Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. / Includes bibliographical references (p. 107-109). / The pricing problem in a multi-period setting is a challenging problem and has attracted much attention in recent years. In this thesis, we consider a monopoly and an oligopoly pricing problem. In the latter, several sellers simultaneously seek an optimal pricing policy for their products. The products are assumed to be differentiated and substitutable. Each seller has the option to set prices for her products at each time period, and her goal is to find a pricing policy that will yield the maximum overall profit. Each seller has a fixed initial inventory of each product to be allocated over the entire time horizon and does not have the option to produce additional inventory between periods. There are no holding costs or back-order costs. In addition, the products are perishable and have no salvage costs. This means that at the end of the entire time horizon, any remaining products will be worthless. The demand function each seller faces for each product is uncertain and is affected by both the prices at the current period and past pricing history for her and her competitors. In this thesis, we address both the uncertain and the competitive aspect of the problem. First, we study the uncertain aspect of the problem in a simplified setting, where there is only one seller and two periods in the model. / (cont.) We use ideas of robust optimization, adjustable robust optimization, dynamic programming and stochastic optimization to find adaptable closed loop pricing policies. Theoretical and numerical results show how the budget of uncertainty, the presence of a reference price, delayed resource allocation, and feedback control affect the quality of the pricing policies. Second, we extend the model to a multi-period setting, where the computation becomes a major issue. We use a delayed constraint generation method to significantly increase the size of the problem that our models can handle. Finally, we consider the pricing problem in an oligopoly setting. We show the existence of solution for both the best response subproblem and the market equilibrium problem for all of the models we discuss in the thesis. We also consider an iterative learning algorithm and illustrate through simulations that an equilibrium pricing policy can be computed for all of our models. / by Lei Zhang. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2017. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 65-74). / Cancer sequencing efforts have largely focused on profiling somatic variants in the protein-coding genome and characterizing their functional impact. In this study, we develop a computational pipeline to identify non-coding mutational drivers across multiple tumor types. We describe the non-coding mutational profiles of 854 samples, spread across 15 tumor types, in the context of their respective tissue type-specific reference epigenomes, using recent pan-cancer whole-genome sequencing data. We develop a novel method to detect significantly recurrent non-coding mutations by reestimating the background mutation density while adjusting for epigenomic covariates. Existing databases on enhancer-gene links allow us to capture the convergence of disparate mutations onto downstream target genes. We then systematically identify key immunomodulatory and tumor-suppressive genes enriched for non-coding mutations in their regulatory neighborhood and evaluate these in a pan-cancer context. Taken together, we show that low-frequency alterations converge into high-frequency recurrent events on downstream targets through tissue-specific regulatory interactions. / by Karthik Murugadoss. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / Includes bibliographical references (p. 57-58). / The present work aims to address the problem of fluid-structure interaction using a discontinuous Galerkin approach. Starting from the Navier-Stokes equations on a fixed domain, an arbitrary Lagrangian Eulerian (ALE) approach is used to derive the equations for the deforming domain. A geometric conservation law (GCL) is then introduced, which guarantees freestream preservation of the numerical scheme. The space discretization is performed using a discontinuous Galerkin method and time integration is performed using either an explicit four stage Runge-Kutta scheme or an implicit BDF2 scheme. The mapping parameters for the ALE formulation are then obtained using algorithms based on radial basis functions (RBF) or linear elasticity. These strategies are robust and can be applied to bodies with arbitrary shapes and undergoing arbitrary motions. The robustness and accuracy of the ALE scheme coupled with these mapping strategies is then demonstrated by solving some model problems. The ability of the scheme to handle complex flow problems is demonstrated by analyzing the low Reynolds number flow over an oscillating circular cylinder. / by Anshul Mohnot. / 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. 63-64). / This thesis aims to solve the periodic-reviewed inventory control problem in supply chain networks with uncertain demand so as to minimize the overall cost of the system over a fixed planning time horizon. In such problems, one seeks to optimally determine ordering quantities at different stages in time. We investigate the class of polynomial policies, where the control policy is directly parametrized polynomially in the observed uncertainties of previous stages. We use sum-of-square relaxations to reformulate the problem into a single semidefinite optimization problem for a specific polynomial degree. We consider both robust and stochastic approaches in order to address the uncertainties in demand. In extensive numerical studies, we find that polynomial policies exhibit better performance over basestock policies across a variety of networks and demand distributions under the mean and standard deviation criteria. However, when the uncertainty set turns out to be larger than planned, basestock policies start outperforming polynomial policies. Comparing the policies obtained under the robust and stochastic frameworks, we find that they are comparable in the average performance criterion, but the robust approach leads to better tail behavior and lower standard deviation in general. / by Liwei He. / 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 45-47). / Geologic C0₂ sequestration is considered a promising tool to reduce anthropogenic C0₂ emissions while allowing continued use of fossil fuels for the current time. The process entails capturing C0₂ at point sources such as coal-fired power plants, and injecting it in its supercritical state into deep saline aquifers for long-term storage. Upon injection, C0₂ partially dissolves in groundwater to form an aqueous solution that is denser than groundwater. The local increase in density triggers a gravitational instability at the boundary layer that further develops into columnar C0₂-rich plumes that sink away. This mechanism, also known as convective mixing, greatly accelerates the dissolution rate of C0₂ into water and provides secure storage of C0₂ underground. Understanding convective mixing in the context of C0₂ sequestration is essential for the design of injection and monitoring strategies that prevent leakage of C0₂ back into the atmosphere. While current studies have elucidated various aspects of this phenomenon in 2D, little is known about this process in 3D. In this thesis we investigate the pattern-formation aspects of convective mixing during geological C0₂ sequestration by means of high-resolution three-dimensional simulation. We find that the C0₂ concentration field self-organizes as a cellular network structure in the diffusive boundary layer right beneath the top boundary. By studying the statistics of the cellular network, we identify various regimes of finger coarsening over time, the existence of a nonequilibrium stationary state, and an universal scaling of 3D convective mixing. We explore the correlation between the observed network pattern and the 3D flow structure predicted by hydrodynamics stability theory. / by Xiaojing Fu. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2017. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 111-115). / Design of complex engineering systems requires coupled analyses of the multiple disciplines affecting system performance. The coupling among disciplines typically contributes significantly to the computational cost of analyzing a system, and can become particularly burdensome when coupled analyses are embedded within a design or optimization loop. In many cases, disciplines may be weakly coupled, so that some of the coupling or interaction terms can be neglected without significantly impacting the accuracy of the system output. However, typical practice derives such approximations in an ad hoc manner using expert opinion and domain experience. In this thesis, we propose a new approach that formulates an optimization problem to find a model that optimally balances accuracy of the model outputs with the sparsity of the discipline couplings. An adaptive sequential Monte Carlo sampling-based technique is used to efficiently search the combinatorial model space of different discipline couplings. Finally, an algorithm for optimal model selection is presented and combined with three tractable approaches to quantify the accuracy of the system outputs with approximate couplings. These algorithms are applied to identify the important discipline couplings in three engineering problems: a fire detection satellite model, a turbine engine cycle analysis model, and a lifting surface aero-structural model. / by Ricardo Miguel Santos Baptista. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2014. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 93-100). / The growing use of autonomous underwater vehicles and underwater gliders for a variety of applications gives rise to new requirements in the operation of these vehicles. One such important requirement is optimization of energy required for undertaking missions that will enable longer endurance and lower operational costs. Our goal in this thesis is to develop a computationally efficient, and rigorous methodology that can predict energy-optimal paths from among all time-optimal paths to complete an underwater mission. For this, we develop rigorous a new stochastic Dynamically Orthogonal Level Set optimization methodology. In our thesis, after a review of existing path planning methodologies with a focus on energy optimality, we present the background of time-optimal path planning using the level set method. We then lay out the questions that inspired the present thesis, provide the goal of the current work and explain an extension of the time-optimal path planning methodology to the time-optimal path planning in the case of variable nominal engine thrust. We then proceed to state the problem statement formally. Thereafter, we develop the new methodology for solving the optimization problem through stochastic optimization and derive new Dynamically Orthogonal Level Set Field equations. We then carefully present different approaches to handle the non-polynomial non-linearity in the stochastic Level Set Hamilton-Jacobi equations and also discuss the computational efficiency of the algorithm. We then illustrate the inner-workings and nuances of our new stochastic DO level set energy optimal path planning algorithm through two simple, yet important, canonical steady flows that simulate a stead front and a steady eddy. We formulate a double energy-time minimization to obtain a semi-analytical energy optimal path for the steady front crossing test case and compare the results to these of our stochastic DO level set scheme. We then apply our methodology to an idealized ocean simulation using Double Gyre flows, and finally show an application with real ocean data for completing a mission in the Middle Atlantic Bight and New Jersey Shelf/Hudson Canyon region. / by Deepak Narayanan Subramani. / 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. 131-137). / IGCC with CO2 capture offers an exciting approach for cleanly using abundant coal reserves of the world to generate electricity. The present state-of-the-art synthesis gas (syngas) cleanup technologies in IGCC involve cooling the syngas from gasifier to room temperature or lower for removing Sulfur, Carbon dioxide and Mercury, leading to a large efficiency loss. It is therefore important to develop processes that remove these impurities from syngas at an optimally high temperature in order to maximize the energy efficiency of an IGCC plant. The high temperature advanced syngas cleanup technologies are presently at various stages of development and it is still not clear which technology and configuration of IGCC process would be most energetically efficient. In this thesis, I present a framework to assess the suitability of various candidate syngas cleanup technologies by developing computational simulations of these processes which are used in conjunction with Aspen Plus® to design various IGCC flowsheet configurations. In particular, we evaluate the use of membranes and sorbents for CO2 separation and capture from hot syngas in IGCC, as a substitute to solutionbased absorption processes. We present a multi-stage model for CO2 separation from multi-component gas mixtures using polymeric membranes based on the solutiondiffusion transport mechanism. A numerical simulation of H2 separation from syngas using Pd-alloy based composite metallic membranes is implemented to assess their performance for CO2 sequestration. / (cont.) In addition, we develop an equilibrium-based combined pressure and temperature swing adsorption-desorption model to estimate the amount of energy required for capturing pollutants using regenerable sorbent beds. We use our models with Aspen Plus® simulations to identify optimum design and operating conditions for membrane and adsorption processes in an IGCC plant. Furthermore, we identify from our simulations desired thermodynamic properties of sorbents and material properties of membranes that are needed to make these technologies work successfully at IGCC conditions. This should serve to provide an appropriate direction and target for ongoing experimental efforts in developing these novel materials. / by Kshitij Prakash. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2011. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 101-104). / The objective of this thesis is to examine trends in Offshore Support Vessel (OSV) design and determine the future characteristics of OSVs based on industry insight and supply chain models. Specifically, this thesis focuses on Platform Supply Vessels (PSVs) and the advantages of certain design characteristics are analyzed by modeling representative offshore exploration and production scenarios and selecting support vessels to minimize costs while meeting supply requirements. A review of current industry practices and literature suggests that offshore exploration and production activities will move into deeper water further from shore and as a result supply requirements will increase significantly. A review of the current fleet and orderbook reveal an aging fleet of traditional vessels with little deepwater capabilities and a growing, young fleet of advanced vessels capable of deepwater support. A single-vessel supply chain analysis shows that traditional vessels outperform larger vessels for shallow-water resupply activities, while modern vessels and vessels significantly larger than modern vessels are more cost-effective for deepwater operations. As offshore oilfield supply is more complicated than a single vessel supplying a single platform, we develop a mixed integer linear program model of the fleet selection process and implement it on representative offshore exploration and production scenarios. The model is used to evaluate the cost-effectiveness of representative vessels and the value of flexibility in vessel design for the oilfield operator. Incorporating industry insight into the results from the supply chain analyses, this study concludes that a) offshore exploration and production will move further offshore into deeper water, b) OSVs will become significantly larger both in response to the increased cargo need as well as to meet upcoming regulations, c) crew transfer will continue to be done primarily by helicopter, d) OSVs will become significantly more fuel efficient, e) high-specification, flexible OSV designs will continue to be built, and f) major oil companies will focus on safety and redundancy in OSV designs. / by Robin Sebastian Koske Rose. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / Includes bibliographical references (p. 67-68). / Forest operations planning is a complex decision process which considers multiple objectives on the strategic, tactical and operational horizons. Decisions such as where to harvest and in what order over different time periods are just some of the many diverse and complex decisions that are needed to be made. An important issue in real-world optimization of forest harvesting planning is how to treat uncertainty of a biological nature, namely the uncertainty due to different growth rates of trees which affects their respective yields. Another important issue is in the effective use of high capital intensive forest harvesting machinery by suitable routing and scheduling assignments. The focus of this thesis is to investigate the effects of incorporating the robust formulation and a machinery assignment problem collectively to a forest harvesting model. The amount of variability in the harvest yield can be measured by sampling from historical data and suitable protection against uncertainty can be set after incorporating the use of a suitable robust formulation. A trade off between robustness to uncertainty with the deterioration in the objective value ensues. Using models based on industrial and slightly modified data, both the robust and routing formulations have been shown to affect the solution and its underlying structure thus making them necessary considerations. A study of feasibility using Monte Carlo simulation is then undertaken to evaluate the difference in average performances of the formulations as well as to obtain a method of setting the required protections with an acceptable probability of infeasibility under a given set of scenarios. / by Lui Cheng, Lim. / S.M.