Thesis: S.M., 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 87-89). / Predicting outcomes for critically ill patients is a topic of considerable interest. The most widely used models utilize data from early in a patient's stay to predict risk of death. While research has shown that use of daily information, including trends in key variables, can improve predictions of patient prognosis, this problem is challenging as the number of variables that must be considered is large and increasingly complex modeling techniques are required. The objective of this thesis is to build a mortality prediction system that improves upon current approaches. We aim to do this in two ways: 1. By incorporating a wider range of variables, including time-dependent features 2. By exploring different predictive modeling techniques beyond standard regression We identify three promising approaches: a random forest model, a best subset regression containing just five variables, and a novel approach called the Univariate Flagging Algorithm (UFA). In this thesis, we show that all three methods significantly outperform a widely-used mortality prediction approach, the Sequential Organ Failure Assessment (SOFA) score. However, we assert that UFA in particular is well-suited for predicting mortality in critical care. It can detect optimal cut-points in data, easily scales to a large number of variables, is easy to interpret, is capable of predicting rare events, and is robust to noise and missing data. As such, we believe it is a valuable step toward individual patient survival estimates. / by Mallory Sheth. / S.M.

Thesis (S.M. in Operations Research)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013. / 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 67-71). / Since chemotherapy began as a treatment for cancer in the 1940s, cancer drug development has become a multi-billion dollar industry. Combination chemotherapy remains the leading treatment for advanced cancers, and cancer drug research and clinical trials are enormous expenses for pharmaceutical companies and the government. We propose an analytics approach for the analysis and design of clinical trials that can discover drug combinations with significant improvements in survival and toxicity. We first build a comprehensive database of clinical trials. We then use this database to develop statistical models from earlier trials that are capable of predicting the survival and toxicity of new combinations of drugs. Then, using these statistical models, we develop optimization models that select novel treatment regimens that could be tested in clinical trials, based on the totality of data available on existing combinations. We present evidence for advanced gastric and gastroesophageal cancers that the proposed analytics approach a) leads to accurate predictions of survival and toxicity outcomes of clinical trials as long as the drugs used have been seen before in different combinations, b) suggests novel treatment regimens that balance survival and toxicity and take into account the uncertainty in our predictions, and c) outperforms the trials run by the average oncologist to give survival improvements of several months. Ultimately, our analytics approach offers promise for improving life expectancy and quality of life for cancer patients at low cost. / by Stephen L. Relyea. / S.M.in Operations Research

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013. / 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 119-122). / In the first part of this thesis, the objective is to identify optimal bidding strategies in the wholesale electricity market. We consider asymmetric producers submitting bids to a system operator. The system operator allocates demand via a single clearing price auction. The highest accepted bid sets the per unit market price payed by consumers. We find a pure Nash equilibrium to the bidding strategies of asymmetric producers unattainable in a symmetric model. Our results show that producers with relatively large capacities are able to exercise market power. However, the market may seem competitive due to the large number of producers serving demand. The objective of the second part of the thesis, is to compare two regulation policies: a fixed transfer price, such as tax regulation, and a permit system, such as cap-and-trade. For this purpose, we analyze an economy where risk neutral manufacturers satisfy price sensitive demand. The objective of the regulation established by the central planner is to achieve an external objective, e.g. reduce pollution or limit consumption of scarce resource. When demand is uncertain, designing these regulations to achieve the same expected level of the external objective results in the same expected consumer price but very different manufacturers' expected profit and central planner revenue. For instance, our results show that when the firms are price takers, the manufacturers with the worst technology always prefer a tax policy. Interestingly, we identify conditions under which the manufacturers with the cleanest technology benefit from higher expected profit as tax rate increases. In the third part of the thesis, we investigate the impact labeling decisions have on the supply chain. We consider a two stage supply chain consisting of a supplier and a retailer. Demand is considered stochastic, decreasing in price and increasing in a quality parameter, e.g. carbon emissions. The unit production cost for the supplier is increasing in the quality level chosen. We identify two different contracts that maximize the efficiency of the supply chain while allowing the different parties to achieve their objectives individually. / by Cristian Ricardo Figueroa Rodriguez. / Ph.D.

Thesis: S.M., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 187-193). / In the Organisation for Economic Co-operation and Development (OECD) area, the production of numerical solid waste (MI\SW) increased by 32% between 1990 and 2011, exceeding 660 million tonnes in 2011; the world-wide production of waste is estimated to grow further due to increasing GDP in developing economies. Given this scenario, effective treatment and recovery of wastes becomes a priority. In developed countries, MSW is usually sent to materials recovery facilities (MRFs), which use mechanical and manual sorting units to extract valuable components. In this work, we define a network flow model to represent a MRF that sorts wastes using multi-output units with recirculating streams. For each material in the system, we define a matrix to describe the sorting process. We then formulate a genetic algorithm (GA) that generates alternative configurations of a MRF having a given set of sorting units with known separation parameters and selects those with highest profit and efficiency. The GA incorporates a heuristic for personnel allocation to manual units. We code the algorithm in Java and apply it to an existing MRF. The results show a 33.4% improvement in profit and a 1.7% improvement in efficiency with respect to the current configuration without hand sorting; and a 6.7% improvement in profit and a 3.9% improvement il efficiency, with respect to the current configuration with hand sorting. / by Mariapaola Testa. / S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2006. / Includes bibliographical references (p. 149-154). / Buyout options allow bidders to instantly purchase at a specified price an item listed for sale through an online auction. A temporary buyout option disappears once a regular bid above the reserve price is made, while a permanent option remains available until it is exercised or the auction ends. Buyout options are widely used in online auctions and have significant economic importance: nearly half of the auctions today are listed with a buyout price and the option is exercised in nearly one fourth of them. We formulate a game-theoretic model featuring time-sensitive bidders with independent private valuations and Poisson arrivals but endogenous bidding times in order to answer the following questions: How should buyout prices be set in order to maximize the seller's discounted revenue? What are the relative benefits of using each type of buyout option? While all existing buyout options we are aware of currently rely on a static buyout price (i.e. with a constant value), what is the potential benefit associated with using instead a dynamic buyout price that varies as the auction progresses? / (cont.) For all buyout option types we exhibit a Nash equilibrium in bidder strategies, argue that this equilibrium constitutes a plausible outcome prediction, and study the problem of maximizing the corresponding seller revenue. In particular, the equilibrium strategy in all cases is such that a bidder exercises the buyout option provided it is still available and his valuation is above a time-dependent threshold. Our numerical experiments suggest that a seller may significantly increase his utility by introducing a buyout option when any of the participants are time-sensitive. Furthermore, while permanent buyout options yield higher predicted revenue than temporary options, they also provide additional incentives for late bidding and may therefore not be always more desirable. The numerical results also imply that the increase in seller's utility (over a fixed buyout price auction) enabled by a dynamic buyout price is small and does not seem to justify the corresponding increase in complexity. / by Shobhit Gupta. / Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 87). / As our technology continues to increase, our military wishes to reduce the risk service members endure by using unmanned vehicles. These unmanned vehicles will, over time, become more independent and trustworthy in our operational military. The goal of this thesis is to improve the intelligence an unmanned vehicle has in its decision making to keep up with ever increasing capabilities. In this thesis, we assume an Unmanned Underwater Vehicle (UUV) is given tasks and must decide which ones to perform (or not perform) in which order. If there is enough time and energy to perform all of the tasks, then the UUV only needs to solve a traveling salesman problem to find the best order. We focus on a tightly constrained situation, where the UUV must choose which tasks to perform to collect the highest reward. In prize collecting traveling salesman problems, authors are often dismissive about stochastic problem parameters, and are satisfied with using expected value of random variables. In this thesis a more rigorous probabilistic model is formulated which establishes a guaranteed confidence level for the probability the UUV breaks mission critical time and energy constraints. The formulation developed takes the stochasticity of the problem parameters into account and produces solutions which are robust. The thesis first presents a linear programming problem which calculates the transition probabilities for a specific route. This linear programming problem is then used to create a constraint which forces the UUV to choose a route that maintains an appropriate confidence level for satisfying the time and energy constraints. Once the exact model is created, heuristics are discussed and analyzed. The heuristics are designed to provide "good"' solutions for larger sized problems and maintain a relatively low run time. / by Jacob Roy Cates. / S.M.

Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 147-150). / The goal of this thesis is to describe, model, and optimize reverse logistics systems commonly used in the Consumer Electronics industry. The context and motivation for this work stem from a collaboration with an industrial partner, a Fortune 500 company that sells consumer electronics and is one of the top retailers in its sector. The thesis is divided into three parts. In the first part of the thesis we model and analyze the problem of forecasting failures of new products. When a new device is introduced to the market there is limited information available about its failure time distribution since most devices have yet to fail. However, there is extensive failure time data for prior devices, as well as evidence that the failure time distribution for new devices can be forecast from the data for prior devices. In this setting, we propose two strategies for forecasting the failure distribution of new products that leverages the censored failure observations for the new devices as well as this massive amount of data collected for prior devices. We validate these strategies using data from our industrial partner and using data from a social enterprise located in the Boston area. The second part of the thesis concerns inventory management in a reverse logistics system that supports the warranty returns and replacement for a consumer electronic device. This system is a closed-loop supply chain since failed devices are refurbished and are kept in inventory to be used as replacement devices or are sold through a side-sales channel. Furthermore, managing inventory in this system is challenging due to the short life-cycle of this type of device and the rapidly declining value for the inventory that could potentially be sold. We propose a stochastic model that captures the dynamics of inventory of this system, including the limited life-cycle and the declining value of inventory that can be sold off. We characterize the structure of the optimal policy for this problem. In addition, we introduce two heuristics: (i) a certainty-equivalent approximation, which leads to a simple closed form policy; and (ii) a dual balancing heuristic, which results in a more tractable newsvendor type model. We also develop a robust version of this model in order to obtain bounds for the overall performance of the system. The performance of these heuristics is analyzed using data from our industrial partner. The final part of the thesis concerns the problem faced by a consumer electronics retailer when matching devices in inventory to customers. More specifically, we analyze a setting where there are two warranties in place: (i) the consumer warranty, offered by the retailer to the consumer, and (ii) the Original Equipment Manufacturer (OEM) warranty, offered by the OEM to the retailer. Both warranties are valid for a limited period (usually 12 months), and once warranties expire, the coverage to replace or repair a faulty device ends. Thus, a customer does not receive a replacement if he/she is out of consumer warranty, and the retailer cannot send the device to the OEM for repairs if it is out of OEM warranty. The retailer would ideally like to have the two warranties for a device being matched, i.e., the customer would have the same time left in his consumer warranty as the device would have left in the OEM warranty. A mismatch between these warranties can incur costs to the retailer beyond the usual processing costs of warranty requests. Namely, since a device can fail multiple times during its lifecycle the replacement device sent to customers that file warranty requests can lead to out-of-OEM-warranty returns. In order to mitigate the number of out-of-OEM-warranty returns, we propose an online algorithm to match customers that have filed warranty claims to refurbished devices in inventory. The algorithm matches the oldest devices in inventory to the oldest customers in each period. We characterize the competitive ratio of this algorithm and, through numerical experiments using historical data, demonstrate that it can significantly reduce out of warranty returns compared to our partner's current strategy. / by Andre du Pin Calmon. / Ph. D.

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013. / 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 105-107). / This thesis considers the tactical reconnaissance asset allocation problem in military operations. Specifically this thesis presents methods to optimize, under uncertain conditions, tactical reconnaissance asset allocation in order to maximize, within acceptable levels of asset risk exposure, the expected total information collection value. We propose a deterministic integer optimization formulation and two robust mixed-integer optimization extensions to address this problem. Robustness is applied to our model using both polyhedral and ellipsoidal uncertainty sets resulting in tractable mixed integer linear and second order cone problems. We show through experimentation that robust optimization leads to overall improvements in solution quality compared to non-robust and typical human generated plans. Additionally we show that by using our robust models, military planners can ensure better solution feasibility compared to non-robust planning methods even if they seriously misjudge their knowledge of the enemy and the battlefield. We also compare the trade-offs of using polyhedral and ellipsoidal uncertainty sets. In our tests our model using ellipsoidal uncertainty sets provided better quality solutions at a cost of longer average solution times to that of the polyhedral uncertainty set model. Lastly we outline a special case of our models that allows us to improve solution time at the cost of some solution quality. / by David M. Culver. / S.M.

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. 189-193). / This thesis addresses the design and analysis of resource allocation policies in largescale stochastic systems, motivated by examples such as the Internet, cloud facilities, wireless networks, etc. A canonical framework for modeling many such systems is provided by "stochastic processing networks" (SPN) (Harrison [28, 29]). In this context, the key operational challenge is efficient and timely resource allocation. We consider two important classes of SPNs: switched networks and bandwidth-sharing networks. Switched networks are constrained queueing models that have been used successfully to describe the detailed packet-level dynamics in systems such as input-queued switches and wireless networks. Bandwidth-sharing networks have primarily been used to capture the long-term behavior of the flow-level dynamics in the Internet. In this thesis, we develop novel methods to analyze the performance of existing resource allocation policies, and we design new policies that achieve provably good performance. First, we study performance properties of so-called Maximum-Weight-[alpha] (MW-[alpha]) policies in switched networks, and of a-fair policies in bandwidth-sharing networks, both of which are well-known families of resource allocation policies, parametrized by a positive parameter [alpha] > 0. We study both their transient properties as well as their steady-state behavior. In switched networks, under a MW-a policy with a 2 1, we obtain bounds on the maximum queue size over a given time horizon, by means of a maximal inequality derived from the standard Lyapunov drift condition. As a corollary, we establish the full state space collapse property when [alpha] > 1. In the steady-state regime, for any [alpha] >/= 0, we obtain explicit exponential tail bounds on the queue sizes, by relying on a norm-like Lyapunov function, different from the standard Lyapunov function used in the literature. Methods and results are largely parallel for bandwidth-sharing networks. Under an a-fair policy with [alpha] >/= 1, we obtain bounds on the maximum number of flows in the network over a given time horizon, and hence establish the full state space collapse property when [alpha] >/= 1. In the steady-state regime, using again a norm-like Lyapunov function, we obtain explicit exponential tail bounds on the number of flows, for any a > 0. As a corollary, we establish the validity of the diffusion approximation developed by Kang et al. [32], in steady state, for the case [alpha] = 1. Second, we consider the design of resource allocation policies in switched networks. At a high level, the central performance questions of interest are: what is the optimal scaling behavior of policies in large-scale systems, and how can we achieve it? More specifically, in the context of general switched networks, we provide a new class of online policies, inspired by the classical insensitivity theory for product-form queueing networks, which admits explicit performance bounds. These policies achieve optimal queue-size scaling, in the conventional heavy-traffic regime, for a class of switched networks, thus settling a conjecture (documented in [51]) on queue-size scaling in input-queued switches. In the particular context of input-queued switches, we consider the scaling behavior of queue sizes, as a function of the port number n and the load factor [rho]. In particular, we consider the special case of uniform arrival rates, and we focus on the regime where [rho] = 1 - 1/f(n), with f(n) >/= n. We provide a new class of policies under which the long-run average total queue size scales as O(n1.5 -f(n) log f(n)). As a corollary, when f(n) = n, the long-run average total queue size scales as O(n2.5 log n). This is a substantial improvement upon prior works [44], [52], [48], [39], where the same quantity scales as O(n3 ) (ignoring logarithmic dependence on n). / by Yuan Zhong. / Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005. / Includes bibliographical references (p. 193-109). / We propose a robust optimization approach to analyzing three distinct classes of problems related to the notion of equilibrium: the nominal variational inequality (VI) problem over a polyhedron, the finite game under payoff uncertainty, and the network design problem under demand uncertainty. In the first part of the thesis, we demonstrate that the nominal VI problem is in fact a special instance of a robust constraint. Using this insight and duality-based proof techniques from robust optimization, we reformulate the VI problem over a polyhedron as a single- level (and many-times continuously differentiable) optimization problem. This reformulation applies even if the associated cost function has an asymmetric Jacobian matrix. We give sufficient conditions for the convexity of this reformulation and thereby identify a class of VIs, of which monotone affine (and possibly asymmetric) VIs are a special case, which may be solved using widely-available and commercial-grade convex optimization software. In the second part of the thesis, we propose a distribution-free model of incomplete- information games, in which the players use a robust optimization approach to contend with payoff uncertainty. / (cont.) Our "robust game" model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative, distribution-free equilibrium concept, for which, in contrast to ex post equilibria, existence is guaranteed. We show that computation of "robust-optimization equilibria" is analogous to that of Nash equilibria of complete- information games. Our results cover incomplete-information games either involving or not involving private information. In the third part of the thesis, we consider uncertainty on the part of a mechanism designer. Specifically, we present a novel, robust optimization model of the network design problem (NDP) under demand uncertainty and congestion effects, and under either system- optimal or user-optimal routing. We propose a corresponding branch and bound algorithm which comprises the first constructive use of the price of anarchy concept. In addition, we characterize conditions under which the robust NDP reduces to a less computationally demanding problem, either a nominal counterpart or a single-level quadratic optimization problem. Finally, we present a novel traffic "paradox," illustrating counterintuitive behavior of changes in cost relative to changes in demand. / by Michele Leslie Aghassi. / Ph.D.