Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 77-78). / Modeling of multiphase flow in fractured media plays an integral role in management and performance prediction of oil and gas reserves. Geological characterization and nmultiphase flow simulations in fractured media are challenging for several reasons, such as uncertainty in fracture location, complexity in fracture geometry. dynamic nature of fractures etc. There is a need for complex sinmulation models that resolve the flow dynamics along fractures and the interaction with the porous matrix. The unstructured finite volume model provides a tool for the numerical simulation of multiphase flow (inmmiscible and incompressible two-phase flow) in two-dimensional fractured media. We use a finite volume formulation, which is locally imass conservative and it allows the use of fully unstructured grids to represent the coimplex geometry of the fracture networks. Fractures are represented as objects of lower diniensionality than that of the domain (in this case, ID objects in a 2D domain). The model permits fine-scale simulation of multiphase transport through fractured media. The non-Fickian transport resulting due to the presence of heterogeneity (as fractures or inhomogeneous permeability distribution) is captured by the traditional advection-diffusion equation using a highly discretized system. Today. many macroscopic flow models are being developed which account for the non-Fickian. non-local flow more accurately and efficiently with less computation. The finite volume simulator niodel described in this thesis will be instrumental as a tool to train and validate the macroscopic flow models which account for anomialous transport behavior. / (cont.) We illustrate the performance of this simulator on several synthetic cases with different fracture geometries and conclude the model effectively captures the miiultiphase fluid flow pattern in fractured media. / by Reena Bajaj. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 77-79). / Hydrogen fuel is considered one of the major emerging renewable substitutes for fossil fuel. A crucial factor as to whether hydrogen will be successful depends on its cost as a substitute. Recently, there has been a growing interest in investigating the feasibility from a supply chain point of view. This thesis intends to provide a comprehensive study of the feasibility of hydrogen as a transportation fuel from a supply chain point of view. The aim is to discover the most efficient, sustainable, and ultimately most cost-effective strategy to meet future transportation demand scenarios. This includes optimizing costs over production, compression, storage, distribution, and dispensation. Moreover, through the decision support model developed in this thesis, insights regarding strategic approaches for hydrogen supply chain infrastructure development are developed, such as the tradeoff between centralized and distributed production. A case study in Spain is presented to illustrate the supply chain. Different models are proposed to estimate electricity generation capacity, hydrogen production scheme, transportation topology, distribution methods and future demands. Six different scenarios, based on different production scheme, future demand level, are tested. Results from the case study indicate that it is more cost effective to transmit electricity from wind farms to locations close to demand sites to do centralized production. In terms of transportation, liquid gas truck is the preferred mode of transportation from production sites to local demand regions. The model can adapt be extended and adapted to consider other configurations of the supply chain network. / by Li Liang. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. / Includes bibliographical references (p. 93-94). / One of the steps in stowage planning is crane split and sequencing, which determines the order of container discharging and loading jobs quay cranes (QCs) perform so that the completion time (or makespan) of ship operation is minimized. The vessel's load profile, number of bays and number of allocated QCs are known to port-planners hours before its arrival, and these are input parameters to the problem. The problem is modeled as a large-scale linear IP where the planning horizon is discretized into time intervals and at most one QC can be assigned to a bay at any period. We introduce clearance constraints, which prevent adjacent QCs from being positioned too close to one another, and yard congestion constraints, which prevent yard storage locations from being overly accessed at any time. This makes the model relevant in an industrial setting. We examine the case only a single ship arrives at port, and the case where multiple ships berth at different times in the planning horizon. The berth time of each ship and number of ships arriving is known. The problem is difficult to solve without any special technique applied. For the single-ship problem, a heuristic approach, which produces high-quality solutions, is developed. / (cont.) A branch-and-price method re-formulates the problem into a set-covering form with huge number of variables; standard variable branching provides optimal solutions very efficiently. For the multiple-ship problem, a solution strategy is developed combining Lagrangian relaxation, branch-and-price and heuristics. After relaxing the yard congestion constraints, the problem decomposes into smaller sub-problems, each involving one ship; the sub-problems are then re-formulated into a column generation form and solved using branch-and-price to obtain Lagrangian solutions and lower-bound values. Lagrangian multipliers are iteratively updated using the sub-gradient method. A primal heuristic detects and eliminates infeasibilities in the Lagrangian solutions which then become an upper bound to the optimal objective. Once the duality gap is sufficiently reduced, the sub-gradient routine is terminated. The availability of efficient commercial modeling software such as OPL Studio and CPLEX allows for larger instances of the problem to be tackled than previously possible. / by Shawn Choo. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, School of Engineering, Center for Computational Engineering, Computation for Design and Optimization Program, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 75-76). / Today, organizations are generating large volumes of data. However, the challenge of extracting valuable information from the data has been a large and long-standing problem. Here, we address the problem of quantifying risks and detecting fraud in heterogeneous financial big data. Great financial losses are pressuring institutions to devise innovative solutions for risk and fraud detection. Current approaches in government suffer from issues such as high false positive rates and low adaptability to the continuous evolution of newer fraud. In this thesis, we propose an open and extensible framework called "Situational Awarness FrAamework for RIsk ranking" (SAFARI). SAFARI aims to quantify and rank risk with unlabeled, complex data in the financial world. The framework integrates and analyzes different perspectives of financial data, and extends risk scores for decision makers. SAFARI also utilizes machine learning techniques to learn from examined cases to improve the calculation of risks and adapt to the changing behavior of fraudulent activities. The work includes designing, implementing, testing, extending and evaluating the proposed framework. In the overpayment detection scenario, results show SAFARI can effectively find overpayments with low false positive rates. Furthermore, SAFARI can be extended to assist decision making in a variety of environment thanks to its general applicability. / by Rongsha Li. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / Includes bibliographical references (p. 75-76). / In this thesis, we study the Projective Re-Normalization method (PRM) for semidefinite programming feasibility problems. To compute a good normalizer for PRM, we propose and study the advantages and disadvantages of a Hit & Run random walk with Dikin ball dilation. We perform this procedure on an ill-conditioned two dimensional simplex to show the Dikin ball Hit & Run random walk mixes much faster than standard Hit & Run random walk. In the last part of this thesis, we conduct computational testing of the PRM on a set of problems from the SDPLIB [3] library derived from control theory and several univariate polynomial problems sum of squares (SOS) problems. Our results reveal that our PRM implementation is effective for problems of smaller dimensions but tends to be ineffective (or even detrimental) for problems of larger dimensions. / by Sai Hei Yeung. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Cataloged from student submitted PDF version of thesis. / Includes bibliographical references (p. 67-68). / We study a periodic-reviewed, infinite horizon serial network inventory control problem. The demands in different periods are independent of each other and follow an identical Poisson distribution. Unsatisfied demands are backlogged until they are satisfied by supply units. In each period, there is a per-unit holding cost is incurred for each unit of supply that stays in the system and a per-unit backorder cost is incurred for each unsatisfied unit of demand. The objective of the inventory control policy is to minimize the long-run expected average cost over an infinite horizon. The goal of the thesis is to evaluate the empirical performance of the dual balancing policy and several other variants of cost balancing policies through numerical simulations. The dual-balancing policy is based on two novel ideas: the marginal cost accounting scheme, which assigns to each decision all the costs that are made inevitable after that decision is made; and the cost balancing idea to balance opposing costs. / (cont.) The dual-balancing policy can be modified in several ways to get other cost balancing policies. It has been proven that the dual-balancing policy has a worst-case guarantee of 2 but this does not indicate the empirical performance. An approximately optimal policy is considered as the benchmark to test the quality of the cost balancing policies. In the computational experiments, the dual-balancing policy shows an average error of 7.74% compared to the approximately optimal policy, much better than the theoretical worst-case guarantee. The three variants of cost balancing policies have made significant improvement on the performance of the dual-balancing policy. The accuracy of the dual-balancing policy is also affected by the system parameters. In addition, with high demand rate and long lead times, we have observed several scenarios when the cost balancing policies dominate the approximately optimal policy. / by Qian Yu. / S.M.

Includes bibliographical references (leaf 49). / Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / In this thesis, we compare computationally four methods for solving optimization problems under uncertainty: * Robust Optimization (RO) * Adaptive Robust Optimization (ARO) * Data Driven Optimization (DDO) * stochastic Programming (SP) We have implemented several computation experiments to demonstrate the different performance of these methods. We conclude that ARO outperform RO, which has a comparable performance with DDO. SP has a comparable performance with RO when the assumed distribution is the same as the true underlying distribution, but under performs RO when the assumed distribution is different from the true distribution. / by Wang, Yanbo. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 65). / This thesis aims to study the network of a nationwide distributor of a commodity product. As we cannot disclose the actual product for competitive reasons, we will present the research in terms of a similar, representative product, namely salt for ice prevention across United States. The distribution network includes four kinds of nodes, sources, buffer locations at sources, storage points and demand regions. It also includes four types of arcs, from sources to buffer locations and to storage points, from buffer locations to storage points, and from storage points to demand regions. The goal is to maximize the total gross margin subject to a set of supply, demand and inventory constraints. In this thesis, we establish two mathematical models to achieve the goal. The first one is a basic model to identify the optimal flows along the arcs across time by treating product prices and market demand as fixed parameters. The model is built in OPL and solved by CPLEX. We then carry out some numerical analyses and tests to validate the correctness of the model and demonstrate its utility. The second one is an advanced model treating product prices and market demand as additional decision variables. The product price and market demand are related by an exponential function, which makes the model difficult to solve with the available commercial solver codes. We then propose several algorithms to reduce the computational complexity of the model so that we can solve with CPLEX. At last, we compare the algorithms to identify the best one. We provide additional numerical tests to show the benefit from including the pricing decisions along with the optimization of the network flows. / by Jie Wang. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009. / In title on title-page, "[epsilon]" appears as the lower case Greek letter. Cataloged from PDF version of thesis. / Includes bibliographical references (p. 59-60). / This research aims to provide tractable approaches to price options using robust optimization. The pricing problem is reduced to a problem of identifying the replicating portfolio which minimizes the worst case arbitrage possible for a given uncertainty set on underlying asset returns. We construct corresponding uncertainty sets based on different levels of risk aversion of investors and make no assumption on specific probabilistic distributions of asset returns. The most significant benefits of our approach are (a) computational tractability illustrated by our ability to price multi-dimensional options and (b) modeling flexibility illustrated by our ability to model the "volatility smile". Specifically, we report extensive computational results that provide empirical evidence that the "implied volatility smile" that is observed in practice arises from different levels of risk aversion for different strikes. We are able to capture the phenomenon by appropriately finding the right risk-aversion as a function of the strike price. Besides European style options which have fixed exercising date, our method can also be adopted to price American style options which we can exercise early. We also show the applicability of this pricing method in the case of exotic and multi-dimensional options, in particular, we provide formulations to price Asian options, Lookback options and also Index options. These prices are compared with market prices, and we observe close matches when we use our formulations with appropriate uncertainty sets constructed based on market-implied risk aversion. / by Si Chen. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Includes bibliographical references (p. 69-72). / A Newton-Krylov method is developed for the solution of the steady compressible Navier-Stokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element Line-Jacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(O)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling used for the element Line-Jacobi preconditioner. This reordering is shown to be far superior to standard reordering techniques (Nested Dissection, One-way Dissection, Quotient Minimum Degree, Reverse Cuthill-Mckee) especially for viscous test cases. The Block-ILU(0) factorization is performed in-place and a novel algorithm is presented for the application of the linearization which reduces both the memory and CPU time over the traditional dual matrix storage format. A linear p-multigrid algorithm using element Line-Jacobi, and Block-ILU(O) smoothing is presented as a preconditioner to GMRES. / (cont.) The coarse level Jacobians are obtained using a simple Galerkin projection which is shown to closely approximate the linearization of the restricted problem except for perturbations due to artificial dissipation terms introduced for shock capturing. The linear multigrid preconditioner is shown to significantly improve convergence in terms of the number of linear iterations as well as to reduce the total CPU time required to obtain a converged solution. A parallel implementation of the linear multi-grid preconditioner is presented and a grid repartitioning strategy is developed to ensure scalable parallel performance. / by Laslo Tibor Diosady. / S.M.