long been a subject treated in operations research. In recent years, research within the public transit area focus on adapting this planning process for electric vehicles. This thesis evaluates a heuristic approach to the vehicle scheduling problem for electrical buses without the use of any licensed software. Among the previous research is an article that presents a mathematical model for scheduling of electrical buses using AMPL and CPLEX. However, due to not finding optimal solutions for all instances of the problem, the question of a heuristic approach is raised. Literature studies indicate that large neighbourhood search (LNS)-based heuristics have shown previous success for scheduling of vehicles. Results from the implementation of a constructive heuristic combined with an LNS-heuristic are compared with the results from the mathematical model and CPLEX. We see some success using the heuristic approach. However, the method we compare against still provide better solutions for almost all instances. More specifically, the difference between the results (number of buses needed) increases with an increasing complexity of the problem. Finally, due to the lacking results, some recommendations are given for improving the performance of the heuristic.

A presente pesquisa aborda um problema de programação de veículos rico, em que a característica mais importante é a demanda de múltiplas embarcações para atendimento a uma única tarefa. Trata-se de uma aplicação real do setor de apoio marítimo \"offshore\", das embarcações que fazem o reboque e o lançamento de linhas de ancoragem de sondas de perfuração e unidades de produção. Como método de solução, aplicaram-se duas heurísticas com uma abordagem híbrida que incluem uma inserção baseada em programação linear inteira, visando a minimização do custo total da operação, dentro de um tempo de processamento aceitável. / This research deals with a rich vehicle scheduling problem, having as the most important feature the demand of multiple vessels per task. It is a real problem present in the oil industry related to the vessels that undertake the towing and the launching of mooring lines of drilling and production units. As a solution method, two heuristics with a hybrid approach were applied which include an insertion based on integer linear programming, aiming at minimizing the total cost of the operation, within an acceptable processing time.

Nesta tese, nós apresentamos uma compilação de três artigos de otimização aplicados no contexto de transporte urbano de ônibus. O principal objetivo foi estudar e implementar heurísticas com base em Pesquisa Operacional para otimizar problemas de (re)escalonamento de veículos off-line e on-line considerando várias garagens e frota heterogênea. No primeiro artigo, foi proposta uma abordagem heurística para o problema de escalonamento de veículos múltiplas garagens. Acreditamos que as principais contribuições são o método de geração de colunas para grandes instâncias e as técnicas de redução do espaço de estados para acelerar as soluções. No segundo artigo, adicionamos complexidade ao considerar a frota heterogênea, denotada como multiple depot vehicle type scheduling problem (MDVTSP). Embora a importância e a aplicabilidade do MDVTSP, formulações matemáticas e métodos de solução para isso ainda sejam relativamente inexplorados. A principal contribuição desse trabalho foi o método de geração de colunas para o problema com frota heterogênea, já que nenhuma outra proposta na literatura foi identificada no momento pelos autores. Na terceira parte desta tese, no entanto, nos concentramos no reescalonamento em tempo real para o caso de quebras definitivas de veículos. A principal contribuição é a abordagem eficiente do reescalonamento sob uma quebra. A abordagem com redução de espaço de estados, solução inicial e método de geração de colunas possibilitou uma ação realmente em tempo real. Em menos de cinco minutos, reescalonando todas as viagens restantes. / In this dissetation we presented a three articles compilation in urban bus transportation optimization. The main objective was to study and implement heuristic solutions method based on Operations Research to optimizing offline and online vehicle (re)scheduling problems considering multiple depots and heterogeneous fleet. In the first paper, a fast heuristic approach to deal with the multiple depot vehicle scheduling problem was proposed. We think the main contributions are the column generation framework for large instances and the state-space reduction techniques for accelerating the solutions. In the second paper, we added complexity when considering the heterogeneous fleet, denoted as "the multiple-depot vehicle-type scheduling problem" (MDVTSP). Although the MDVTSP importance and applicability, mathematical formulations and solution methods for it are still relatively unexplored. We think the main contribution is the column generation framework for instances with heterogeneous fleet since no other proposal in the literature has been identified at moment by the authors. In the third part of this dissertation, however, we focused on the real-time schedule recovery for the case of serious vehicle failures. Such vehicle breakdowns require that the remaining passengers from the disabled vehicle, and those expected to become part of the trip, to be picked up. In addition, since the disabled vehicle may have future trips assigned to it, the given schedule may be deteriorated to the extent where the fleet plan may need to be adjusted in real-time depending on the current state of what is certainly a dynamic system. Usually, without the help of a rescheduling algorithm, the dispatcher either cancels the trips that are initially scheduled to be implemented by the disabled vehicle (when there are upcoming future trips planned that could soon serve the expected demand for the canceled trips), or simply dispatches an available vehicle from a depot. In both cases, there may be considerable delays introduced. This manual approach may result in a poor solution. The implementation of new technologies (e.g., automatic vehicle locators, the global positioning system, geographical information systems, and wireless communication) in public transit systems makes it possible to implement real-time vehicle rescheduling algorithms at low cost. The main contribution is the efficient approach to rescheduling under a disruption. The approach with integrated state-space reduction, initial solution, and column generation framework enable a really real-time action. In less than five minutes rescheduling all trips remaining.

Column generation has during the last years been popular in vehicle scheduling as it for larger problems can find an optimum faster than using an ordinary mixed-integer programming (MIP) model. We study the problem of finding optimal schedules for electric buses by means of column generation. The motive for this approach is that when the size of the problem becomes very large in terms of variables and different solutions, solving it with a mixed- integer programming model can take a lot time. The purpose of this work is to investigate how the best found integral solution and the solution time vary between different column generation methods and how these methods perform compared to a MIP. This has been done by implementing these methods on a test problem for scheduling of electric buses. The results indicate that column generation methods can be very efficient in terms of time and best found integral solution for larger problems. A modified column generation method has been created in order to accelerate the generation of columns, which is better than standard column generation in terms of solution time and best found integral solution.

Os problemas logísticos estão se apoiando de forma bastante expressiva na pesquisa operacional a fim de obter uma maior eficiência em suas operações. Dentre os vários problemas relacionados à designação de veículos em um sistema logístico, o de escalonamento de veículos com múltiplas garagens, MDVSP (Multiple Depot Vehicle Scheduling Problem), vem sendo abordado em diversas pesquisas. O MDVSP pressupõe a existência de garagens que interferem no planejamento das sequências com as quais as viagens devem ser executadas. Frequentemente, métodos exatos não podem resolver as grandes instâncias encontradas na prática e, para poder levá-las em consideração, várias abordagens heurísticas estão sendo desenvolvidas. O principal objetivo deste trabalho, portanto, foi solucionar o MDVSP através de uma heurística utilizando o método de busca-tabu. A principal motivação para a realização deste trabalho surgiu a partir da indicação de que apenas recentemente o uso de meta-heurísticas está sendo aplicado ao MDVSP (Pepin et al. 2008) e das limitações elencadas no estudo de Rohde (2008), o qual utilizou o algoritmo branch-and-bound em uma das etapas da heurística apresentada para resolver o problema, o que fez aumentar o tempo de resolução do problema. O método de pesquisa para solução deste problema foi baseado em adaptações das tradicionais técnicas de pesquisa operacional, e propiciou a resolução do MDVSP apresentando resultados bastante competitivos quanto ao custo da função objetivo, número de veículos utilizados e tempo computacional necessário. / Currently the logistical problems are relying quite significantly on Operational Research in order to achieve greater efficiency in their operations. Among the various problems related to the vehicles scheduling in a logistics system, the Multiple Depot Vehicle Scheduling Problem (MDVSP) has been addressed in several studies. The MDVSP presupposes the existence of depots that affect the planning of sequences to which travel must be performed. Often, exact methods cannot solve large instances encountered in practice and in order to take them into account, several heuristic approaches are being developed. The aim of this study was thus to solve the MDVSP using a meta-heuristic based on tabu-search method. The main motivation for this work came from the indication that only recently the use of meta-heuristics is being applied to MDVSP context (Pepin et al. 2008) and, also, the limitations listed by Rohde (2008) in his study, which used the branch-and-bound in one of the steps of the heuristic presented to solve the problem, which has increased the time resolution. The research method for solving this problem was based on adaptations of traditional techniques of Operational Research, and provided resolutions presenting very competitive results for the MDVSP such as the cost of the objective function, number of vehicles used and computational time.

Nesta tese, nós apresentamos uma compilação de três artigos de otimização aplicados no contexto de transporte urbano de ônibus. O principal objetivo foi estudar e implementar heurísticas com base em Pesquisa Operacional para otimizar problemas de (re)escalonamento de veículos off-line e on-line considerando várias garagens e frota heterogênea. No primeiro artigo, foi proposta uma abordagem heurística para o problema de escalonamento de veículos múltiplas garagens. Acreditamos que as principais contribuições são o método de geração de colunas para grandes instâncias e as técnicas de redução do espaço de estados para acelerar as soluções. No segundo artigo, adicionamos complexidade ao considerar a frota heterogênea, denotada como multiple depot vehicle type scheduling problem (MDVTSP). Embora a importância e a aplicabilidade do MDVTSP, formulações matemáticas e métodos de solução para isso ainda sejam relativamente inexplorados. A principal contribuição desse trabalho foi o método de geração de colunas para o problema com frota heterogênea, já que nenhuma outra proposta na literatura foi identificada no momento pelos autores. Na terceira parte desta tese, no entanto, nos concentramos no reescalonamento em tempo real para o caso de quebras definitivas de veículos. A principal contribuição é a abordagem eficiente do reescalonamento sob uma quebra. A abordagem com redução de espaço de estados, solução inicial e método de geração de colunas possibilitou uma ação realmente em tempo real. Em menos de cinco minutos, reescalonando todas as viagens restantes. / In this dissetation we presented a three articles compilation in urban bus transportation optimization. The main objective was to study and implement heuristic solutions method based on Operations Research to optimizing offline and online vehicle (re)scheduling problems considering multiple depots and heterogeneous fleet. In the first paper, a fast heuristic approach to deal with the multiple depot vehicle scheduling problem was proposed. We think the main contributions are the column generation framework for large instances and the state-space reduction techniques for accelerating the solutions. In the second paper, we added complexity when considering the heterogeneous fleet, denoted as "the multiple-depot vehicle-type scheduling problem" (MDVTSP). Although the MDVTSP importance and applicability, mathematical formulations and solution methods for it are still relatively unexplored. We think the main contribution is the column generation framework for instances with heterogeneous fleet since no other proposal in the literature has been identified at moment by the authors. In the third part of this dissertation, however, we focused on the real-time schedule recovery for the case of serious vehicle failures. Such vehicle breakdowns require that the remaining passengers from the disabled vehicle, and those expected to become part of the trip, to be picked up. In addition, since the disabled vehicle may have future trips assigned to it, the given schedule may be deteriorated to the extent where the fleet plan may need to be adjusted in real-time depending on the current state of what is certainly a dynamic system. Usually, without the help of a rescheduling algorithm, the dispatcher either cancels the trips that are initially scheduled to be implemented by the disabled vehicle (when there are upcoming future trips planned that could soon serve the expected demand for the canceled trips), or simply dispatches an available vehicle from a depot. In both cases, there may be considerable delays introduced. This manual approach may result in a poor solution. The implementation of new technologies (e.g., automatic vehicle locators, the global positioning system, geographical information systems, and wireless communication) in public transit systems makes it possible to implement real-time vehicle rescheduling algorithms at low cost. The main contribution is the efficient approach to rescheduling under a disruption. The approach with integrated state-space reduction, initial solution, and column generation framework enable a really real-time action. In less than five minutes rescheduling all trips remaining.

Nesta tese, nós apresentamos uma compilação de três artigos de otimização aplicados no contexto de transporte urbano de ônibus. O principal objetivo foi estudar e implementar heurísticas com base em Pesquisa Operacional para otimizar problemas de (re)escalonamento de veículos off-line e on-line considerando várias garagens e frota heterogênea. No primeiro artigo, foi proposta uma abordagem heurística para o problema de escalonamento de veículos múltiplas garagens. Acreditamos que as principais contribuições são o método de geração de colunas para grandes instâncias e as técnicas de redução do espaço de estados para acelerar as soluções. No segundo artigo, adicionamos complexidade ao considerar a frota heterogênea, denotada como multiple depot vehicle type scheduling problem (MDVTSP). Embora a importância e a aplicabilidade do MDVTSP, formulações matemáticas e métodos de solução para isso ainda sejam relativamente inexplorados. A principal contribuição desse trabalho foi o método de geração de colunas para o problema com frota heterogênea, já que nenhuma outra proposta na literatura foi identificada no momento pelos autores. Na terceira parte desta tese, no entanto, nos concentramos no reescalonamento em tempo real para o caso de quebras definitivas de veículos. A principal contribuição é a abordagem eficiente do reescalonamento sob uma quebra. A abordagem com redução de espaço de estados, solução inicial e método de geração de colunas possibilitou uma ação realmente em tempo real. Em menos de cinco minutos, reescalonando todas as viagens restantes. / In this dissetation we presented a three articles compilation in urban bus transportation optimization. The main objective was to study and implement heuristic solutions method based on Operations Research to optimizing offline and online vehicle (re)scheduling problems considering multiple depots and heterogeneous fleet. In the first paper, a fast heuristic approach to deal with the multiple depot vehicle scheduling problem was proposed. We think the main contributions are the column generation framework for large instances and the state-space reduction techniques for accelerating the solutions. In the second paper, we added complexity when considering the heterogeneous fleet, denoted as "the multiple-depot vehicle-type scheduling problem" (MDVTSP). Although the MDVTSP importance and applicability, mathematical formulations and solution methods for it are still relatively unexplored. We think the main contribution is the column generation framework for instances with heterogeneous fleet since no other proposal in the literature has been identified at moment by the authors. In the third part of this dissertation, however, we focused on the real-time schedule recovery for the case of serious vehicle failures. Such vehicle breakdowns require that the remaining passengers from the disabled vehicle, and those expected to become part of the trip, to be picked up. In addition, since the disabled vehicle may have future trips assigned to it, the given schedule may be deteriorated to the extent where the fleet plan may need to be adjusted in real-time depending on the current state of what is certainly a dynamic system. Usually, without the help of a rescheduling algorithm, the dispatcher either cancels the trips that are initially scheduled to be implemented by the disabled vehicle (when there are upcoming future trips planned that could soon serve the expected demand for the canceled trips), or simply dispatches an available vehicle from a depot. In both cases, there may be considerable delays introduced. This manual approach may result in a poor solution. The implementation of new technologies (e.g., automatic vehicle locators, the global positioning system, geographical information systems, and wireless communication) in public transit systems makes it possible to implement real-time vehicle rescheduling algorithms at low cost. The main contribution is the efficient approach to rescheduling under a disruption. The approach with integrated state-space reduction, initial solution, and column generation framework enable a really real-time action. In less than five minutes rescheduling all trips remaining.

Os problemas logísticos estão se apoiando de forma bastante expressiva na pesquisa operacional a fim de obter uma maior eficiência em suas operações. Dentre os vários problemas relacionados à designação de veículos em um sistema logístico, o de escalonamento de veículos com múltiplas garagens, MDVSP (Multiple Depot Vehicle Scheduling Problem), vem sendo abordado em diversas pesquisas. O MDVSP pressupõe a existência de garagens que interferem no planejamento das sequências com as quais as viagens devem ser executadas. Frequentemente, métodos exatos não podem resolver as grandes instâncias encontradas na prática e, para poder levá-las em consideração, várias abordagens heurísticas estão sendo desenvolvidas. O principal objetivo deste trabalho, portanto, foi solucionar o MDVSP através de uma heurística utilizando o método de busca-tabu. A principal motivação para a realização deste trabalho surgiu a partir da indicação de que apenas recentemente o uso de meta-heurísticas está sendo aplicado ao MDVSP (Pepin et al. 2008) e das limitações elencadas no estudo de Rohde (2008), o qual utilizou o algoritmo branch-and-bound em uma das etapas da heurística apresentada para resolver o problema, o que fez aumentar o tempo de resolução do problema. O método de pesquisa para solução deste problema foi baseado em adaptações das tradicionais técnicas de pesquisa operacional, e propiciou a resolução do MDVSP apresentando resultados bastante competitivos quanto ao custo da função objetivo, número de veículos utilizados e tempo computacional necessário. / Currently the logistical problems are relying quite significantly on Operational Research in order to achieve greater efficiency in their operations. Among the various problems related to the vehicles scheduling in a logistics system, the Multiple Depot Vehicle Scheduling Problem (MDVSP) has been addressed in several studies. The MDVSP presupposes the existence of depots that affect the planning of sequences to which travel must be performed. Often, exact methods cannot solve large instances encountered in practice and in order to take them into account, several heuristic approaches are being developed. The aim of this study was thus to solve the MDVSP using a meta-heuristic based on tabu-search method. The main motivation for this work came from the indication that only recently the use of meta-heuristics is being applied to MDVSP context (Pepin et al. 2008) and, also, the limitations listed by Rohde (2008) in his study, which used the branch-and-bound in one of the steps of the heuristic presented to solve the problem, which has increased the time resolution. The research method for solving this problem was based on adaptations of traditional techniques of Operational Research, and provided resolutions presenting very competitive results for the MDVSP such as the cost of the objective function, number of vehicles used and computational time.

Os problemas logísticos estão se apoiando de forma bastante expressiva na pesquisa operacional a fim de obter uma maior eficiência em suas operações. Dentre os vários problemas relacionados à designação de veículos em um sistema logístico, o de escalonamento de veículos com múltiplas garagens, MDVSP (Multiple Depot Vehicle Scheduling Problem), vem sendo abordado em diversas pesquisas. O MDVSP pressupõe a existência de garagens que interferem no planejamento das sequências com as quais as viagens devem ser executadas. Frequentemente, métodos exatos não podem resolver as grandes instâncias encontradas na prática e, para poder levá-las em consideração, várias abordagens heurísticas estão sendo desenvolvidas. O principal objetivo deste trabalho, portanto, foi solucionar o MDVSP através de uma heurística utilizando o método de busca-tabu. A principal motivação para a realização deste trabalho surgiu a partir da indicação de que apenas recentemente o uso de meta-heurísticas está sendo aplicado ao MDVSP (Pepin et al. 2008) e das limitações elencadas no estudo de Rohde (2008), o qual utilizou o algoritmo branch-and-bound em uma das etapas da heurística apresentada para resolver o problema, o que fez aumentar o tempo de resolução do problema. O método de pesquisa para solução deste problema foi baseado em adaptações das tradicionais técnicas de pesquisa operacional, e propiciou a resolução do MDVSP apresentando resultados bastante competitivos quanto ao custo da função objetivo, número de veículos utilizados e tempo computacional necessário. / Currently the logistical problems are relying quite significantly on Operational Research in order to achieve greater efficiency in their operations. Among the various problems related to the vehicles scheduling in a logistics system, the Multiple Depot Vehicle Scheduling Problem (MDVSP) has been addressed in several studies. The MDVSP presupposes the existence of depots that affect the planning of sequences to which travel must be performed. Often, exact methods cannot solve large instances encountered in practice and in order to take them into account, several heuristic approaches are being developed. The aim of this study was thus to solve the MDVSP using a meta-heuristic based on tabu-search method. The main motivation for this work came from the indication that only recently the use of meta-heuristics is being applied to MDVSP context (Pepin et al. 2008) and, also, the limitations listed by Rohde (2008) in his study, which used the branch-and-bound in one of the steps of the heuristic presented to solve the problem, which has increased the time resolution. The research method for solving this problem was based on adaptations of traditional techniques of Operational Research, and provided resolutions presenting very competitive results for the MDVSP such as the cost of the objective function, number of vehicles used and computational time.

The electricity transmission and distribution (T&D) grid is undergoing a paradigm shift as renewable generation explodes while flexible, storage-like loads are being massively adopted. We address the intermittency and volatility issues of renewable resources in connection with spatiotemporal distribution location-specific marginal-cost-based prices (DLMPs) that guide flexible loads to utilize their significant degrees of freedom for the purpose of providing valuable storage-like services to the grid including demand response, energy charge/discharge arbitrage and regulation reserve services. Dynamic DLMPs can induce socially optimal energy and reserve schedules to be adopted by flexible load. To this end, existing transmission wholesale markets must be extended to include distribution network connected participants. Since the inclusion of the complex preferences of many flexible loads renders familiar centralized transmission market designs intractable, we propose and investigate tractable decentralized market designs with Electric Vehicle (EV) battery charging selected as the representative flexible load. We address the equilibrium existence, uniqueness, and efficiency issues that arise with decentralized market designs, using game theory techniques. We investigate various multi-hour and multi-commodity (energy and reserves) market designs including EV self-scheduling under distribution network information aware/unaware conditions, and single or multiple load aggregator(s) scheduling groups of EVs. We investigate the role of network related information in enabling partially price anticipating EVs to acquire market power and self-schedule to achieve individual benefits at the expense of social welfare. Our contribution is the proof of existence and uniqueness of decentralized market equilibria, as well as analytical and numerical comparative analysis. Secondly, we depart from the usual ideal battery assumption, employing instead a realistic two bucket model. We then develop a novel Markovian Decision Process (MDP) application to estimate the regulation tracking cost incurred over an hour by an EV charger employing an optimal controller to respond to the regulation signal which is reset every two seconds by the system operator. The hourly tracking error increases when the EV promises higher regulation reserves while at the same time demanding an achievable albeit high average charging rate. We solve the MDP repeatedly, in fact off line, to capture the impact of the average charging rate and the regulation reserves promised at the beginning of an hour to the resulting hourly regulation tracking error. We then estimate a convex closed form relationship mapping hourly charging rate and regulation reserve offerings to the expected hourly tracking error cost. These convex tracking cost functions provide crucial input to the day ahead hourly energy bids and regulation reserve offers made by individual EVs to the Day Ahead market in response to spatiotemporal DLMPs.