Dissertations / Theses on the topic 'Transportation Management Mathematical models'

This research focuses on fleet management in freight transportation systems. Effective management requires effective planning and control decisions. Plans are often generated using estimates of how the system will evolve in the future; during execution, control decisions need to be made to account for differences between actual realizations and estimates. The benefits of minimum cost plans can be negated by performing costly adjustments during the operational phase. A planning approach that permits effective control during execution is proposed in this dissertation. This approach is inspired by recent work in robust optimization, and is applied to (i) dynamic asset management and (ii) vehicle routing problems. In practice, the fleet management planning is usually decomposed in two parts; the problem of repositioning empty, and the problem of allocating units to customer demands. An alternative integrated dynamic model for asset management problems is proposed. A computational study provides evidence that operating costs and fleet sizes may be significantly reduced with the integrated approach. However, results also illustrate that not considering inherent demand uncertainty generates fragile plans with potential costly control decisions. A planning approach for the empty repositioning problem is proposed that incorporates demand and supply uncertainty using interval around nominal forecasted parameters. The intervals define the uncertainty space for which buffers need to be built into the plan in order to make it a robust plan. Computational evidence suggests that this approach is tractable. The traditional approach to address the Vehicle Routing Problem with Stochastic Demands (VRPSD) is through cost expectation minimization. Although this approach is useful for building routes with low expected cost, it does not directly consider the maximum potential cost that a vehicle might incur when traversing the tour. Our approach aims at minimizing the maximum cost. Computational experiments show that our robust optimization approach generates solutions with expected costs that compare favorably to those obtained with the traditional approach, but also that perform better in worst-case scenarios. We also show how the techniques developed for this problem can be used to address the VRPSD with duration constraints.

Transportation procurement problem (TPP) is the problem of setting transportation service prices, delivery timing and quantity, and controlling costs and capacity to reduce empty movements and improve market efficiency. The purchase of transportation service is traditionally achieved using a request for proposal and long-term contracts. However, as business relationships become ever more flexible and dynamic, there has been an increasing need to hedge the risks of traditional transportation procurement such as entrance of new carriers and sudden drop in fuel price. This thesis proposes a holistic aution-based solution for the TPP. Four typical scenarios are investigated. The first scenario incorporates bilateral bidding into auction mechanism design for multi-unit TPP. This scenario considers one-sided Vickrey-Clarke-Groves (O-VCG) combinatorial auctions for a complex transportation marketplace with multiple lanes. This scenario then designs three alternative multi-unit trade reduction (MTR) mechanisms for the bilateral exchange transportation marketplace where all the lanes are partitioned into distinct markets. Proposed mechanisms ensure incentive compatibility, individual rationality, budget balance and asymptotical efficiency. The second scenario presents a double auction model for the TPP in a dynamic single-lane transportation environment. This scenario first addresses the TPP in a transportation spot market with stochastic but balanced or “symmetric” demand and supply. A periodic sealed double auction (PSDA) is proposed. This scenario then devises a modified PSDA (M-PSDA) to address the TPP with “asymmetric” demand and supply. The auctioneer is likely to gain higher profits from setting a relatively short auction length. However, it is optimal to run the auction (either PSDA or MPSDA) with a relatively large auction length, when maximizing either the social welfare or the utility of shippers and carriers (agents). When the degree of supply-demand imbalance is low, the auctioneer’s myopic optimal expected profit under supply-demand imbalance is larger than that under symmetric demand and supply. This third scenario presents an auction-based model for the TPP in make-toorder systems. The optimality of dynamic base-stock type (S(x)-like policy) is established. The optimal allocation can be achieved by running an O-VCG auction or a first-price auction with closed-form reserve prices. By mild technical modifications, the results derived in the infinite horizon case can all be extended to the finite horizon case. The fourth scenario proposes allocatively efficient auction mechanisms for the distributed transportation procurement problem (DTPP), which is generally the problem of matching demands and supplies over a transportation network. This scenario constructs an O-VCG combinatorial auction for the DTPP where carriers are allowed to bid on bundles of lanes. To simplify the execution of auction, this scenario next proposes a primal-dual Vickrey (PDV) auction based on insights from the known Ausubel auctions and the primal-dual algorithm. The PDV auction realizes VCG payments and truthful bidding under the condition of seller-submodularity, which implies that the effect of each individual carrier is decreasing when the coalition increases.
published_or_final_version
Industrial and Manufacturing Systems Engineering
Doctoral
Doctor of Philosophy

This dissertation proposes approaches that enable effective planning and control of mobile transportation resources in large-scale consolidation networks. We develop models, algorithms, and methodologies that are applied to fleet sizing and fleet repositioning. Three specific but interrelated problems are studied. The first two relate to the trade-offs between fleet size and repositioning costs in transportation resource management, while the third involves a dynamic empty repositioning problem with explicit consideration of the uncertainty of future requirements that will be revealed over time. Chapter 1 provides an overview of freight trucking, including the consolidation trucking systems that will be the focus of this research. Chapter 2 proposes an optimization modeling approach for analyzing the trade-off between the cost of a larger fleet of tractors and the cost of repositioning tractors for a trucking company operating a consolidation network, such as a less-than-truckload (LTL) company. Specifically, we analyze the value of using extra tractor repositioning moves (in addition to the ones required to balance resources throughout the network) to attain savings in the fixed costs of owning or leasing a tractor fleet during a planning horizon. The primary contributions of the research in this chapter are that (1) we develop the first optimization models that explore the impact of fleet size reductions via repositioning strategies that have regularity and repeatability properties, and (2) we demonstrate that substantial savings in operational costs can be achieved by repositioning tractors in anticipation of regional changes in freight demand. Chapter 3 studies the optimal Pareto frontiers between the fleet size and repositioning costs of resources required to perform a fixed aperiodic or periodic schedule of transportation requests. We model resource schedules in two alternative ways: as flows on event-based, time-expanded networks; and as perfect matchings on bipartite networks. The main contributions from this chapter are that (1) we develop an efficient re-optimization procedure to compute adjacent Pareto points that significantly reduces the time to compute the entire Pareto frontier of fleet size versus repositioning costs in aperiodic networks, (2) we show that the natural extension to compute adjacent Pareto points in periodic networks does not work in general as it may increase the fleet size by more than one unit, and (3) we demonstrate that the perfect matching modeling framework is frequently intractable for large-scale instances. Chapter 4 considers robust models for dynamic empty-trailer repositioning problems in very large-scale consolidation networks. We investigate approaches that deploy two-stage robust optimization models in a rolling horizon framework to address a multistage dynamic empty repositioning problem in which information is revealed over time. Using real data from a national package/parcel express carrier, we develop and use a simulation to evaluate the performance of repositioning plans in terms of unmet loaded requests and execution costs. The main contributions from this chapter are that (1) we develop approaches for embedding two-stage robust optimization models within a rolling horizon framework for dynamic empty repositioning, (2) we demonstrate that such approaches enable the solution of very large-scale instances, and (3) we show that less conservative implementations of robust optimization models are required within rolling horizon frameworks. Finally, Chapter 5 summarizes the main conclusions from this dissertation and discusses directions for further research.

Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Co-Chair: Erera, Alan L.; Committee Co-Chair: Savelsbergh, Martin W. P.; Committee Member: Ergun, Ozlem; Committee Member: Ferguson, Mark; Committee Member: Kleywegt, Anton J.. Part of the SMARTech Electronic Thesis and Dissertation Collection.

This dissertation is about games with a continuum of players and horizontal differentiation. The first chapter explains how price dispersion can be a feature of a competitive market with homogenous information and production costs. The second chapter extends the study to group consumption. The third chapter is about multiple equilibria in urban transportation.
Doctorat en Sciences économiques et de gestion
info:eu-repo/semantics/nonPublished

Many supply chain problems involve discrete decisions in a dynamic environment. The inventory routing problem is an example that combines the dynamic control of inventory at various facilities in a supply chain with the discrete routing decisions of a fleet of vehicles that moves product between the facilities. We study these problems modeled as mixed-integer programs and propose a time decomposition based on approximate inventory valuation. We generate the approximate value function with an algorithm that combines data fitting, discrete optimization and dynamic programming methodology. Our framework allows the user to specify a class of piecewise linear, concave functions from which the algorithm chooses the value function. The use of piecewise linear concave functions is motivated by intuition, theory and practice. Intuitively, concavity reflects the notion that inventory is marginally more valuable the closer one is to a stock-out. Theoretically, piecewise linear concave functions have certain structural properties that also hold for finite mixed-integer program value functions. (Whether the same properties hold in the infinite case is an open question, to our knowledge.) Practically, piecewise linear concave functions are easily embedded in the objective function of a maximization mixed-integer or linear program, with only a few additional auxiliary continuous variables. We evaluate the solutions generated by our value functions in a case study using maritime inventory routing instances inspired by the petrochemical industry. The thesis also includes two other contributions. First, we review various data fitting optimization models related to piecewise linear concave functions, and introduce new mixed-integer programming formulations for some cases. The formulations may be of independent interest, with applications in engineering, mixed-integer non-linear programming, and other areas. Second, we study a discounted, infinite-horizon version of the canonical single-item lot-sizing problem and characterize its value function, proving that it inherits all properties of interest from its finite counterpart. We then compare its optimal policies to our algorithm's solutions as a proof of concept.

Thesis (MBA)--Stellenbosch University, 2008.
ENGLISH ABSTRACT: Auto Carrier Transport (ACT) is the motor ferrying division of Grindrod South Africa (Pty) Ltd and is contracted to transport the product of 15 different vehicle manufacturers. The division is responsible for ensuring that the combined annual volumes of each contract, totalling over 300 000 vehicles per year, are delivered to the right place, at the right time, and in the right condition. ACT's operating mandate thus focuses on the outbound logistics of new vehicles, which implies moving cars from either the local manufacturing plants, or from the import facilities at the ports, to the respective dealer networks all across Southern Africa. One of the key operational processes regarding the transportation of vehicles is the allocation of cars to carrier loads, also known as load building. Once cars have been allocated to a load, a carrier is then used to transport the load. The existing load building operation is completely manual, with operators simply assigning cars to loads as best they see fit. No support systems exist. Thus, given the complexity of the load building problem, and the manual processes used, existing load building practices result in suboptimal payload performances. A Linear Programming Model was developed to improve the manner in which vehicles are categorised, and then assigned to loads. When compared against the results of load building operators, it was found that the model could potentially improve the company's contribution margin by 5.8 percent.
AFRIKAANSE OPSOMMING: Auto Carrier Transport (ACT) is die motorvoertuig vervoerafdeling van Grindrod Suid Afrika (Edms) Bpk en word gekontrakteer vir die vervoer van die produkte van 15 verskillende motorvervaardigers. Die afdeling is verantwoorde1ik om te verseker dat die jaarlikse volume van elke kontrak (met 'n gekombineerde volume van meer as 300 000 motorvoertuie per jaar) betyds afgelewer word, op die regte plek en in die regte toestand. ACT se operasionele mandaat fokus dus op die uitgaande logistiek van nuwe motorvoertuie met die implikasie dat motorvoertuie vanaf die plaaslike vervaardingsaanleg, of die invoer fasiliteit by die hawens, na die ooreenstemende handelaarsnetwerke in Suider Afrika vervoer word. Een van die kern operasionele prosesse rakende die vervoer van motorvoertuie, wat bekendstaan as vragtoekening, is die toedeling van motorvoertuie tot vragmotor vragte. Sodra 'n motorvoertuig aan 'n vrag toegeken is, word dit deur middel van 'n vragmotor vervoer. Die bestaande vragtoekeningsproses word per hand uitgevoer deur operateurs wat eenvoudig motorvoertuie aan vragte toedeel soos hulle goeddink sonder die gebruik van enige besluitnemingsondersteuningstelsels. Aangesien vragtoekening 'n baie komplekse probleem is wat per hand uitgevoer word, is die resultate suboptimaal. 'n Lineêre programeeringsmodel is ontwikkel om die klassifikasie van motorvoertuie te verbeter waarna die motorvoertuie aan vragte toegeken word. In 'n vergelyking tussen die model se resultate en die van die operateurs is daar bevind dat die model die maatskappy se wins per eenheid met 5.8 persent kan verbeter.

Energy and environmental impacts are two factors that will influence urban region composition in the near future. One emerging issue is the effect on water usage resulting from changes in regional or urban transportation trends. With many regions experiencing stresses on water availability, transportation planners and users need to combine information on transportation-related water consumption for any region and assess potential impacts on local water resources from the expansion of alternative transportation modes. This thesis will focus on use-phase water consumption factors for multiple vehicle modes, energy and fuel pathways, roads, and vehicle infrastructure for a given transportation network. While there are studies examining life cycle impacts for energy generation and vehicle usage, few repeatable models exist for assessing overall water consumption across several transportation modes within urban regions. As such, the question is: is it possible to develop a traceable decision support model that combines and assesses water consumption from transportation modes and related mobility infrastructure for a given mobility network? Based on this, an object-oriented system model of transportation elements was developed using the Systems Modeling Language (SysML) and Model-Based Systems Engineering principles to compare water consumption across vehicle modes for assessing the resiliency of existing infrastructure and water resources. To demonstrate the intent of this model, daily network usage water consumption will be analyzed for current and alternative network scenarios projected by policies regarding the expansion of alternative energy. The model is expected to show variations in water consumption due to fluctuations in energy pathways, market shares, and driving conditions, from which the model should help determine the feasibility of expanding alterative vehicles and fuels in these networks. While spatially explicit data is limited compared to the national averages that are used as model inputs, the analytical framework within this model closely follows that of existing assessments and the reusable nature of SysML model elements allows for the future expansion of additional transportation modes and infrastructure as well as other environmental analyses.

Este trabalho utiliza Programação Linear Inteira Mista (PLIM) para propor uma nova abordagem para a atividade de sequenciamento de bateladas em uma rede de dutos real. O modelo proposto está imerso em uma estrutura de otimização que auxilia a tarefa de programação scheduling do transporte de derivados leves, ou derivados claros, de petróleo. A rede de dutos em estudo é composta por 14 nós (ou áreas) sendo 4 refinarias, 2 terminais portuários, 2 clientes finais, 5 terminais de distribuição e um entroncamento de válvulas e bombas, interligados por 30 dutos. Nesta rede trafegam mais de 35 derivados claros de petróleo. O processo de programação das atividades de transferência e estocagem envolve restrições operacionais complexas, sendo um problema combinatorial de otimização de difícil resolução. Devido à complexidade do problema, uma estratégia de decomposição é empregada para a modelagem. Esta estratégia tem por base uma divisão hierárquica nos três elementos chaves do scheduling: Alocação dos Recursos, Sequenciamento das Atividades e Determinação Temporal. No presente trabalho aborda-se o módulo de Sequenciamento das Atividades. Desenvolveu-se um modelo PLIM com abordagem temporal contínua que representa o transporte de derivados claros de petróleo por dutos. Objetiva-se obter a ordem de bombeamento das bateladas nas origens, bem como a sequência de passagem pelos dutos da rede, relevando-se gerenciamentos de inventários. Adicionalmente, no contexto do módulo de Sequenciamento, restrições para evitar a necessidade de reversões de fluxo ou inserção de produtos selo devido às incompatibilidades de produtos são modeladas. Testes são realizados usando cenários reais para um horizonte de tempo de, aproximadamente, 30 dias. São apresentados resultados comparativos com um método heurístico e entre versões derivadas do modelo proposto, a fim de investigar o incremento do custo computacional com a inclusão de novas características de modelagem. Os resultados obtidos sugerem a possibilidade de significativa redução do custo operacional com adequado gerenciamento de inventários.
This work applies Mixed Integer Linear Programming for a new approach to batch sequencing in a real-world pipeline network. The proposed model is immersed in an optimization framework to aid the operational scheduling of light oil derivatives. The considered pipeline network consists of 14 nodes (areas), with 4 refineries, 2 harbors, 2 final clients, 5 distribution terminals, and a node that links valves and pumps, interconnected by 30 pipelines. In this network, 35 light oil derivatives can be transported. The scheduling process involves complex operational constraints for determining transfer and storage activities, being a combinatorial optimization problem difficult to solve. Due to the complexity of the problem, a decomposition approach is applied for modeling purposes. This strategy is based on a hierarchical division in the three key elements of scheduling: Assignment, Sequencing, and Timing. The Sequencing Module is addressed within this work. It is developed a continuous time MILP model that represents the transportation of light oil derivatives through pipelines. The aim is to obtain the pumping sequencing of batches in the sources, as well as the transportation sequences in pipelines, considering the management of inventories. Additionally, within the sequencing module, constraints to avoid flow reversions or insertion of plug products are modeled. Tests are performed using real scenarios for a time horizon of, approximately, 30 days. Comparative results with a heuristic approach and derived versions of the proposed model are presented in order to investigate the computational cost increase with the addition of new modeling features. The obtained results suggest the possibility of significant operational cost reductions with an adequate management of inventories.

[ES] En la actualidad, uno de los principales desafíos a los que se enfrentan las grandes áreas metropolitanas es la congestión provocada por el tráfico, la cual se ha convertido en un problema importante al que se enfrentan las autoridades de cada ciudad. Para abordar este problema es necesario implementar una solución eficiente para controlar el tráfico que genere beneficios para los ciudadanos, como reducir los tiempos de viaje de los vehículos y, en consecuencia, el consumo de combustible, el ruido, y la contaminación ambiental. De hecho, al analizar adecuadamente la demanda de tráfico, es posible predecir las condiciones futuras del tráfico, y utilizar esa información para la optimización de las rutas tomadas por los vehículos. Este enfoque puede ser especialmente efectivo si se aplica en el contexto de los vehículos autónomos, que tienen un comportamiento más predecible, lo cual permite a los administradores de la ciudad mitigar los efectos de la congestión, como es la contaminación, al mejorar el flujo de tráfico de manera totalmente centralizada. La validación de este enfoque generalmente requiere el uso de simulaciones que deberían ser lo más realistas posible. Sin embargo, lograr altos grados de realismo puede ser complejo cuando los patrones de tráfico reales, definidos a través de una matriz de Origen/Destino (O-D) para los vehículos en una ciudad, son desconocidos, como ocurre la mayoría de las veces. Por lo tanto, la primera contribución de esta tesis es desarrollar una heurística iterativa para mejorar el modelado de la congestión de tráfico; a partir de las mediciones de bucle de inducción reales hechas por el Ayuntamiento de Valencia (España), pudimos generar una matriz O-D para la simulación de tráfico que se asemeja a la distribución de tráfico real. Si fuera posible caracterizar el estado del tráfico prediciendo las condiciones futuras del tráfico para optimizar la ruta de los vehículos automatizados, y si se pudieran tomar estas medidas para mitigar de manera preventiva los efectos de la congestión con sus problemas relacionados, se podría mejorar el flujo de tráfico en general. Por lo tanto, la segunda contribución de esta tesis es desarrollar una Ecuación de Predicción de Tráfico para caracterizar el comportamiento en las diferentes calles de la ciudad en términos de tiempo de viaje con respecto al volumen de tráfico, y aplicar una regresión logística a esos datos para predecir las condiciones futuras del tráfico. La tercera y última contribución de esta tesis apunta directamente al nuevo paradigma de gestión de tráfico previsto, tratándose de un servidor de rutas capaz de manejar todo el tráfico en una ciudad, y equilibrar los flujos de tráfico teniendo en cuenta las condiciones de congestión del tráfico presentes y futuras. Por lo tanto, realizamos un estudio de simulación con datos reales de congestión de tráfico en la ciudad de Valencia (España), para demostrar cómo se puede mejorar el flujo de tráfico en un día típico mediante la solución propuesta. Los resultados experimentales muestran que nuestra solución, combinada con una actualización frecuente de las condiciones del tráfico en el servidor de rutas, es capaz de lograr mejoras sustanciales en términos de velocidad promedio y tiempo de trayecto, ambos indicadores de un menor grado de congestión y de una mejor fluidez del tráfico.
[CA] En l'actualitat, un dels principals desafiaments als quals s'enfronten les grans àrees metropolitanes és la congestió provocada pel trànsit, que s'ha convertit en un problema important al qual s'enfronten les autoritats de cada ciutat. Per a abordar aquest problema és necessari implementar una solució eficient per a controlar el trànsit que genere beneficis per als ciutadans, com reduir els temps de viatge dels vehicles i, en conseqüència, el consum de combustible, el soroll, i la contaminació ambiental. De fet, en analitzar adequadament la demanda de trànsit, és possible predir les condicions futures del trànsit, i utilitzar aqueixa informació per a l'optimització de les rutes preses pels vehicles. Aquest enfocament pot ser especialment efectiu si s'aplica en el context dels vehicles autònoms, que tenen un comportament més predictible, i això permet als administradors de la ciutat mitigar els efectes de la congestió, com és la contaminació, en millorar el flux de trànsit de manera totalment centralitzada. La validació d'aquest enfocament generalment requereix l'ús de simulacions que haurien de ser el més realistes possible. No obstant això, aconseguir alts graus de realisme pot ser complex quan els patrons de trànsit reals, definits a través d'una matriu d'Origen/Destinació (O-D) per als vehicles en una ciutat, són desconeguts, com ocorre la majoria de les vegades. Per tant, la primera contribució d'aquesta tesi és desenvolupar una heurística iterativa per a millorar el modelatge de la congestió de trànsit; a partir dels mesuraments de bucle d'inducció reals fetes per l'Ajuntament de València (Espanya), vam poder generar una matriu O-D per a la simulació de trànsit que s'assembla a la distribució de trànsit real. Si fóra possible caracteritzar l'estat del trànsit predient les condicions futures del trànsit per a optimitzar la ruta dels vehicles automatitzats, i si es pogueren prendre aquestes mesures per a mitigar de manera preventiva els efectes de la congestió amb els seus problemes relacionats, es podria millorar el flux de trànsit en general. Per tant, la segona contribució d'aquesta tesi és desenvolupar una Equació de Predicció de Trànsit per a caracteritzar el comportament en els diferents carrers de la ciutat en termes de temps de viatge respecte al volum de trànsit, i aplicar una regressió logística a aqueixes dades per a predir les condicions futures del trànsit. La tercera i última contribució d'aquesta tesi apunta directament al nou paradigma de gestió de trànsit previst. Es tracta d'un servidor de rutes capaç de manejar tot el trànsit en una ciutat, i equilibrar els fluxos de trànsit tenint en compte les condicions de congestió del trànsit presents i futures. Per tant, realitzem un estudi de simulació amb dades reals de congestió de trànsit a la ciutat de València (Espanya), per a demostrar com es pot millorar el flux de trànsit en un dia típic mitjançant la solució proposada. Els resultats experimentals mostren que la nostra solució, combinada amb una actualització freqüent de les condicions del trànsit en el servidor de rutes, és capaç d'aconseguir millores substancials en termes de velocitat faig una mitjana i de temps de trajecte, tots dos indicadors d'un grau menor de congestió i d'una fluïdesa millor del trànsit.
[EN] Currently, one of the main challenges that large metropolitan areas have to face is traffic congestion, which has become an important problem faced by city authorities. To address this problem, it becomes necessary to implement an efficient solution to control traffic that generates benefits for citizens, such as reducing vehicle journey times and, consequently, use of fuel, noise and environmental pollution. In fact, by properly analyzing traffic demand, it becomes possible to predict future traffic conditions, and to use that information for the optimization of the routes taken by vehicles. Such an approach becomes especially effective if applied in the context of autonomous vehicles, which have a more predictable behavior, thus enabling city management entities to mitigate the effects of traffic congestion and pollution by improving the traffic flow in a city in a fully centralized manner. Validating this approach typically requires the use of simulations, which should be as realistic as possible. However, achieving high degrees of realism can be complex when the actual traffic patterns, defined through an Origin/Destination (O-D) matrix for the vehicles in a city, are unknown, as occurs most of the times. Thus, the first contribution of this thesis is to develop an iterative heuristic for improving traffic congestion modeling; starting from real induction loop measurements made available by the City Hall of Valencia, Spain, we were able to generate an O-D matrix for traffic simulation that resembles the real traffic distribution. If it were possible to characterize the state of traffic by predicting future traffic conditions for optimizing the route of automated vehicles, and if these measures could be taken to preventively mitigate the effects of congestion with its related problems, the overall traffic flow could be improved. Thereby, the second contribution of this thesis was to develop a Traffic Prediction Equation to characterize the different streets of a city in terms of travel time with respect to the vehicle load, and applying logistic regression to those data to predict future traffic conditions. The third and last contribution of this thesis towards our envisioned traffic management paradigm was a route server capable of handling all the traffic in a city, and balancing traffic flows by accounting for present and future traffic congestion conditions. Thus, we perform a simulation study using real data of traffic congestion in the city of Valencia, Spain, to demonstrate how the traffic flow in a typical day can be improved using our proposed solution. Experimental results show that our proposed solution, combined with frequent updating of traffic conditions on the route server, is able to achieve substantial improvements in terms of average travel speeds and travel times, both indicators of lower degrees of congestion and improved traffic fluidity.
Finally, I want to thank the Ecuatorian Republic through the "Secretaría de Educación Superior, Ciencia, Tecnología e Innovación" (SENESCYT), for granting me the scholarship to finance my studies.
Zambrano Martínez, JL. (2019). Efficient Traffic Management in Urban Environments [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/129865
TESIS

Most existing activity-based travel demand models are implemented in a tour-based microsimulation framework. Due to the significant computational and data storage benefits, the demand microsimulation allows a greater amount of flexibility in terms of demographic market segmentation, temporal scale, and spatial resolution, and thus the models can represent a wider range of travel behavior aspects associated with various policies and scenarios. This dissertation proposes three innovative methodologies, one for each of the three key dimensions, to fulfill the greater level of details toward a more mature state of activity-based travel demand models.

In this study, the seat inventory control problem is considered for airline networks from the perspective of a risk-averse decision maker. In the revenue management literature, it is generally assumed that the decision makers are risk-neutral. Therefore, the expected revenue is maximized without taking the variability or any other risk factor into account. On the other hand, risk-sensitive approach provides us with more information about the behavior of the revenue. The risk measure we consider in this study is the probability that revenue is less than a predetermined threshold level. In the risk-neutral cases, while the expected revenue is maximized, the probability of revenue being less than such a predetermined level might be high. We propose three mathematical models to incorporate the risk measure under consideration. The optimal allocations obtained by these models are numerically evaluated in simulation studies for example problems. Expected revenue, coefficient of variation, load factor and probability of the poor performance are the performance measures in the simulation studies. According to the results of these simulations, it shown that the proposed models can decrease the variability of the revenue considerably. In other words, the probability of revenue being less than the threshold level is decreased. Moreover, expected revenue can be increased in some scenarios by using the proposed models. The approach considered in this thesis is especially proposed for small scale airlines because risk of obtaining revenue less than the threshold level is more for this type of airlines as compared to large scale airlines.

In recent years, the Markov Regime-Switching model and the class of Archimedean copulas have been widely applied to a variety of finance-related fields. The Markov Regime-Switching model can reflect the reality that the underlying economy is changing over time. Archimedean copulas are one of the most popular classes of copulas because they have closed form expressions and have great flexibility in modeling different kinds of dependencies. In the thesis, we first consider a discrete-time risk process based on the compound binomial model with regime-switching. Some general recursive formulas of the expected penalty function have been obtained. The orderings of ruin probabilities are investigated. In particular, we show that if there exists a stochastic dominance relationship between random claims at different regimes, then we can order ruin probabilities under different initial regimes. Regarding capital allocation problems, which are important areas in finance and risk management, this thesis studies the problems of optimal allocation of policy limits and deductibles when the dependence structure among risks is modeled by an Archimedean copula. By employing the concept of arrangement increasing and stochastic dominance, useful qualitative results of the optimal allocations are obtained. Then we turn our attention to a new family of risk measures satisfying a set of proposed axioms, which includes the class of distortion risk measures with concave distortion functions. By minimizing the new risk measures, we consider the optimal allocation of policy limits and deductibles problems based on the assumption that for each risk there exists an indicator random variable which determines whether the risk occurs or not. Several sufficient conditions to order the optimal allocations are obtained using tools in stochastic dominance theory.
published_or_final_version
Statistics and Actuarial Science
Doctoral
Doctor of Philosophy

In this thesis, efforts are devoted to the stochastic modeling, measurement and evaluation of credit risks, the development of mathematical and statistical tools to estimate and predict these risks, and methods for solving the significant computational problems arising in this context. The reduced-form intensity based credit risk models are studied. A new type of reduced-form intensity-based model is introduced, which can incorporate the impacts of both observable trigger events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with trigger events. In addition, this thesis focuses on the relationship between structural firm value model and reduced-form intensity based model. A continuous time structural asset value model for the asset value of two correlated firms with a two-dimensional Brownian motion is studied. With the incomplete information introduced, the information set available to the market participants includes the default time of each firm and the periodic asset value reports. The original structural model is first transformed into a reduced-form model. Then the conditional distribution of the default time as well as the asset value of each name are derived. The existence of the intensity processes of default times is proven and explicit form of intensity processes is given in this thesis. Discrete-time Markovian models in credit crisis are considered. Markovian models are proposed to capture the default correlation in a multi-sector economy. The main idea is to describe the infection (defaults) in various sectors by using an epidemic model. Green’s model, an epidemic model, is applied to characterize the infectious effect in each sector and dependence structures among various sectors are also proposed. The models are then applied to the computation of Crisis Value-at-Risk (CVaR) and Crisis Expected Shortfall (CES). The relationship between correlated defaults of different industrial sectors and business cycles as well as the impacts of business cycles on modeling and predicting correlated defaults is investigated using the Probabilistic Boolean Network (PBN). The idea is to model the credit default process by a PBN and the network structure can be inferred by using Markov chain theory and real-world data. A reduced-form model for economic and recorded default times is proposed and the probability distributions of these two default times are derived. The numerical study on the difference between these two shows that our proposed model can both capture the features and fit the empirical data. A simple and efficient method, based on the ordered default rate, is derived to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. Analytical expressions for the ordered default time distributions with recursive formulas for the coefficients are given, which makes the calculation fast and efficient in finding rates of basket CDSs.
published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy

Forecast models are investigated and developed for use in local water management to aid in determining short term water requirements and availability. The forecast models include precipitation occurrence and depth using a Markov chain model, temperature and solar radiation with a multivariate autoregressive model, and streamflow with autoregressive-moving average models. The precipitation, temperature, and solar radiation forecasts are used with a soil moisture model to determine water demands. A state space approach to the Muskingum-Cunge streamflow routing technique is developed. The forecast water demands and streamflow forecasts are used as inputs to this routing model. Forecast model errors and propagation of these errors from one model into the next are investigated.

This thesis contributes to the literature on the choice of transport mode for commuting trips, with special focus on the difference between urban and rural commuting in Scotland. The thesis begins by giving an overview of discrete choice theory and some empirical models consistent with this theory, before reviewing the literature on empirical applications of mode choice models for commuting trips. In the following, multinomial, nested and mixed logit models using data from a survey of commuters in the University of St Andrews are developed. The models are used to estimate aggregate mode-choice elasticities that can assist the development of efficient car reduction policies in St Andrews and other small towns in rural areas. The direct elasticities of the car mode are found to be comparable to estimates reported in studies of urban commuting, while the demand for public transport is found to be considerably more elastic. The value of in-vehicle travel time is found to be lower than in most studies of urban commuting, reflecting that the roads in the St Andrews area are relatively uncongested. Subsequently, current car drivers' willingness to use a Park and Ride service prior to the implementation of such a service are examined. The results show that the modal shift away from parking on-site will be small unless the new service is accompanied by measures aimed at making parking on-site less attractive such as introducing parking charges. Finally, the effect of the 'compact city' on modal split and congestion are examined. As well as making urban transport more sustainable as a result of an increase in the use of public transport, making cities more compact is found to contribute to lower levels of congestion in urban areas through a reduction in complex trip chains.

Over the past decades, researchers in economics, financial mathematics and actuarial science have introduced results to the concept of comonotonicity in their respective fields of interest. Comonotonicity is a very strong dependence structure and is very often mistaken as a dependence structure that is too extreme and unrealistic. However, the concept of comonotonicity is actually a useful tool for solving several research and practical problems in capital allocation, risk sharing and optimal allocation. The first topic of this thesis is focused on the application of comonotonicity in optimal capital allocation. The Enterprise Risk Management process of a financial institution usually contains a procedure to allocate the total risk capital of the company into its different business units. Dhaene et al. (2012) proposed a unifying capital allocation framework by considering some general deviation measures. This general framework is extended to a more general optimization problem of minimizing separable convex function with a linear constraint and box constraints. A new approach of solving this constrained minimization problem explicitly by the concept of comonotonicity is developed. Instead of the traditional Kuhn-Tucker theory, a method of expressing each convex function as the expected stop-loss of some suitable random variable is used to solve the optimization problem. Then, some results in convex analysis with infimum-convolution are derived using the result of this new approach. Next, Borch's theorem is revisited from the perspective of comonotonicity. The optimal solution to the Pareto optimal risk-sharing problem can be obtained by the Lagrangian method or variational arguments. Here, I propose a new method, which is based on a Breeden-Litzanbeger type integral representation formula for increasing convex functions. It enables the transform of the objective function into a sum of mixtures of stop-losses. Necessary conditions for the existence of optimal solution are then discussed. The explicit solution obtained allows us to show that the risk-sharing problem is indeed a “point-wise” problem, and hence the value function can be obtained immediately using the notion of supremum-convolution in convex analysis. In addition to the above classical risk-sharing and capital allocation problems, the problem of minimizing a separable convex objective subject to an ordering restriction is then studied. Best et al. (2000) proposed a pool adjacent violators algorithm to compute the optimal solution. Instead, we show that using the concept of comonotonicity and the technique of dynamic programming the solution can be derived in a recursive manner. By identifying the right-hand derivative of the convex functions with distribution functions of some suitable random variables, we rewrite the objective function into a sum of expected deviations. This transformation and the fact that the expected deviation is a convex function enable us to solve the minimizing problem.
published_or_final_version
Statistics and Actuarial Science
Doctoral
Doctor of Philosophy

In this thesis, two problems of time consistent mean-variance portfolio selection have been studied: mean-variance asset-liability management with regime switchings and mean-variance optimization with state-dependent risk aversion under short-selling prohibition. Due to the non-linear expectation term in the mean-variance utility, the usual Tower Property fails to hold, and the corresponding optimal portfolio selection problem becomes time-inconsistent in the sense that it does not admit the Bellman Optimality Principle. Because of this, in this thesis, time-consistent equilibrium solution of two mean-variance optimization problems is established via a game theoretic approach. In the first part of this thesis, the time consistent solution of the mean-variance asset-liability management is sought for. By using the extended Hamilton-Jacobi- Bellman equation for equilibrium solution, equilibrium feedback control of this MVALM and the corresponding equilibrium value function can be obtained. The equilibrium control is found to be affine in liability. Hence, the time consistent equilibrium control of this problem is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the simple classical mean-variance problem in Björk and Murgoci (2010), in which it was independent of the state. In the second part of this thesis, the time consistent equilibrium strategies for the mean-variance portfolio selection with state dependent risk aversion under short-selling prohibition is studied in both a discrete and a continuous time set- tings. The motivation that urges us to study this problem is the recent work in Björk et al. (2012) that considered the mean-variance problem with state dependent risk aversion in the sense that the risk aversion is inversely proportional to the current wealth. There is no short-selling restriction in their problem and the corresponding time consistent control was shown to be linear in wealth. However, we discovered that the counterpart of their continuous time equilibrium control in the discrete time framework behaves unsatisfactory, in the sense that the corresponding “optimal” wealth process can take negative values. This negativity in wealth will change the investor into a risk seeker which results in an unbounded value function that is economically unsound. Therefore, the discretized version of the problem in Bjork et al. (2012) might yield solutions with bankruptcy possibility. Furthermore, such “bankruptcy” solution can converge to the solution in continuous counterpart as Björk et al. (2012). This means that the negative risk aversion drawback could appear in implementing the solution in Björk et al. (2012) discretely in practice. This drawback urges us to prohibit short-selling in order to eliminate the chance of getting non-positive wealth. Using backward induction, the equilibrium control in discrete time setting is explicit solvable and is shown to be linear in wealth. An application of the extended Hamilton-Jacobi-Bellman equation leads us to conclude that the continuous time equilibrium control is also linear in wealth. Also, the investment to wealth ratio would satisfy an integral equation which is uniquely solvable. The discrete time equilibrium controls are shown to converge to that in continuous time setting.
published_or_final_version
Mathematics
Master
Master of Philosophy

The problem of selecting a multicriterion decision making (MCDM) technique for watershed resources management is investigated. Of explicit concern in this research is the matching of a watersned resources management problem with an appropriate MCDM technique. More than seventy techniques are recognized while reviewing the area of MCDM. A new classification scheme is developed to categorize these techniques into four groups on the bases of each algorithm's structural formulation and the possible results obtained by using the algorithm. Other standard classification schemes are also discussed to better understand the differences and similarities among the techniques and thereby demonstrate the importance of matching a particular multicriterion decision problem with an appropriate MCDM technique. The desire for selecting the most appropriate MCDM technique for watershed resources management lead to the development of 49 technique choice criteria and an algorithm for selecting a technique. The algorithm divides the technique choice criteria into four groups: (1) DM/analyst-related criteria, (2) technique-related criteria, (3) problem-related criteria and (4) solution-related criteria. To analyze the applicability of MCDM techniques to a particular problem, the levels of performance of the techniques in solving the problem are, at first, evaluated with respect to the choice criteria in each criterion group resulting in four sets of preference rankings. These four sets are then linearly combined using a set of trade-off parameters to determine the overall preference ranking of the techniques. The MUM technique selection process is itself modeled as a multiobjective problem. In this research, for example, a set of 15 techniques, the author is familiar with, are analyzed for their appropriateness to solve a watershed resources management problem. The performance levels of the 15 MCDM techniques in solving such a problem are evaluated with respect to a selected set of technique choice criteria in each criterion group leading to a set of four evaluation matrices of choice criteria versus alternative techniques. This technique choice problem is then analyzed using a two-stage evaluation procedure known as composite programming. The final product of the process resulted in a preference ranking of the alternative MCDM techniques.

It is observed that transit riders are responding to service changes while transit planning is responding to ridership changes, or that transit patronage and service supply are highly interrelated. It is also noticed that transit riders transfer from route to route, the introduction of new service may draw some riders from the existing routes, which implies transit patronage on a route is also affected by other parallel and intersecting routes. An analytic tool is needed to examine these complex relationships in the transit system. This study has developed a quantitative model by incorporating these interactions into a simultaneous system. The simultaneity of transit demand, supply and the interrelationship of inter-route effects are addressed in a three-equation simultaneous model: a demand equation, a supply equation and an equation for competing routes. These equations are estimated simultaneously using the three-stage-least-squares estimation method. The model is estimated at the route-segment level by the time of a day, and by the inbound and outbound directions. Data from Portland, Oregon metropolitan area are used as an extended case study. The socioeconomic and demographic data are allocated to an one-quarter-mile distance service area around a transit route by utilizing the technique of Geographic Information Systems (GIS). The data allocation significantly reduces the measurement error. Inter-route relationships are also identified using GIS. The estimation results show that a service change on a route increases the transit patronage on that route, but it also decreases the ridership on its competing routes, so the net effect of that service improvement is smaller than the ridership increase on the subject route. A conventional single equation model under-estimates the ridership responses on the subject route, and over-estimates the net patronage response. This study is the first research to discuss the net effects of a service change at the route level. The model can be implemented for system-level policy analysis and route-level service and land use planning. It is especially useful for "what-if" scenario analysis at the route level to simulate the ridership impacts of service and land use changes.

Philosophiae Doctor - PhD
The aim of this study is to construct and propose continuous-time mathematical models for optimal management of bank capital, reserves and liquidity. This aim emanates from the global financial crisis of 2007 − 2009. In this regard and as a first task, our objective is to determine an optimal investment strategy for a commercial bank subject to capital requirements as prescribed by the Basel III Accord. In particular, the objective of the aforementioned problem is to maximize the expected return on the bank capital portfolio and minimize the variance of the terminal wealth. We apply classical tools from stochastic analysis to achieve the optimal strategy of a benchmark portfolio selection problem which minimizes the expected quadratic distance of the terminal risk capital reserves from a predefined benchmark. Secondly, the Basel Committee on Banking Supervision (BCBS) introduced strategies to protect banks from running out of liquidity. These measures included an increase of the minimum reserves that the bank ought to hold, in response to the global financial crisis. We propose a model to minimize risk for a bank by finding an appropriate mix of diversification, balanced against return on the portfolio. Thirdly and finally, in response to the financial crises, the Basel Committee on Banking Supervision (BCBS) designed a set of precautionary measures (known as Basel III) for liquidity imposed on banks and one of its purposes is to protect the economy from deteriorating. Recently, bank regulators wanted banks to depend on sources such as core deposits and long-term funding from small businesses and less on short-term wholesale funding.

Increasingly, large volumes of aircraft data are being recorded in an effort to adapt aircraft maintenance procedures from being time-based towards condition-based techniques. This study uses techniques of artificial intelligence and develops mathematical models to analyse this data to enable improvements to be made in aircraft management, affordability, availability, airworthiness and performance. In addition, it highlights the need to assess the integrity of data before further analysis and presents the benefits of fusing all relevant data sources together. The research effort consists of three separate investigations that were undertaken and brought together in order to provide a unified set of methods aimed at providing a safe, reliable, effective and efficient overall procedure. The three investigations are: 1. The management of helicopter Health Usage Monitoring System (HUMS) Condition Indicators (CIs) and their analysis, using a number of techniques, including adaptive thresholds and clustering. These techniques were applied to millions of CI values from Chinook HUMS data. 2. The identification of fixed-wing turbojet engine performance degradation, using anomaly detection techniques, applied to thousands of in-service engine runs from Tornado aircraft. 3. The creation of models to identify unusual aircraft behaviour, such as uncommanded flight control movements. Two Chinook helicopter systems were modelled and the models were applied to over seven hundred in-service flights. In each case, the existing techniques were directed toward a condition-based maintenance approach, giving improved detection and earlier warning of faults.

This thesis presents a series of integrated models for simultaneous optimization of location, capacity, product range, and production technology decisions in production-distribution systems. The interactions between these decisions can be significant. This thesis draws its motivation from these interactions. In order to benefit from the capital and/or employment subsidies, preferential tax rates, and free trade zones provided by governments, firms need to take the interdependencies between their location, capacity and technology decisions into account. These decisions could be further complicated due to varying scale and scope economies inherent in different production technologies.
The models proposed in this thesis are based on two fundamentally different but equally central approaches. The first approach builds on traditionally popular integer programming formulation in facility location theory, in which two such models presented in this thesis. The first one assumes that there are a number of dedicated production technologies for each product whereas, the second one assumes that a set of flexible technologies is also present. Analytical properties of the models are described, which lead to the development of exact and heuristic solution procedures. Results of several sets of computational experiments are also reported. The second approach is based on continuous approximation (also known as continuum mechanics), which has not been used to its potential in the literature. The third model in this thesis is proposed for a system with single product. It is based on the use of continuous functions in representing spatial distribution of cost parameters and decision variables. In this model, the focus is to compute the service regions leaving the precise plant locations to a subsequent analysis. This model lends itself to closed form solutions and allows derivation of a number of insights on the impact of several cost factors on facility design decisions. Then, it is utilized in an analytical framework to analyze several plant focus decisions of firms in a multi-product environment. The closed form solution is used to analyze several product and market focus strategies, which have provided several insights into more sophisticated plant focus decisions and into the impact of different production technologies on these decisions.