Operations Research - Ph.D. / Sc.D.
http://hdl.handle.net/1721.1/7719
2016-06-29T00:15:39ZStochastic analysis via robust optimization
http://hdl.handle.net/1721.1/103246
Stochastic analysis via robust optimization
Youssef, Nataly
To evaluate the performance and optimize systems under uncertainty, two main avenues have been suggested in the literature: stochastic analysis and optimization describing the uncertainty probabilistically and robust optimization describing the uncertainty deterministically. Instead, we propose a novel paradigm which leverages the conclusions of probability theory and the tractability of the robust optimization approach to approximate and optimize the expected behavior in a given system. Our framework models the uncertainty via polyhedral sets inspired by the limit laws of probability. We characterize the uncertainty sets by variability parameters that we treat as random variables. We then devise a methodology to approximate and optimize the average performance of the system via a robust optimization formulation. Our framework (a) avoids the challenges of fitting probability distributions to the uncertain variables, (b) eliminates the need to generate scenarios to describe the states of randomness, and (c) demonstrates the use of robust optimization to evaluate and optimize expected performance. We illustrate the applicability of our methodology to analyze the performance of queueing networks and optimize the inventory policy for supply chain networks. In Part I, we study the case of a single queue. We develop a robust theory to study multi-server queues with possibly heavy-tailed primitives. Our methodology (a) provides approximations that match the diffusion approximations for light-tailed queues in heavy traffic, and (b) extends the framework to analyze the transient behavior of heavy-tailed queues. In Part II, we study the case of a network of queues. Our methodology provides accurate approximations of (a) the expected steady-state behavior in generalized queueing networks, and (b) the expected transient behavior in feedforward queueing networks. Our approach achieves significant computational tractability and provides accurate approximations relative to simulated values. In Part III, we study the case of a supply chain network. Our methodology (a) obtains optimal base-stock levels that match the optimal solutions obtained via stochastic optimization, (b) yields optimal affine policies which oftentimes exhibit better results compared to optimal base-stock policies, and (c) provides optimal policies that consistently outperform the solutions obtained via the traditional robust optimization approach.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2016.; Cataloged from student-submitted PDF version of thesis.; Includes bibliographical references (pages 167-174).
2016-01-01T00:00:00ZApplications of optimal portfolio management
http://hdl.handle.net/1721.1/101292
Applications of optimal portfolio management
Bisias, Dimitrios
This thesis revolves around applications of optimal portfolio theory. In the first essay, we study the optimal portfolio allocation among convergence trades and mean reversion trading strategies for a risk averse investor who faces Value-at-Risk and collateral constraints with and without fear of model misspecification. We investigate the properties of the optimal trading strategy, when the investor fully trusts his model dynamics. Subsequently, we investigate how the optimal trading strategy of the investor changes when he mistrusts the model. In particular, we assume that the investor believes that the data will come from an unknown member of a set of unspecified alternative models near his approximating model. The investor believes that his model is a pretty good approximation in the sense that the relative entropy of the alternative models with respect to his nominal model is small. Concern about model misspecification leads the investor to choose a robust optimal portfolio allocation that works well over that set of alternative models. In the second essay, we study how portfolio theory can be used as a framework for making biomedical funding allocation decisions focusing on the National Institutes of Health (NIH). Prioritizing research efforts is analogous to managing an investment portfolio. In both cases, there are competing opportunities to invest limited resources, and expected returns, risk, correlations, and the cost of lost opportunities are important factors in determining the return of those investments. Can we apply portfolio theory as a systematic framework of making biomedical funding allocation decisions? Does NIH manage its research risk in an efficient way? What are the challenges and limitations of portfolio theory as a way of making biomedical funding allocation decisions? Finally in the third essay, we investigate how risk constraints in portfolio optimization and fear of model misspecification affect the statistical properties of the market returns. Risk sensitive regulation has become the cornerstone of international financial regulations. How does this kind of regulation affect the statistical properties of the financial market? Does it affect the risk premium of the market? What about the volatility or the liquidity of the market?
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2015.; 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 (pages 183-188).
2015-01-01T00:00:00ZPricing for retail, social networks and green technologies
http://hdl.handle.net/1721.1/101291
Pricing for retail, social networks and green technologies
Cohen, Maxime C
What is the right price to charge your customers? Many retailers and researchers are facing this question. In the last three decades, tremendous progress was made, both in the academic and business worlds. In this thesis, we investigate four novel pricing applications. In the first part, we study the promotion optimization problem for supermarket retailers. One needs to decide which products to promote, the depth of price discounts and when to schedule the promotions. To capture the stockpiling behavior of consumers, we propose two general classes of demand functions that can be easily estimated from data. We then develop an approximation that allows us to solve the problem efficiently and derive analytical results on its accuracy. The second part is motivated by the ubiquity of social networking platforms. We consider a setting where a monopolist sells an indivisible good to consumers embedded in a social network. First, the firm designs prices to maximize its profits. Subsequently, consumers choose whether to purchase the item or not. Assuming positive externalities, we show the existence of a pure Nash equilibrium. Using duality theory and integer programming techniques, we reformulate the problem into a linear mixed-integer program. We then derive efficient ways of optimally solving the problem for discriminative and uniform pricing strategies. The third part considers the problem of pricing a product for which demand information is very limited. We impose minimal assumptions on the problem: that is, only the constant marginal cost and the maximal price the firm can set are known. We propose a simple way of pricing the product by approximating the true inverse demand by a linear function. Surprisingly, we show that this approximation yields a good profit performance for a wide range of demand curves. In the final part, we consider green technology products such as electric vehicles. We propose a Stackelberg model where the government offers consumer subsidies in order to encourage the technology adoption, whereas the supplier decides price and production to maximize profits. We address the question: How does demand uncertainty affect the government, the industry and the consumers, when designing policies.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2015.; 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.
2015-01-01T00:00:00ZAnalytics for Improved Cancer Screening and Treatment
http://hdl.handle.net/1721.1/101290
Analytics for Improved Cancer Screening and Treatment
Silberholz, John
Cancer is a leading cause of death both in the United States and worldwide. In this thesis we use machine learning and optimization to identify effective treatments for advanced cancers and to identify effective screening strategies for detecting early-stage disease. In Part I, we propose a methodology for designing combination drug therapies for advanced cancer, evaluating our approach using advanced gastric cancer. First, we build a database of 414 clinical trials testing chemotherapy regimens for this cancer, extracting information about patient demographics, study characteristics, chemotherapy regimens tested, and outcomes. We use this database to build statistical models to predict trial efficacy and toxicity outcomes. We propose models that use machine learning and optimization to suggest regimens to be tested in Phase II and III clinical trials, evaluating our suggestions with both simulated outcomes and the outcomes of clinical trials testing similar regimens. In Part II, we evaluate how well the methodology from Part I generalizes to advanced breast cancer. We build a database of 1,490 clinical trials testing drug therapies for breast cancer, train statistical models to predict trial efficacy and toxicity outcomes, and suggest combination drug therapies to be tested in Phase II and III studies. In this work we model differences in drug effects based on the receptor status of patients in a clinical trial, and we evaluate whether combining clinical trial databases of different cancers can improve clinical trial toxicity predictions. In Part III, we propose a methodology for decision making when multiple mathematical models have been proposed for a phenomenon of interest, using our approach to identify effective population screening strategies for prostate cancer. We implement three published mathematical models of prostate cancer screening strategy outcomes, using optimization to identify strategies that all models find to be effective.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2015.; 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 (pages 139-156).
2015-01-01T00:00:00Z