Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2016. / 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 204-209). / Modern business decisions exceed human decision making ability: often, they are of a large scale, their outcomes are uncertain, and they are made in multiple stages. At the same time, firms have increasing access to data and models. Faced with such complex decisions and increasing access to data and models, how do we transform data and models into effective decisions? In this thesis, we address this question in the context of four important problems: the dynamic control of large-scale stochastic systems, the design of product lines under uncertainty, the selection of an assortment from historical transaction data and the design of a personalized assortment policy from data. In the first chapter, we propose a new solution method for a general class of Markov decision processes (MDPs) called decomposable MDPs. We propose a novel linear optimization formulation that exploits the decomposable nature of the problem data to obtain a heuristic for the true problem. We show that the formulation is theoretically stronger than alternative proposals and provide numerical evidence for its strength in multi-armed bandit problems. In the second chapter, we consider to how to make strategic product line decisions under uncertainty in the underlying choice model. We propose a method based on robust optimization for addressing both parameter uncertainty and structural uncertainty. We show using a real conjoint data set the benefits of our approach over the traditional approach that assumes both the model structure and the model parameters are known precisely. In the third chapter, we propose a new two-step method for transforming limited customer transaction data into effective assortment decisions. The approach involves estimating a ranking-based choice model by solving a large-scale linear optimization problem, and solving a mixed-integer optimization problem to obtain a decision. Using synthetic data, we show that the approach is scalable, leads to accurate predictions and effective decisions that outperform alternative parametric and non-parametric approaches. In the last chapter, we consider how to leverage auxiliary customer data to make personalized assortment decisions. We develop a simple method based on recursive partitioning that segments customers using their attributes and show that it improves on a "uniform" approach that ignores auxiliary customer information. / by Velibor V. Mišić. / Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2008. / Includes bibliographical references (p. 125-129). / Annual influenza outbreaks incur great expenses in both human and monetary terms, and billions of dollars are being allocated for influenza pandemic preparedness in an attempt to avert even greater potential losses. Vaccination is a primary weapon for fighting influenza outbreaks. The influenza vaccine supply chain has characteristics that resemble the Newsvendor problem, but possesses several characteristics that distinguish it from many other supply chains. Differences include a nonlinear value of sales (caused by the nonlinear health benefits of vaccination that are due to infection dynamics) and vaccine production yield issues. In this thesis we present two models in the interface of operations and supply chain management and public health policy. In the first model, we focus on a supply chain with a government and a manufacturer. We show that production risks, taken currently by the vaccine manufacturer, lead to an insufficient supply of vaccine. Several supply contracts that coordinate buyer (governmental public health service) and supplier (vaccine manufacturer) incentives in many other industrial supply chains can not fully coordinate the influenza vaccine supply chain. We design a variant of the cost sharing contract and show that it provides incentives to both parties so that the supply chain achieves global optimization and hence improves the supply of vaccines. In the second mode, we consider the influenza vaccine supply chain with multiple countries. / (cont.) Each government purchases and administers vaccines in order to achieve an efficient cost-benefit tradeoff. Typically different countries have different economics sensitivities to public outcomes of infection and vaccination. It turns out that the initiating country, while having a significant role in the spread of the disease, does not receive enough vaccine stockpiles. Our model indicates that lack of coordination results in vaccine shortfalls in the most needed countries and vaccine excess in the regions where are not as effective, if the governments in the model act rationally. We show the role of contracts to modify monetary flows that purchase vaccination programs, and therefore modify infectious disease flows. / by Hamed Mamani. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2003. / Includes bibliographical references (p. 127-130). / Traditional inventory models focus on effective replenishment strategies and typically assume that a commodity's price is exogenously determined. In recent years, however, a number of industries have used innovative pricing strategies to manage their inventory effectively. These developments call for models that integrate inventory control and pricing strategies. Such models are clearly important not only in the retail industry, where price-dependent demand plays an important role, but also in manufacturing environments in which production/distribution decisions can be complemented with pricing strategies to improve the firm's bottom line. To date, the literature has confined itself mainly to models with variable ordering costs but no fixed costs. Extending some of these models to include a fixed cost component is the main focus of this thesis. In this thesis, we start by analyzing a single product, periodic review joint inventory control and pricing model, and characterizing the structure of the optimal policy under various conditions. Specifically, for the finite horizon periodic review case, we show, by employing the classical k-convexity concept, that a simple policy, called (s, S, p), is optimal when the demand functions are additive. For the model with more general demand functions, we show that an (s, S, p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-convex functions, and apply it to provide a characterization of the optimal policy. Surprisingly, in the infinite horizon periodic review case, the concept of symmetric k-convex functions allows us to show that a stationary (s, S, p) policy is optimal for both discounted and average profit models even for general demand functions. / (cont.) Our approach developed for the infinite horizon periodic review joint inventory control and pricing problem is then extended to a corresponding continuous review model. In this case, we prove that a stationary (s, S, p) policy is optimal under fairly general assumptions. Finally, the symmetric k-convexity concept developed in this thesis is employed to characterize the optimal policy for the stochastic cash balance problem. / by Xin Chen. / Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 163-166). / Data mining is a versatile and expanding field of study. We show the applications and uses of a variety of techniques in two very different realms: Emergency department (ED) length of stay prediction and visual analytics. For the ED, we investigate three data mining techniques to predict a patient's length of stay based solely on the information available at the patient's arrival. We achieve good predictive power using Decision Tree Analysis. Our results show that by using main characteristics about the patient, such as chief complaint, age, time of day of the arrival, and the condition of the ED, we can predict overall patient length of stay to specific hourly ranges with an accuracy of 80%. For visual analytics, we demonstrate how to mathematically determine the optimal number of clusters for a geospatial dataset containing both numeric and categorical data and then how to compare each cluster to the entire dataset as well as consider pairwise differences. We then incorporate our analytical methodology in visual display. Our results show that we can quickly and effectively measure differences between clusters and we can accurately find the optimal number of clusters in non-noisy datasets. / by Ashley M. Snyder. / S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007. / Includes bibliographical references (p. 139-150). / Investors commonly use stopping rules to help them get in and out of their investment positions. Despite their widespread use and support from behavioral finance, there has been little discussion of their impact on portfolio performance in classic portfolio choice theory. In this thesis, I remedy this situation by discussing the performance impact of stopping rules, highlighting the stop-loss rule. Stop-loss rules-predetermined policies that reduce a portfolio's exposure after reaching a certain threshold of cumulative losses-are commonly used by retail and institutional investors to manage the risks of their investments, but have also been viewed with some skepticism by critics who question their efficacy. I develop a simple framework for measuring the impact of stop-loss rules on the expected return and volatility of an arbitrary portfolio strategy, and derive conditions under which stop-loss rules add or subtract value to that portfolio strategy. I show that under the Random Walk Hypothesis, simple 0/1 stop-loss rules always decrease a strategy's expected return, but in the presence of momentum, stop-loss rules can add value. To illustrate the practical relevance of this framework, / (cont.) I provide an empirical analysis of a stop-loss policy applied to a buy-and-hold strategy in U.S. equities, where the stop-loss asset is U.S. long-term government bonds. Using monthly returns data from January 1950 to December 2004, I find that certain stop-loss rules add 50 to 100 basis points per month to the buy-and-hold portfolio during stop-out periods. By computing performance measures for several price processes, including a new regime-switching model that implies periodic "flights-to-quality," I provide a possible explanation for our empirical results and connections to the behavioral finance literature. Consistent with the traditional investor's problem, I discuss a generalization of this approach to general stopping rules, which are superimposed on arbitrary portfolio strategies. I define a stopping utility premium and discuss how uncertainty about the true stochastic process can explain a potential value added or value lost by the use of stopping rules in practice. / by Kathryn Margaret Kaminski. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 169-174). / This thesis studies the price of anarchy in supply chains, congested systems and joint ventures. It consists of three main parts. In the first part, we investigate the impact of imperfect competition with nonlinear demand. We focus on a distribution channel with a single supplier and multiple downstream retailers. To evaluate the performance, we consider several metrics, including market penetration, total profit, social welfare and rent extraction. We quantify the performance with tight upper and lower bounds. We show that with substitutes, while competition improves the efficiency of a decentralized supply chain, the asymmetry among the retailers deteriorates the performance. The reverse happens when retailers carry complements. We also show that efficiency of a supply chain with concave (convex) demand is higher (lower) than that with affine demand. The second part of the thesis studies the impact of congestion in an oligopoly by incorporating convex costs. Costs could be fully self-contained or have a spillover component, which depends on others' output. We show that when costs are fully self-contained, the welfare loss in an oligopoly is at most 25% of the social optimum, even in the presence of highly convex costs. With spillover cost, the performance of an oligopoly depends on the relative magnitude of spillover cost to the marginal benefit to consumers. In particular, when spillover cost outweighs the marginal benefit, the welfare loss could be arbitrarily bad. The third part of the thesis focuses on capacity planning with resource pooling in joint ventures under demand uncertainties. We distinguish heterogeneous and homogeneous resource pooling. When resources are heterogeneous, the effective capacity in a joint venture is constrained by the minimum individual contribution. We show that there exists a unique constant marginal revenue sharing scheme which induces the same outcome in a Nash equilibrium, Nash Bargaining and the system optimum. The optimal scheme rewards every participant proportionally with respect to his marginal cost. When resources are homogeneous, we show that the revenue sharing ratio should be inversely proportional to a participant's marginal cost. / by Wei Sun. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 185-188). / Maintenance scheduling is an integral part of many complex systems. For instance, without effective maintenance scheduling, the combined effects of preventative and corrective maintenance can have severe impacts on the availability of those systems. Based on current Air Force trends including maintenance manpower, dispersed aircraft basing, and increased complexity, there has been a renewed focus on preventative maintenance. To address these concerns, this thesis develops two models for preventative maintenance scheduling for complex systems, the first of interest in the system concept development and design phase, and the second of interest during operations. Both models are highly complex and intractable to solve in their original forms. For the first model, we develop approximation algorithms that yield high quality and easily implementable solutions. To address the second model, we propose a decomposition strategy that produces submodels that can be solved via existing algorithms or via specialized algorithms we develop. While much of the literature has examined stochastically failing systems, preventative maintenance of usage limited systems has received less attention. Of particular interest is the design of modular systems whose components must be repaired/replaced to prevent a failure. By making cost tradeoffs early in development, program managers, designers, engineers, and test conductors can better balance the up front costs associated with system design and testing with the long term cost of maintenance. To facilitate such a tradeoff, the Modular Maintenance Scheduling Problem provides a framework for design teams to evaluate different design and operations concepts and then evaluate the long term costs. While the general Modular Maintenance Scheduling Problem does not require maintenance schedules with specific structure, operational considerations push us to consider cyclic schedules in which components are maintained at a fixed frequency. In order to efficiently find cyclic schedules, we propose the Cycle Rounding algorithm, which has an approximation guarantee of 2, and a family of Shifted Power-of-Two algorithms, which have an approximation guarantee of 1/ ln(2) ~ 1.4427. Computational results indicate that both algorithms perform much better than their associated performance guarantees providing solutions within 15%-25% of a lower bound. Once a modular system has moved into operations, manpower and transportation scheduling become important considerations when developing maintenance schedules. To address the operations phase, we develop the Modular Maintenance and System Assembly Model to balance the tradeoffs between inventory, maintenance capacity, and transportation resources. This model explicitly captures the risk-pooling effects of a central repair facility while also modeling the interaction between repair actions at such a facility. The full model is intractable for all but the smallest instances. Accordingly, we decompose the problem into two parts, the system assembly portion and module repair portion. Finally, we tie together the Modular Maintenance and System Assembly Model with key concepts from the Modular Maintenance Scheduling Problem to propose an integrated methodology for design and operation. / by Eric Jack Zarybnisky. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2003. / Includes bibliographical references (p. 89-90). / The World Health Organization (WHO) is responsible for making annual vaccine strains recommendation to countries around the globe. However, various studies have found that the WHO vaccine selection strategy has not been effective in some years. This motivates the search for a better strategy for choosing vaccine strains. In this work, we use recent results from theoretical immunology to formulate the vaccine selection problem as a discrete-time stochastic dynamic program with a high-dimensional continuous state space. We discuss the techniques that were developed for solving this difficult dynamic program, and present an effective and robust heuristic policy. We compare the performance of the heuristic policy, the follow policy, and the no-vaccine policy and show that the heuristic policy is the best among the three. After taking the cost of implementation into account, however, we conclude that the WHO policy is a cost-effective influenza vaccine strain selection policy. / by Joseph T. Wu. / Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2017. / 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 159-166). / This thesis is concerned with the design and analysis of new algorithms for sequential optimization problems with limited feedback on the outcomes of alternatives when the environment is not perfectly known in advance and may react to past decisions. Depending on the setting, we take either a worst-case approach, which protects against a fully adversarial environment, or a hindsight approach, which adapts to the level of adversariality by measuring performance in terms of a quantity known as regret. First, we study stochastic shortest path problems with a deadline imposed at the destination when the objective is to minimize a risk function of the lateness. To capture distributional ambiguity, we assume that the arc travel times are only known through confidence intervals on some statistics and we design efficient algorithms minimizing the worst-case risk function. Second, we study the minimax achievable regret in the online convex optimization framework when the loss function is piecewise linear. We show that the curvature of the decision maker's decision set has a major impact on the growth rate of the minimax regret with respect to the time horizon. Specifically, the rate is always square root when the set is a polyhedron while it can be logarithmic when the set is strongly curved. Third, we study the Bandits with Knapsacks framework, a recent extension to the standard Multi-Armed Bandit framework capturing resource consumption. We extend the methodology developed for the original problem and design algorithms with regret bounds that are logarithmic in the initial endowments of resources in several important cases that cover many practical applications such as bid optimization in online advertising auctions. Fourth, we study more specifically the problem of repeated bidding in online advertising auctions when some side information (e.g. browser cookies) is available ahead of submitting a bid. Optimizing the bids is modeled as a contextual Bandits with Knapsacks problem with a continuum of arms. We design efficient algorithms with regret bounds that scale as square root of the initial budget. / by Arthur Flajolet. / Ph. D.

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 1999. / Includes bibliographical references (leaves 107-111). / We develop various algorithms for solving mixed integer-quadratic problems. These problems exhibit exponential complexity resulting from the presence of integer variables. Traditional approaches that apply in pure integer programming are not very helpful, since the existence of continuous variables in our problems complicates their use. Vie develop relaxation and heuristic algorithms designed so as to provide tight lower and upper bounds to the optimal solution of the mixed combinatorial problem. In some cases the obtained range, in which the optimum lies, is small enough to be considered satisfactory by itself. This has been accomplished in problems with up to 150 variables. Exact algorithms have also been developed and guarantee the optimal solution upon termination. The idea of Branch and Bound enhanced with the use of lower and upper bounds obtained with the aforementioned methods is implemented for that purpose. Problems with up to 70 variables have been solved. Our ideas and algorithms are applied to the Problem of Index and Portfolio Replication with a limited number of assets. This problem arises in Finance, but, in its more general form, can find application in various areas ranging from Statistics to Optimal Control and Manufacturing. / by Constantine Nikolaos Tziligakis. / S.M.