Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007. / Includes bibliographical references (p. 93-94). / A new approach is proposed for finding all solutions of systems of nonlinear equations with bound constraints. The zero finding problem is converted to a global optimization problem whose global minima with zero objective value, if any, correspond to all solutions of the initial problem. A branch-and-bound algorithm is used with McCormick's nonsmooth convex relaxations to generate lower bounds. An inclusion relation between the solution set of the relaxed problem and that of the original non-convex problem is established which motivates a method to generate automatically reasonably close starting points for a local Newton-type method. A damped-Newton method with natural level functions employing the restrictive monotonicity test is employed to find solutions robustly and rapidly. Due to the special structure of the objective function, the solution of the convex lower bounding problem yields a nonsmooth root exclusion test which is found to perform better than earlier interval based exclusion tests. The Krawczyk operator based root inclusion and exclusion tests are also embedded in the proposed algorithm to refine the variable bounds for efficient fathoming of the search space. The performance of the algorithm on a variety of test problems from the literature is presented and for most of them the first solution is found at the first iteration of the algorithm due to the good starting point generation. / by Vinay Kumar. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. / Includes bibliographical references (leaf 95). / In this thesis, we present a modification of an existing methodology to obtain a hierarchy of lower and upper bounds on moments of solutions of linear differential equations. The motivation for change is to obtain tighter bounds by solving smaller semidefinite problems. The modification we propose involves partitioning the domain and normalizing each partition to ensure numerical stability. Using the adjoint operator, linear constraints involving the boundary conditions and moments of the solution are developed for each partition. Semidefinite constraints are imposed on the moments, and an optimization problem is solved to obtain the bounds. We have demonstrated the algorithm by calculating bounds on moments of various one-dimensional case differential equations including the Bessel ODE, and Legendre polynomials. In the two-dimensional case we have demonstrated the algorithm by calculating bounds on various PDEs including the Helmholtz equation, and heat equation. In both cases, the results were encouraging with tighter bounds on moments being obtained by solving smaller problems with domain partitioning. / by Sandeep Sethuraman. / 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. 79-82). / We study the use of inverse and robust optimization to address two problems in transportation: finding the travel times and designing a transportation network. We assume that users choose the route selfishly and the flow will eventually reach an equilibrium state (User Equilibrium). The first part of the thesis demonstrates how inverse and robust optimization can be used to find the actual travel times given a stable flow on the network and some noisy information on travel times from different users. We model the users' perception of travel times using three different sets and solve the robust inverse problem for all of them. We also extend the idea to find parametric functional forms for travel times given historical data. Our numerical results illustrate the significant improvement obtained by our models over a simple fitting model. The second part of the thesis considers the network design problem under demand uncertainty. We show that for affine travel time functions, the deterministic problem can be formulated as a mixed integer programming problem with quadratic objective and linear constraints. For the robust network design problem, we propose a decomposition scheme: breaking a tri-level programming problem into two smaller problems and re-iterating until a good solution is obtained. To deal with the expensive computation required by large networks, we also propose a heuristic robust simulated annealing approach. The heuristic algorithm is computationally tractable and provides some encouragingly results in our simulations. / by Thai Dung Nguyen. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 81-82). / This dissertation examines retweeting activities as the information spreading function of Twitter. First, we investigated what kind of features of a tweet help to get retweets. We construct a model that describes peoples' decision making on retweets, and with related observation, we show that more retweeted tweets get retweeted more. In terms of specific features of tweets, it has been shown that the number of followers and the number of retweets are positively correlated, and hashtags attract more retweets than the tweets without hashtags. On the other hand, we also found that including hashtags and getting one or more retweets are statistically independent. Moreover, we showed including URLs or user-mentions in tweets and getting one or more retweets are statistically independent. In our results, including a picture is slightly effective to get this sense of retweetability. Second, we compare the retweeters of tweets including a picture and only text, especially focusing on distance from the original tweeters. Comparing the ratio of retweets by followers of the author of the original tweets among the initial 50 retweets, tweets with a picture have a slightly lower ratio, though there is no significant difference between the average for tweets with pictures and without pictures at the 95% significance level. We also investigate how many retweets are posted by users in followers' network connected to the original tweeter, and show that the depths of retweeters' network for tweets with picture have larger variance than that of tweets without pictures. This result implies that a tweet including picture can reach more people than a tweet without a picture potentially. / by Tomoaki Sakamoto. / 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. 69-70). / The purpose of this project is to incorporate a Poisson disease model into the Spatiotemporal Epidemiological Modeler (STEM) and visualize the disease spread on Google Earth. It is done through developing a Poisson disease model plug-in using the Eclipse Modeling Framework (EMF), a modeling framework and code generation facility for building tools and other applications based on a structured data model. The project consists of two stages. First, it develops a disease model plug-in of a Poisson disease model of a homogenous population, which is built as an extension of the implemented SI disease model in the STEM. Next, it proposes an algorithm to port a Poisson disease model of a heterogeneous population into the STEM. The development of the two new diseases plugins explores the maximum compatibility of the STEM and sets model for potential users to flexibly construct their own disease model for simulation. / by Hui Zhang. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 144-146). / As cities evolve in size and complexity, their component systems become more interconnected. Comprehensive modeling and simulation is needed to capture interactions and correctly assess the impact of changes. This thesis presents a methodology for modeling cities from a systems of systems perspective. The framework supplies general modeling guidelines and key steps. Also addressed are the importance of stakeholder interactions, creating the model structure, using smart city sensor data, and applying the methodology to larger, traditional cities. As an initial step, four city modeling including CityNet, CityOne, Sim City 4, and SoSAT software programs were evaluated from both a user and mathematical perspective. From the assessments, a list was developed of features critical to successful city modeling software including visualization, a streamlined user interface, accurate mathematics, the ability to specify systems and attributes, and the ability to model interconnections between systems. SoSAT was selected as the modeling tool for the case study, which involved modeling the Army's Base Camp Integration Laboratory. A model of the camp's baseline configuration was built and the camp was simulated for 30 days with results recorded at one hour intervals. 100 trials were run with averaged results presented by time intervals and for the total simulation time. Results were presented at all levels of structural aggregation. Two sensitivity analyses were conducted to analyze the impact of maintenance personnel and the frequency of potable water deliveries. Adding or subtracting a maintenance person impacted the availability of the generator systems that were being serviced, in turn impacting the performance of the micro grid. Extending the time between deliveries by 24 and 48 hours revealed two systems experienced resource depletions. Lastly, two technology insertions cases were conducted to assess the impact of adding a laundry water reuse system (LWRS) and a solar powered hot water heater (SHWH). The LWRS provided 70% of the laundry system's water needs, significantly reducing dependency upon deliveries. The SHWH was expected to decrease electricity consumption and increase fuel consumption. However, the reduction in energy demand meant fewer generators were needed to power the micro grid and both electricity and fuel consumption decreased. / by Amanda M. Wachtel. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / Includes bibliographical references (p. 93-94). / It is important for companies to manage their revenues and -reduce their costs efficiently. These goals can be achieved through effective pricing and inventory control strategies. This thesis studies a joint multi-period pricing and inventory control problem for a make-to-stock manufacturing system. Multiple products are produced under shared production capacity over a finite time horizon. The demand for each product is a function of the prices and no back orders are allowed. Inventory and production costs are linear functions of the levels of inventory and production, respectively. In this thesis, we introduce an iterative gradient-based algorithm. A key idea is that given a demand realization, the cost minimization part of the problem becomes a linear transportation problem. Given this idea, if we knew the optimal demand, we could solve the production problem efficiently. At each iteration of the algorithm, given a demand vector we solve a linear transportation problem and use its dual variables in order to solve a quadratic optimization problem that optimizes the revenue part and generates a new pricing policy. We illustrate computationally that this algorithm obtains the optimal production and pricing policy over the finite time horizon efficiently. The computational experiments in this thesis use a wide range of simulated data. The results show that the algorithm we study in this thesis indeed computes the optimal solution for the joint pricing and inventory control problem and is efficient as compared to solving a reformulation of the problem directly using commercial software. The algorithm proposed in this thesis solves large scale problems and can handle a wide range of nonlinear demand functions. / by Tingting Rao. / 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. 83-85). / This thesis proposes a decentralized reward-based incentive mechanism to address the problem of noncomplying subsidiaries when the parent company wish to meet its targeted energy consumption level. Besides its effectiveness in ensuring compliance, the proposed mechanism is advantageous as it is able to induce the optimal subsidiary behavior that maximizes the company profit given a carefully chosen reward allocation scheme. In addition, when the company is willing to trade part of its profit for an operationally simple mechanism, simple uniform allocation scheme is highly effective when the subsidiaries exhibit certain degree of symmetry. The results above are drawn from our investigation on a more general model: Cournot competition under a joint constraint. For this model, we study the equilibrium behavior under free competition and compare the profit and total surplus achieved with the corresponding values when different levels of coordination are introduced in the market (i.e., the Monopoly market and the society-wide coordinated market). We establish tight upper bounds for the profit and total surplus loss due to lack of coordination as functions of various market characteristics (i.e., number of firms, intensity of competition and asymmetry between firms). / by Jingxi Wang. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / Includes bibliographical references (p. 89-92). / The semiconductor industry is an exciting and challenging industry. Strong demand at the application end, plus the high capital intensity and rapid technological innovation in manufacturing, makes it difficult to manage supply chain planning and investment in technology transitions. Better understanding the essence of the industry dynamics will help firms win competitive advantages in this turbulent market. In this thesis, we will study semiconductor industry dynamics from three different angles: quantitative modeling, industry dynamics simulation, and strategic analysis. First, we develop a stochastic linear optimization model to address the supplier's "order fulfillment dilemma" suggested by previous empirical studies. The model provides optimal equipment production decisions that minimize the total cost under stochastic demand. To solve the large scale problem, we introduce the Bender's Decomposition, which is proven to outperform the pure Simplex method. Furthermore, we extend the basic model to multiple periods, allowing equipment inventory planning over a period of time. Second, we build a macro-level industry dynamic model using the methodology of System Dynamics. The model includes components of electronics demand projection, fabrication capacity allocation, fabrication cost structure, technology roadmapping as well as equipment production and R&D. The model generates projections of demand , industry productivity, schedule of building new fabrication, adoption of the latest process technology, etc., which are validated by actual industry data. In addition, we devise a control panel in the software that enables the users to implement flexible scenario and sensitivity analysis. Third, we propose a strategic framework for companies to pinpoint the root causes of the supply-demand mismatch problem. / (cont.) This framework considers long lead times, fast clockspeeds, Moore's Law, and risky product and technology, which transitions contribute to the pronounced volatility amplification occurring in the semiconductor industry. This framework, along with several industry successful practices, will assist companies to mitigate the demand volatility and improve their supply chain performance. / by Kailiang Wu. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007. / Includes bibliographical references (p. 67-68). / Transportation procurement is one of the most critical sourcing decisions to be made in many companies. This thesis addresses a real-life industrial problem of creating package bids for a company's transportation procurement auction. The purpose of offering package bids is to increase the carriers' capacity and to improve the reliability of services. In this thesis, we investigate the possibility of forming packages using the company's own distribution network. Effective distribution of packages requires balanced cycles. A balanced cycle is a cycle containing no more than 3 nodes with equal loads (or volume of package) on every link in the cycle. We develop mixed-integer programs to find the maximum amount of network volume that can be covered by well-balanced cycles. These models are deterministic models that provide a rough guide on the optimal way of package formation when loads are known in advance. Since demand is random in real life, we perform a stochastic analysis of the problem using various techniques including simulation, probabilistic analysis and stochastic programming. Results from the stochastic analysis show that the effectiveness of package distribution depends on how we allocate the volumes on the lanes to create balanced cycles. If we always assign a fixed proportion of the lanes' volumes to the cycles, then it is only possible to have well-balanced cycles when the average volumes on the lanes are very large, validating the advantage of joint bids between several companies. However, if we assign a different proportion of the lanes' volumes to the cycles each time demand changes, then it is possible to create cycles that are balanced most of the time. An approximated solution method is provided to obtain a set of balanced cycles that can be bid out. / by Qian Wang. / S.M.