Models and Solution Algorithms for Asymmetric Traffic and Transit Assignment Problems

Modeling the transportation system is important because it provides a “common ground” for discussing policy and examining the future transportation plan required in practices. Generally, modeling is a simplified representation of the real world; however, this research added value to the modeling practice by investigating the asymmetric interactions observed in the real world in order to explore potential improvements of the transportation modeling. The Asymmetric Transportation Equilibrium Problem (ATEP) is designed to precisely model actual transportation systems by considering asymmetric interactions of flows. The enhanced representation of the transportation system by the ATEP is promising because there are various asymmetric interactions in real transportation such as intersections, highway ramps, and toll roads and in the structure of the transit fares. This dissertation characterizes the ATEP with an appropriate solution algorithm and its applications. First, the research investigates the factors affecting the convergence of the ATEP. The double projection method is applied to various asymmetric types and complexities in the different sizes of networks in order to identify the influential factors including demand intensities, network configuration, route composition between modes, and sensitivity of the cost function. Secondly, the research develops an enhancement strategy for improvement in computational speed for the double projection method. The structural characteristics of the ATEP are used to develop the convergence enhancement strategy that significantly reduces the computational burdens. For the application side, instances of asymmetric interactions observed in in-vehicle crowding and the transit fare structure are modeled to provide a suggestion on policy approach for a transit agency. The direct application of the crowding model into the real network indicates that crowd modeling with multi user classes could influence the public transportation system planning and the revenue achievement of transit agencies. Moreover, addition of the disutility factor, crowding, not always causes the increase of disutility from the transit uses. The application of the non-additive fare structure in the Utah Transit Authority (UTA) network addresses the potential of the distance-based fare structure should the UTA make a transition to this fare structure from their current fare model. The analysis finds that the zero base fare has the highest potential for increasing the transit demand. However, collecting less than $0.50 with a certain buffer distance for the first boarding has potential for attracting the users to UTA\u27s transit market upon the fare structure change

PDE–Based Modelling and Control Strategies for Manufacturing Processes

This work aims to design boundary control strategies to solve demand tracking and backlog problems for manufacturing systems in terms of conservation laws coupled with ODEs in different network topologies. The OCPs are investigated in the dispersing and the merging networks. The problems are optimized utilizing open-loop optimal control based on the direct and the indirect approaches. The proposed approaches enable the solution of the OCPs. All of the approaches, in general, reach a local minima with similar behaviour that leads to the steady-state. The results analysis reveals that each method has its own distinct characteristics. The indirect methodology is characterized by excellent accuracy and minimal processing burden; yet, due to the information necessary to compute the gradient, it is a sensitive method. The ease of use and flexibility to any problem distinguishes the direct method. However, this approach takes substantially longer to achieve a solution when compared to the indirect method. Also, the AMPC was introduced to investigate demand tracking and backlog problems in the context of the complex network of production systems. The addressed network includes structures that are dispersing and merging. Furthermore, the appropriate way to handle the parameters of the AMPC for both control and prediction horizons is addressed. Moreover, the proposed AMPC provides for the solutions of demand tracking and backlog problems. In general, AMPC and traditional MPC attain local minima with similar behaviour that leads to steady-state convergence. When compared to a typical MPC, the AMPC's performance shows a considerable reduction in computational time. Additionally, because it provides a mathematical insight into the method's structure, the AMPC allows for great accuracy of optimal solutions. Finally, the AMPC is characterized by its robustness according to perturbation effects

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Stochastic optimal control and regime switching : applications in economics

Economic decisions under uncertainty generally involve a change of stochastic regime. This thesis examines the formal conditions for optimizing such decisions and looks at applications to exchange rate intervention, physical investment and consumption behaviour. Many of these economic regime switchings can be mathematically formulated as stopping problems. Global optimality is achieved by applying Hamilton-Jacobi-Bellman equations in each regime, together with the joining conditions at the switching boundaries. Chapter 1 establishes the framework for optimisation and provides various boundary conditions for different switching cases. Chapter 2 applies optimal stopping techniques to derive optimal “time-consistent” exchange rate target zones in the presence of proportional/lump sum intervention costs. It further shows that such discretionary equilibria can be improved upon by a credible commitment to an exchange rate mechanism (such as ERM). Chapter 3 characterises the irreversible oil investment decision in the North Sea as an optimal regime switching problem. In the absence of Petroleum Revenue Tax (PRT), it shows how the optimal development decision will be deferred when real oil prices follow a geometric Brownian motion. In chapter 4, an intertemporal partial equilibrium model of investment is used to assess the effects of stochastic capital depreciation on optimal investment behaviour, in a context where a sales constraint effectively decomposes the problem into two distinct regimes. The presence of the uncertainty about depreciation reduces firm’s demand for investment; and increasing the variability of capital depreciation further reduces investment. The uncertainty also makes investment “smoother” than that under certainty. Finally, chapter 5 and 6 deal with optimal consumption/portfolio decisions in a two-asset model with shortselling and borrowing restrictions imposed. Chapter 5 formulates a regime switching problem due to the presence of the borrowing constraint and specifies the corresponding boundary conditions. Chapter 6 characterises optimal solutions to various combinations of parameters for constant relative and constant absolute risk aversion utility functions. In many cases, if labour income is fully diversifiable, the borrowing constraint only binds when the wealth level falls below a threshold, and risk taking behaviour at the low level of wealth is associated with a convex portion of the indirect utility function (value function). In such regime-switch cases, the introduction of the borrowing constraint makes consumption more volatile relative to income. It also generates the precautionary motive for saving