Decomposition of Variational Inequalities with Applications to Nash-Cournot Models in Time of Use Electricity Markets

This thesis proposes equilibrium models to link the wholesale and retail electricity markets which allow for reconciliation of the differing time scales of responses of producers (e.g., hourly) and consumers (e.g., monthly) to changing prices. Electricity market equilibrium models with time of use (TOU) pricing scheme are formulated as large-scale variational inequality (VI) problems, a unified and concise approach for modeling the equilibrium. The demand response is dynamic in these models through a dependence on the lagged demand. Different market structures are examined within this context. With an illustrative example, the welfare gains/losses are analyzed after an implementation of TOU pricing scheme over the single pricing scheme. An approximation of the welfare change for this analysis is also presented. Moreover, break-up of a large supplier into smaller parts is investigated. For the illustrative examples presented in the dissertation, overall welfare gains for consumers and lower prices closer to the levels of perfect competition can be realized when the retail pricing scheme is changed from single pricing to TOU pricing. These models can be useful policy tools for regulatory bodies i) to forecast future retail prices (TOU or single prices), ii) to examine the market power exerted by suppliers and iii) to measure welfare gains/losses with different retail pricing schemes (e.g., single versus TOU pricing). With the inclusion of linearized DC network constraints into these models, the problem size grows considerably. Dantzig-Wolfe (DW) decomposition algorithm for VI problems is used to alleviate the computational burden and it also facilitates model management and maintenance. Modification of the DW decomposition algorithm and approximation of the DW master problem significantly improve the computational effort required to find the equilibrium. These algorithms are applied to a two-region energy model for Canada and a realistic Ontario electricity test system. In addition to empirical analysis, theoretical results for the convergence properties of the master problem approximation are presented for DW decomposition of VI problems

Decomposition methods for large-scale network expansion problems

Network expansion problems are a special class of multi-period network design problems in which arcs can be opened gradually in different time periods but can never be closed. Motivated by practical applications, we focus on cases where demand between origin-destination pairs expands over a discrete time horizon. Arc opening decisions are taken in every period, and once an arc is opened it can be used throughout the remaining horizon to route several commodities. Our model captures a key timing trade-off: the earlier an arc is opened, the more periods it can be used for, but its fixed cost is higher, since it accounts not only for construction but also for maintenance over the remaining horizon. An overview of practical applications indicates that this trade-off is relevant in various settings. For the capacitated variant, we develop an arc-based Lagrange relaxation, combined with local improvement heuristics. For uncapacitated problems, we develop four Benders decompositi

Assignment and control in road traffic networks

The thesis studies the traffic assignment problem in the context of: i) deterministic queue modelling where demand and link traffic flows are time-varying, (ii) the steady-state network design problem, and (iii) signal-controlled road network. In studying the traffic assignment problem in the context of deterministic queue modelling, a model is proposed to determine time- varying link flows in congested road networks where drivers are assumed to be cooperative in minimising total transportation costs. The model is approximate for a network of general topology where there is more than a single commodity and many bottlenecks, but optimal when there is only one active bottleneck along the routes connecting each origin-destination pair. In regards the second context, the thesis offers a method for solving the network design problem that is similar in outer form to the method given in Marcotte (1383). The difference here is being in the way the subproblem, step 2 in Marcotte's method, is attempted. Some computational results are provided, after having implemented the method in a computer code, further, the method is compared against other familiar methods that are found in the literature. As for studying the traffic assignment problem in the context of signal-controlled road networks, the thesis deals with time-variant and time-invariant control and traffic assignment. In both, this is done by alternating between assignment and control, so as to keep the traffic lights in tune with the link flows. Control here is expressed by means of three traffic control policies, with a view to comparing network performance under each of these policies and at different levels of congestion. The three control policies in time-invariant control and assignment are: the standard "delay minimisation" policy, as stated in Allsop (1971), the standard equisaturation method proposed by Webster (1966); and the P0 policy; introduced in Smith (1979b). The control policies in the steady state are compared within a gently rising control model that is described in this thesis to simulate the long run effect of the signal control policies on traffic redistribution. Regarding time-variant control and assignment, CONTRAM (Leonard et al (1978)) was used as an assignment program and modified to incorporate two redefined policies of the three control policies and account for vehicle occupancy

Network Maintenance and Capacity Management with Applications in Transportation

abstract: This research develops heuristics to manage both mandatory and optional network capacity reductions to better serve the network flows. The main application discussed relates to transportation networks, and flow cost relates to travel cost of users of the network. Temporary mandatory capacity reductions are required by maintenance activities. The objective of managing maintenance activities and the attendant temporary network capacity reductions is to schedule the required segment closures so that all maintenance work can be completed on time, and the total flow cost over the maintenance period is minimized for different types of flows. The goal of optional network capacity reduction is to selectively reduce the capacity of some links to improve the overall efficiency of user-optimized flows, where each traveler takes the route that minimizes the traveler’s trip cost. In this dissertation, both managing mandatory and optional network capacity reductions are addressed with the consideration of network-wide flow diversions due to changed link capacities. This research first investigates the maintenance scheduling in transportation networks with service vehicles (e.g., truck fleets and passenger transport fleets), where these vehicles are assumed to take the system-optimized routes that minimize the total travel cost of the fleet. This problem is solved with the randomized fixed-and-optimize heuristic developed. This research also investigates the maintenance scheduling in networks with multi-modal traffic that consists of (1) regular human-driven cars with user-optimized routing and (2) self-driving vehicles with system-optimized routing. An iterative mixed flow assignment algorithm is developed to obtain the multi-modal traffic assignment resulting from a maintenance schedule. The genetic algorithm with multi-point crossover is applied to obtain a good schedule. Based on the Braess’ paradox that removing some links may alleviate the congestion of user-optimized flows, this research generalizes the Braess’ paradox to reduce the capacity of selected links to improve the efficiency of the resultant user-optimized flows. A heuristic is developed to identify links to reduce capacity, and the corresponding capacity reduction amounts, to get more efficient total flows. Experiments on real networks demonstrate the generalized Braess’ paradox exists in reality, and the heuristic developed solves real-world test cases even when commercial solvers fail.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

Mathematical programming models to design and analyse efficient and robust raiway freight transport networks

(English) Searching to achieve an ambitious reduction in greenhouse gas emissions, the European Union has set as a goal a modal shift in freight transport of 30\% by rail or waterborne for the near future. The increasing efforts of many governments to intensify rail freight transport often must face the difficulties involved in improving both infrastructure and rail operations. Moreover, infrastructure management and business operations usually correspond to different entities with highly contradictory economic interests. Making progress on the reliability of the railway network is one of the main factors to be considered to make the use of the train more attractive as a means of transport for industry. Also, focusing on shippers' response to road and rail competition and the role of different rail undertakings competing with each other may help boost the use of rail for freight transport. Seeking to reinforce these two goals, this thesis introduces two independent mathematical optimisation models, which may also be complementary, and which have been developed under a common conceptual framework of data structures and variables to guarantee their compatibility. The first model is a mathematical programming-based design model for evaluating the impact on a mixed railway network from proposals for infrastructure improvement and capacity expansion that are oriented mainly toward increasing freight transportation. The model has been applied to extend elements of an existing mixed railway network, perform relatively less costly actions on the network, and enhance capacity by adding new blocking/control systems at specific locations. These aspects are usually not considered in models for regional planning. Rather than a model whose sole focus is on railway capacity expansion, this approach combines capacity-expansion with network design. Because the way investments generate returns to the freight transportation system is of utmost relevance for these types of problems, this model is based on the efficient frontier between investment and operating costs. The second model is a combined model for jointly evaluating the modal split road-rail, and the resulting railway freight flows on the railway network. This combined modal split-traffic assignment model is addressed to the case when a modal split based on a random utility model is available, and some of its coefficients may present a non-negligible variability. To this end, after the initial deterministic formulation, a robust counterpart of the model is developed. The model, formulated as a non-linear integer programming problem, is oriented to a multi-carrier environment and includes constraints to consider the interactions between the different types of flows on the railway network, allowing a detailed evaluation of the cost types of the carriers and the network capacity. An algorithmic solution based on the outer approximation method is shown to provide accurate solutions in a reasonable computational time for the robust and non-robust versions of the model. Examples centred on a section of the Trans-European Transport Network, the TEN-T Core network corridors, are reported to test the applicability of the models. Results show the effectiveness of both models. The design model can be a helpful tool for analysing the impact infrastructure investments may have on operating costs, where (implicit) capacity limitations in the scenarios to be evaluated may necessarily be taken into account. At the same time, it can be complemented with the combined modal split-traffic assignment model by assessing the possible shippers' response to the different railway carriers' services competing with each other and the road.(Español) Tratando de lograr una significativa y ambiciosa reducción de las emisiones de gases de efecto invernadero, la Unión Europea se ha marcado como objetivo que los modos de transporte de mercancías alternativos a la carretera, como el ferrocarril o la navegación fluvial, alcancen una cuota del 30% sobre el total de mercancías transportadas por tierra en Europa en los próximos años. Los crecientes esfuerzos que llevan a cabo los diferentes gobiernos se enfrentan con demasiada frecuencia con las dificultades que suponen mejorar de forma simultánea infraestructura y operaciones ferroviarias, habitualmente gestionados por entes diferentes con intereses económicos enfrentados. Mejorar la fiabilidad de la red ferroviaria es uno de los principales factores a tener en cuenta para hacer más atractivo el uso del tren como medio de transporte para la industria. Por otro lado, centrarse en los criterios que pueden llevar a las empresas a elegir entre carretera o tren, y en el papel que juegan las diferentes compañías ferroviarias en esta elección, compitiendo entre sí, puede ayudar a incrementar el uso del tren para el transporte de mercancías. Con la idea de reforzar estos dos objetivos, este trabajo de tesis presenta dos modelos matemáticos de optimización, independientes pero a la vez complementarios, y desarrollados bajo un marco conceptual de estructuras de datos y variables común para garantizar su compatibilidad. El primer modelo es un modelo de diseño basado en programación matemática para evaluar el impacto que pueden tener, sobre una red ferroviaria de uso mixto, propuestas de mejora de la infraestructura y de ampliación de la capacidad dirigidas principalmente a incrementar el uso del tren para el transporte de mercancías. El modelo se ha orientado a la modificación de elementos de una red ferroviaria de uso mixto existente, proponiendo intervenciones en la red relativamente poco costosas, y aumentando la capacidad añadiendo nuevos sistemas de bloqueo y control en ubicaciones específicas. Para este tipo de problemas, es de la máxima relevancia la manera en que las inversiones generan retornos al sistema de transporte ferroviario. Por eso, este modelo está basado en el óptimo equilibrio entre la inversión y los costes de operación. El segundo modelo es un modelo combinado para evaluar de forma conjunta el reparto modal entre carretera y tren, y los flujos de mercancías en la red ferroviaria resultantes. Este modelo está enfocado hacia aquellas situaciones en que hay un modelo de utilidad aleatoria disponible, pero algunos de sus coeficientes pueden presentar una variabilidad que no debe ser ignorada. Con esta finalidad, tras la formulación inicial del modelo determinístico se presenta una versión robusta de la formulación. El modelo, formulado como un problema de programación no lineal entera, está enfocado hacia un entorno en el que conviven (y compiten) diferentes compañías ferroviarias. Se detalla un algoritmo para resolver el modelo, basado en el método de aproximaciones externas, que permite obtener soluciones precisas con un tiempo computacional razonable, tanto para la versión determinística como para la versión robusta. Ejemplos basados en una sección de la Red Trans-Europea de Transporte (TEN-T por sus siglas en inglés) permiten validar la aplicabilidad y eficacia de los modelos. El modelo de diseño puede ser una herramienta útil para analizar el impacto que las inversiones en infraestructura pueden tener en los costes de operación, teniendo en cuenta las limitaciones de capacidad que existen en los escenarios evaluados. De la misma forma, se puede complementar este análisis con el modelo combinado de reparto modal y asignación de flujos, en el que se puede comprobar la posible respuesta de las empresas que requieren transportar sus productos ante los diferentes servicios ofrecidos por las compañías ferroviarias compitiendo entre si, y compitiendo con la carretera.Estadística i investigació operativ

Mathematical programming models to design and analyse efficient and robust raiway freight transport networks

(English) Searching to achieve an ambitious reduction in greenhouse gas emissions, the European Union has set as a goal a modal shift in freight transport of 30\% by rail or waterborne for the near future. The increasing efforts of many governments to intensify rail freight transport often must face the difficulties involved in improving both infrastructure and rail operations. Moreover, infrastructure management and business operations usually correspond to different entities with highly contradictory economic interests. Making progress on the reliability of the railway network is one of the main factors to be considered to make the use of the train more attractive as a means of transport for industry. Also, focusing on shippers' response to road and rail competition and the role of different rail undertakings competing with each other may help boost the use of rail for freight transport. Seeking to reinforce these two goals, this thesis introduces two independent mathematical optimisation models, which may also be complementary, and which have been developed under a common conceptual framework of data structures and variables to guarantee their compatibility. The first model is a mathematical programming-based design model for evaluating the impact on a mixed railway network from proposals for infrastructure improvement and capacity expansion that are oriented mainly toward increasing freight transportation. The model has been applied to extend elements of an existing mixed railway network, perform relatively less costly actions on the network, and enhance capacity by adding new blocking/control systems at specific locations. These aspects are usually not considered in models for regional planning. Rather than a model whose sole focus is on railway capacity expansion, this approach combines capacity-expansion with network design. Because the way investments generate returns to the freight transportation system is of utmost relevance for these types of problems, this model is based on the efficient frontier between investment and operating costs. The second model is a combined model for jointly evaluating the modal split road-rail, and the resulting railway freight flows on the railway network. This combined modal split-traffic assignment model is addressed to the case when a modal split based on a random utility model is available, and some of its coefficients may present a non-negligible variability. To this end, after the initial deterministic formulation, a robust counterpart of the model is developed. The model, formulated as a non-linear integer programming problem, is oriented to a multi-carrier environment and includes constraints to consider the interactions between the different types of flows on the railway network, allowing a detailed evaluation of the cost types of the carriers and the network capacity. An algorithmic solution based on the outer approximation method is shown to provide accurate solutions in a reasonable computational time for the robust and non-robust versions of the model. Examples centred on a section of the Trans-European Transport Network, the TEN-T Core network corridors, are reported to test the applicability of the models. Results show the effectiveness of both models. The design model can be a helpful tool for analysing the impact infrastructure investments may have on operating costs, where (implicit) capacity limitations in the scenarios to be evaluated may necessarily be taken into account. At the same time, it can be complemented with the combined modal split-traffic assignment model by assessing the possible shippers' response to the different railway carriers' services competing with each other and the road.(Español) Tratando de lograr una significativa y ambiciosa reducción de las emisiones de gases de efecto invernadero, la Unión Europea se ha marcado como objetivo que los modos de transporte de mercancías alternativos a la carretera, como el ferrocarril o la navegación fluvial, alcancen una cuota del 30% sobre el total de mercancías transportadas por tierra en Europa en los próximos años. Los crecientes esfuerzos que llevan a cabo los diferentes gobiernos se enfrentan con demasiada frecuencia con las dificultades que suponen mejorar de forma simultánea infraestructura y operaciones ferroviarias, habitualmente gestionados por entes diferentes con intereses económicos enfrentados. Mejorar la fiabilidad de la red ferroviaria es uno de los principales factores a tener en cuenta para hacer más atractivo el uso del tren como medio de transporte para la industria. Por otro lado, centrarse en los criterios que pueden llevar a las empresas a elegir entre carretera o tren, y en el papel que juegan las diferentes compañías ferroviarias en esta elección, compitiendo entre sí, puede ayudar a incrementar el uso del tren para el transporte de mercancías. Con la idea de reforzar estos dos objetivos, este trabajo de tesis presenta dos modelos matemáticos de optimización, independientes pero a la vez complementarios, y desarrollados bajo un marco conceptual de estructuras de datos y variables común para garantizar su compatibilidad. El primer modelo es un modelo de diseño basado en programación matemática para evaluar el impacto que pueden tener, sobre una red ferroviaria de uso mixto, propuestas de mejora de la infraestructura y de ampliación de la capacidad dirigidas principalmente a incrementar el uso del tren para el transporte de mercancías. El modelo se ha orientado a la modificación de elementos de una red ferroviaria de uso mixto existente, proponiendo intervenciones en la red relativamente poco costosas, y aumentando la capacidad añadiendo nuevos sistemas de bloqueo y control en ubicaciones específicas. Para este tipo de problemas, es de la máxima relevancia la manera en que las inversiones generan retornos al sistema de transporte ferroviario. Por eso, este modelo está basado en el óptimo equilibrio entre la inversión y los costes de operación. El segundo modelo es un modelo combinado para evaluar de forma conjunta el reparto modal entre carretera y tren, y los flujos de mercancías en la red ferroviaria resultantes. Este modelo está enfocado hacia aquellas situaciones en que hay un modelo de utilidad aleatoria disponible, pero algunos de sus coeficientes pueden presentar una variabilidad que no debe ser ignorada. Con esta finalidad, tras la formulación inicial del modelo determinístico se presenta una versión robusta de la formulación. El modelo, formulado como un problema de programación no lineal entera, está enfocado hacia un entorno en el que conviven (y compiten) diferentes compañías ferroviarias. Se detalla un algoritmo para resolver el modelo, basado en el método de aproximaciones externas, que permite obtener soluciones precisas con un tiempo computacional razonable, tanto para la versión determinística como para la versión robusta. Ejemplos basados en una sección de la Red Trans-Europea de Transporte (TEN-T por sus siglas en inglés) permiten validar la aplicabilidad y eficacia de los modelos. El modelo de diseño puede ser una herramienta útil para analizar el impacto que las inversiones en infraestructura pueden tener en los costes de operación, teniendo en cuenta las limitaciones de capacidad que existen en los escenarios evaluados. De la misma forma, se puede complementar este análisis con el modelo combinado de reparto modal y asignación de flujos, en el que se puede comprobar la posible respuesta de las empresas que requieren transportar sus productos ante los diferentes servicios ofrecidos por las compañías ferroviarias compitiendo entre si, y compitiendo con la carretera.Postprint (published version

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject