Operations Research - Ph.D. / Sc.D.
http://hdl.handle.net/1721.1/7719
Wed, 10 Dec 2014 03:46:07 GMT2014-12-10T03:46:07ZStochastic models and data driven simulations for healthcare operations
http://hdl.handle.net/1721.1/92055
Stochastic models and data driven simulations for healthcare operations
Anderson, Ross Michael
This thesis considers problems in two areas in the healthcare operations: Kidney Paired Donation (KPD) and scheduling medical residents in hospitals. In both areas, we explore the implications of policy change through high fidelity simulations. We then build stochastic models to provide strategic insight into how policy decisions affect the operations of these healthcare systems. KPD programs enable patients with living but incompatible donors (referred to as patient-donor pairs) to exchange kidneys with other such pairs in a centrally organized clearing house. Exchanges involving two or more pairs are performed by arranging the pairs in a cycle, where the donor from each pair gives to the patient from the next pair. Alternatively, a so called altruistic donor can be used to initiate a chain of transplants through many pairs, ending on a patient without a willing donor. In recent years, the use of chains has become pervasive in KPD, with chains now accounting for the majority of KPD transplants performed in the United States. A major focus of our work is to understand why long chains have become the dominant method of exchange in KPD, and how to best integrate their use into exchange programs. In particular, we are interested in policies that KPD programs use to determine which exchanges to perform, which we refer to as matching policies. First, we devise a new algorithm using integer programming to maximize the number of transplants performed on a fixed pool of patients, demonstrating that matching policies which must solve this problem are implementable. Second, we evaluate the long run implications of various matching policies, both through high fidelity simulations and analytic models. Most importantly, we find that: (1) using long chains results in more transplants and reduced waiting time, and (2) the policy of maximizing the number of transplants performed each day is as good as any batching policy. Our theoretical results are based on introducing a novel model of a dynamically evolving random graph. The analysis of this model uses classical techniques from Erdos-Renyi random graph theory as well as tools from queueing theory including Lyapunov functions and Little's Law. In the second half of this thesis, we consider the problem of how hospitals should design schedules for their medical residents. These schedules must have capacity to treat all incoming patients, provide quality care, and comply with regulations restricting shift lengths. In 2011, the Accreditation Council for Graduate Medical Education (ACGME) instituted a new set of regulations on duty hours that restrict shift lengths for medical residents. We consider two operational questions for hospitals in light of these new regulations: will there be sufficient staff to admit all incoming patients, and how will the continuity of patient care be affected, particularly in a first day of a patients hospital stay, when such continuity is critical? To address these questions, we built a discrete event simulation tool using historical data from a major academic hospital, and compared several policies relying on both long and short shifts. The simulation tool was used to inform staffing level decisions at the hospital, which was transitioning away from long shifts. Use of the tool led to the following strategic insights. We found that schedules based on shorter more frequent shifts actually led to a larger admitting capacity. At the same time, such schedules generally reduce the continuity of care by most metrics when the departments operate at normal loads. However, in departments which operate at the critical capacity regime, we found that even the continuity of care improved in some metrics for schedules based on shorter shifts, due to a reduction in the use of overtime doctors. We develop an analytically tractable queueing model to capture these insights. The analysis of this model requires analyzing the steady-state behavior of the fluid limit of a queueing system, and proving a so called "interchange of limits" result.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2014.; 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 251-257).
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/1721.1/920552014-01-01T00:00:00ZData-driven models for uncertainty and behavior
http://hdl.handle.net/1721.1/91301
Data-driven models for uncertainty and behavior
Gupta, Vishal, Ph. D. Massachusetts Institute of Technology
The last decade has seen an explosion in the availability of data. In this thesis, we propose new techniques to leverage these data to tractably model uncertainty and behavior. Specifically, this thesis consists of three parts: In the first part, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using hypothesis testing. The approach is flexible and widely applicable, and robust optimization problems built from our new data driven sets are computationally tractable, both theoretically and practically. Optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee. Computational evidence from classical applications of robust optimization { queuing and portfolio management { confirm that our new data-driven sets significantly outperform traditional robust optimization techniques whenever data is available. In the second part, we examine in detail an application of the above technique to the unit commitment problem. Unit commitment is a large-scale, multistage optimization problem under uncertainty that is critical to power system operations. Using real data from the New England market, we illustrate how our proposed data-driven uncertainty sets can be used to build high-fidelity models of the demand for electricity, and that the resulting large-scale, mixed-integer adaptive optimization problems can be solved efficiently. With respect to this second contribution, we propose new data-driven solution techniques for this class of problems inspired by ideas from machine learning. Extensive historical back-testing confirms that our proposed approach generates high quality solutions that compare with state-of-the-art methods. In the third part, we focus on behavioral modeling. Utility maximization (single agent case) and equilibrium modeling (multi-agent case) are by far the most common behavioral models in operations research. By combining ideas from inverse optimization with the theory of variational inequalities, we develop an efficient, data-driven technique for estimating the primitives of these models. Our approach supports both parametric and nonparametric estimation through kernel learning. We prove that our estimators enjoy a strong generalization guarantee even when the model is misspecified. Finally, we present computational evidence from applications in economics and transportation science illustrating the effectiveness of our approach and its scalability to large-scale instances.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2014.; This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.; 117; Cataloged from student-submitted PDF version of thesis.; Includes bibliographical references (pages 173-180).
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/1721.1/913012014-01-01T00:00:00ZData-driven optimization and analytics for operations management applications
http://hdl.handle.net/1721.1/85695
Data-driven optimization and analytics for operations management applications
Uichanco, Joline Ann Villaranda
In this thesis, we study data-driven decision making in operation management contexts, with a focus on both theoretical and practical aspects. The first part of the thesis analyzes the well-known newsvendor model but under the assumption that, even though demand is stochastic, its probability distribution is not part of the input. Instead, the only information available is a set of independent samples drawn from the demand distribution. We analyze the well-known sample average approximation (SAA) approach, and obtain new tight analytical bounds on the accuracy of the SAA solution. Unlike previous work, these bounds match the empirical performance of SAA observed in extensive computational experiments. Our analysis reveals that a distribution's weighted mean spread (WMS) impacts SAA accuracy. Furthermore, we are able to derive distribution parametric free bound on SAA accuracy for log-concave distributions through an innovative optimization-based analysis which minimizes WMS over the distribution family. In the second part of the thesis, we use spread information to introduce new families of demand distributions under the minimax regret framework. We propose order policies that require only a distribution's mean and spread information. These policies have several attractive properties. First, they take the form of simple closed-form expressions. Second, we can quantify an upper bound on the resulting regret. Third, under an environment of high profit margins, they are provably near-optimal under mild technical assumptions on the failure rate of the demand distribution. And finally, the information that they require is easy to estimate with data. We show in extensive numerical simulations that when profit margins are high, even if the information in our policy is estimated from (sometimes few) samples, they often manage to capture at least 99% of the optimal expected profit. The third part of the thesis describes both applied and analytical work in collaboration with a large multi-state gas utility. We address a major operational resource allocation problem in which some of the jobs are scheduled and known in advance, and some are unpredictable and have to be addressed as they appear. We employ a novel decomposition approach that solves the problem in two phases. The first is a job scheduling phase, where regular jobs are scheduled over a time horizon. The second is a crew assignment phase, which assigns jobs to maintenance crews under a stochastic number of future emergencies. We propose heuristics for both phases using linear programming relaxation and list scheduling. Using our models, we develop a decision support tool for the utility which is currently being piloted in one of the company's sites. Based on the utility's data, we project that the tool will result in 55% reduction in overtime hours.
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 163-166).
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/1721.1/856952013-01-01T00:00:00ZEmission regulations in the electricity market : an analysis from consumers, producers and central planner perspectives
http://hdl.handle.net/1721.1/84716
Emission regulations in the electricity market : an analysis from consumers, producers and central planner perspectives
Figueroa Rodriguez, Cristian Ricardo
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.
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).
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/1721.1/847162013-01-01T00:00:00Z