Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2016. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 153-157). / With the advances in information technology and the increased availability of data, new approaches that integrate learning and decision making have emerged in operations management. The learning-and-optimizing approaches can be used when the decision maker is faced with incomplete information in a dynamic environment. We first consider a network revenue management problem where a retailer aims to maximize revenue from multiple products with limited inventory constraints. The retailer does not know the exact demand distribution at each price and must learn the distribution from sales data. We propose a dynamic learning and pricing algorithm, which builds upon the Thompson sampling algorithm used for multi-armed bandit problems by incorporating inventory constraints. Our algorithm proves to have both strong theoretical performance guarantees as well as promising numerical performance results when compared to other algorithms developed for similar settings. We next consider a dynamic pricing problem for a single product where the demand curve is not known a priori. Motivated by business constraints that prevent sellers from conducting extensive price experimentation, we assume a model where the seller is allowed to make a bounded number of price changes during the selling period. We propose a pricing policy that incurs the smallest possible regret up to a constant factor. In addition to the theoretical results, we describe an implementation at Groupon, a large e-commerce marketplace for daily deals. The field study shows significant impact on revenue and bookings. Finally, we study a supply chain risk management problem. We propose a hybrid strategy that uses both process flexibility and inventory to mitigate risks. The interplay between process flexibility and inventory is modeled as a two-stage robust optimization problem: In the first stage, the firm allocates inventory, and in the second stage, after disruption strikes, the firm schedules its production using process flexibility to minimize demand shortage. By taking advantage of the structure of the second stage problem, we develop a delayed constraint generation algorithm that can efficiently solve the two-stage robust optimization problem. Our analysis of this model provides important insights regarding the impact of process flexibility on total inventory level and inventory allocation pattern. / by He Wang. / Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004. / Includes bibliographical references (p. 169-171). / We propose new methodologies in robust optimization that promise greater tractability, both theoretically and practically than the classical robust framework. We cover a broad range of mathematical optimization problems, including linear optimization (LP), quadratic constrained quadratic optimization (QCQP), general conic optimization including second order cone programming (SOCP) and semidefinite optimization (SDP), mixed integer optimization (MIP), network flows and 0 - 1 discrete optimization. Our approach allows the modeler to vary the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, while keeping the problem tractable. Specifically, for LP, MIP, SOCP, SDP, our approaches retain the same complexity class as the original model. The robust QCQP becomes a SOCP, which is computationally as attractive as the nominal problem. In network flows, we propose an algorithm for solving the robust minimum cost flow problem in polynomial number of nominal minimum cost flow problems in a modified network. For 0 - 1 discrete optimization problem with cost uncertainty, the robust counterpart of a polynomially solvable 0 - 1 discrete optimization problem remains polynomially solvable and the robust counterpart of an NP-hard o-approximable 0-1 discrete optimization problem, remains a-approximable. / (cont.) Under an ellipsoidal uncertainty set, we show that the robust problem retains the complexity of the nominal problem when the data is uncorrelated and identically distributed. For uncorrelated, but not identically distributed data, we propose an approximation method that solves the robust problem within arbitrary accuracy. We also propose a Frank-Wolfe type algorithm for this case, which we prove converges to a locally optimal solution, and in computational experiments is remarkably effective. / by Melvyn Sim. / Ph.D.

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). / 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? / by Dimitrios Bisias. / Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2018. / 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 217-226). / For the past 30 years, decision tree methods have been one of the most widely-used approaches in machine learning across industry and academia, due in large part to their interpretability. However, this interpretability comes at a price--the performance of classical decision tree methods is typically not competitive with state-of-the-art methods like random forests and gradient boosted trees. A key limitation of classical decision tree methods is their use of a greedy heuristic for training. The tree is therefore constructed one locally-optimal split at a time, and so the final tree as a whole may be far from global optimality. Motivated by the increase in performance of mixed-integer optimization methods over the last 30 years, we formulate the problem of constructing the optimal decision tree using discrete optimization, allowing us to construct the entire decision tree in a single step and hence find the single tree that best minimizes the training error. We develop high-performance local search methods that allow us to efficiently solve this problem and find optimal decision trees with both parallel (axes-aligned) and hyperplane splits. We show that our approach using modern optimization results in decision trees that improve significantly upon classical decision tree methods. In particular, across a suite of synthetic and real-world classification and regression examples, our methods perform similarly to random forests and boosted trees whilst maintaining the interpretability advantage of a single decision tree, thus alleviating the need to choose between performance and interpretability. We also adapt our approach to the problem of prescription, where the goal is to make optimal prescriptions for each observation. While constructing the tree, our method simultaneously infers the unknown counterfactuals in the data and learns to make optimal prescriptions. This results in a decision tree that optimizes both the predictive and prescriptive error, and delivers an interpretable solution that offers significant improvements upon the existing state-of-the-art in prescriptive problems. / by Jack William Dunn. / Ph. D.

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010. / Page 170 blank. Cataloged from PDF version of thesis. / Includes bibliographical references (p. 167-169). / The emergence of less restricted fare structures in the airline industry reduced the capability of airlines to segment demand through restrictions such as Saturday night minimum stay, advance purchase, non-refundability, and cancellation fees. As a result, new forecasting techniques such as Hybrid Forecasting and optimization methods such as Fare Adjustment were developed to account for passenger willingness-to- pay. This thesis explores statistical methods for estimating sell-up, or the likelihood of a passenger to purchase a higher fare class than they originally intended, based solely on historical booking data available in revenue management databases. Due to the inherent sparseness of sell-up data over the booking period, sell-up estimation is often difficult to perform on a per-market basis. On the other hand, estimating sell-up over an entire airline network creates estimates that are too broad and over-generalized. We apply the K-Means clustering algorithm to cluster markets with similar sell-up estimates in an attempt to address this problem, creating a middle ground between system-wide and per-market sell-up estimation. This thesis also formally introduces a new regression-based forecasting method known as Rational Choice. Rational Choice Forecasting creates passenger type categories based on potential willingness-to-pay levels and the lowest open fare class. Using this information, sell-up is accounted for within the passenger type categories, making Rational Choice Forecasting less complex than Hybrid Forecasting. This thesis uses the Passenger Origin-Destination Simulator to analyze the impact of these forecasting and sell-up methods in a controlled, competitive airline environment. The simulation results indicate that determining an appropriate level of market sell-up aggregation through clustering both increases revenue and generates sell-up estimates with a sufficient number of observations. In addition, the findings show that Hybrid Forecasting creates aggressive forecasts that result in more low fare class closures, leaving room for not only sell-up, but for recapture and spill-in passengers in higher fare classes. On the contrary, Rational Choice Forecasting, while simpler than Hybrid Forecasting with sell-up estimation, consistently generates lower revenues than Hybrid Forecasting (but still better than standard pick-up forecasting). To gain a better understanding of why different markets are grouped into different clusters, this thesis uses regression analysis to determine the relationship between a market's characteristics and its estimated sell-up rate. These results indicate that several market factors, in addition to the actual historical bookings, may predict to some degree passenger willingness-to-pay within a market. Consequently, this research illustrates the importance of passenger willingness-to-pay estimation and its relationship to forecasting in airline revenue management. / by Christopher A. Boyer. / S.M.

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). / 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. / by Nataly Youssef. / Ph. D.

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. / 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. / by Maxime C. Cohen. / Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2009. / 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. 137-140). / This thesis studies the learning problem of a set of agents connected via a general social network. We address the question of how dispersed information spreads in social networks and whether the information is efficiently aggregated in large societies. The models developed in this thesis allow us to study the learning behavior of rational agents embedded in complex networks. We analyze the perfect Bayesian equilibrium of a dynamic game where each agent sequentially receives a signal about an underlying state of the world, observes the past actions of a stochastically-generated neighborhood of individuals, and chooses one of two possible actions. The stochastic process generating the neighborhoods defines the network topology (social network). We characterize equilibria for arbitrary stochastic and deterministic social networks and characterize the conditions under which there will be asymptotic learning -- that is, the conditions under which, as the social network becomes large, the decisions of the individuals converge (in probability) to the right action. We show that when private beliefs are unbounded (meaning that the implied likelihood ratios are unbounded), there will be asymptotic learning as long as there is some minimal amount of expansion in observations. This result therefore establishes that, with unbounded private beliefs, there will be asymptotic learning in almost all reasonable social networks. Furthermore, we provide bounds on the speed of learning for some common network topologies. We also analyze when learning occurs when the private beliefs are bounded. / (cont.) We show that asymptotic learning does not occur in many classes of network topologies, but, surprisingly, it happens in a family of stochastic networks that has infinitely many agents observing the actions of neighbors that are not sufficiently persuasive. Finally, we characterize equilibria in a generalized environment with heterogeneity of preferences and show that, contrary to a nave intuition, greater diversity (heterogeneity) 3 facilitates asymptotic learning when agents observe the full history of past actions. In contrast, we show that heterogeneity of preferences hinders information aggregation when each agent observes only the action of a single neighbor. / by Ilan Lobel. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004. / Includes bibliographical references (p. 103-107). / In the first part of the thesis we combine ideas from cutting plane and interior point methods to solve variational inequality problems efficiently. In particular, we introduce "smarter" cuts into two general methods for solving these problems. These cuts utilize second order information on the problem through the use of a gap function. We establish convergence results for both methods, as well as complexity results for one of the methods. Finally, we compare the performance of an approach that combines affine scaling and cutting plane methods with other methods for solving variational inequalities. The second part of the thesis considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multi-period environment. At each period the retailer places orders to the suppliers in response to the prices and capacities they announce. Our model allows the retailer to carry inventory. Furthermore, suppliers can expand their capacity at an additional cost; the retailer faces exogenous, price-dependent, stochastic demand. We analyze discrete as well as continuous time versions of the model: (i) we illustrate the existence of equilibrium policies; (ii) we characterize the structure of these policies; (iii) we consider coordination mechanisms; and (iv) we present some computational results. We also consider a modified model that uses option contracts and finally present some extensions. / by Marina Zaretsky. / Ph.D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2002. / Includes bibliographical references (p. 137-141). / An important issue in real-world optimization problems is how to treat uncertain coefficients. Robust optimization is a modeling methodology that takes a deterministic view: the optimal solution is required to remain feasible for any realization of the uncertain coefficients within prescribed uncertainty sets. The focus of this thesis is on robust linear programming problems in which the uncertainty sets are polytopes. The assumption of polyhedral uncertainty leads to compact, efficiently solvable linear formulations. In the first part of the thesis, we study special types of polyhedral uncertainty sets that allow for incorporating moment information about the distribution of the uncertain coefficients, and for controlling the tradeoff between robustness and optimality. We provide probabilistic guarantees on the feasibility of optimal solutions obtained with such uncertainty sets for any realization of the uncertain coefficients. We then illustrate the versatility of robust polyhedral formulations by studying three financial applications: single period portfolio optimization, multiperiod portfolio management, and credit risk estimation. In the area of single period portfolio optimization, we propose ways of modeling inaccuracy in parameter estimates, and explore the benefits of robust optimal strategies through computational experiments with the statistical estimation of a particular measure of portfolio risk - sample shortfall. We emphasize the advantages of linear, as opposed to nonlinear, robust formulations in large portfolio problems with integrality constraints. / (cont.) In the area of multiperiod portfolio management, we propose robust polyhedral formulations that use some minimal information about long-term direction of movement of asset returns to make informed decisions about portfolio rebalancing over the short term. The suggested formulations allow for including considerations of transaction costs and taxes while keeping the dimension of the problem low. In the area of credit risk estimation, we propose a model for estimating the survival probability distribution and the fair prices of credit risky bonds from market prices of similar credit risky securities. We address the issue of uncertainty in key parameters of the model, such as discount factors, by using robust optimization modeling. We also suggest a method for classification of credit risky bonds based on integer programming techniques. / by Dessislava A. Pachamanova. / Ph.D.