Operations Research - Ph.D. / Sc.D.
http://hdl.handle.net/1721.1/7903
Thu, 23 Nov 2017 03:29:18 GMT2017-11-23T03:29:18ZNew applications in Revenue Management
http://hdl.handle.net/1721.1/112085
New applications in Revenue Management
Thraves Cortés-Monroy, Charles Mark
Revenue Management (RM) is an area with important advances in theory and practice in the last thirty years. This thesis presents three different new applications in RM with a focus on: the firms' perspective, the government's perspective as a policy maker, and the consumers' perspective (in terms of welfare). In this thesis, we first present a two-part tariff pricing problem faced by a satellite data provider. We estimate unobserved data with parametric density functions in order to generate instances of the problem. We propose a mixed integer programming formulation for pricing. As the problem is hard to solve, we propose heuristics that make use of the MIP formulation together with intrinsic properties of the problem. Furthermore, we contrast this approach with a dynamic programming approach. Both methodologies outperform the current pricing strategy of the satellite provider, even assuming misspecifications in the assumptions made. Subsequently, we study how the government can encourage green technology adoption through a rebate to consumers. We model this setting as a Stackleberg game where firms interact in a price-setting competing newsvendor problem where the government gives a rebate to consumers in the first stage. We show the trade-off between social welfare when the government decides an adoption target instead of a utilitarian objective. Then, we study the impact of competition and demand uncertainty on the three agents involved: firms, government, and consumers. This thesis recognizes the need to measure consumers' welfare for multiple items under demand uncertainty. As a result, this thesis builds on existing theory in order to incorporate demand uncertainty in Consumer Surplus. In many settings, produced quantities might not meet the realized demand at a given market price. This comes as an obstacle in the computation of consumer surplus. To address this, we define the concept of an allocation rule. In addition, we study the impact of uncertainty on consumers for different demand noise (additive and multiplicative) and for various allocation rules.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2017.; Cataloged from PDF version of thesis.; Includes bibliographical references.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1721.1/1120852017-01-01T00:00:00ZAdaptive optimization problems under uncertainty with limited feedback
http://hdl.handle.net/1721.1/112015
Adaptive optimization problems under uncertainty with limited feedback
Flajolet, Arthur
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.
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).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1721.1/1120152017-01-01T00:00:00ZCombinatorial structures in online and convex optimization
http://hdl.handle.net/1721.1/112014
Combinatorial structures in online and convex optimization
Gupta, Swati, Ph. D. Massachusetts Institute of Technology
Motivated by bottlenecks in algorithms across online and convex optimization, we consider three fundamental questions over combinatorial polytopes. First, we study the minimization of separable strictly convex functions over polyhedra. This problem is motivated by first-order optimization methods whose bottleneck relies on the minimization of a (often) separable, convex metric, known as the Bregman divergence. We provide a conceptually simple algorithm, Inc-Fix, in the case of submodular base polyhedra. For cardinality-based submodular polytopes, we show that Inc-Fix can be speeded up to be the state-of-the-art method for minimizing uniform divergences. We show that the running time of Inc-Fix is independent of the convexity parameters of the objective function. The second question is concerned with the complexity of the parametric line search problem in the extended submodular polytope P: starting from a point inside P, how far can one move along a given direction while maintaining feasibility. This problem arises as a bottleneck in many algorithmic applications like the above-mentioned Inc-Fix algorithm and variants of the Frank-Wolfe method. One of the most natural approaches is to use the discrete Newton's method, however, no upper bound on the number of iterations for this method was known. We show a quadratic bound resulting in a factor of n6 reduction in the worst-case running time from the previous state-of-the-art. The analysis leads to interesting extremal questions on set systems and submodular functions. Next, we develop a general framework to simulate the well-known multiplicative weights update algorithm for online linear optimization over combinatorial strategies U in time polynomial in log /U/, using efficient approximate general counting oracles. We further show that efficient counting over the vertex set of any 0/1 polytope P implies efficient convex minimization over P. As a byproduct of this result, we can approximately decompose any point in a 0/1 polytope into a product distribution over its vertices. Finally, we compare the applicability and limitations of the above results in the context of finding Nash-equilibria in combinatorial two-player zero-sum games with bilinear loss functions. We prove structural results that can be used to find certain Nash-equilibria with a single separable convex minimization.
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 157-163).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1721.1/1120142017-01-01T00:00:00ZA robust optimization approach to online problems
http://hdl.handle.net/1721.1/112013
A robust optimization approach to online problems
Korolko, Nikita (Nikita E.)
In this thesis, we consider online optimization problems that are characterized by incrementally revealed input data and sequential irrevocable decisions that must be made without complete knowledge of the future. We employ a combination of mixed integer optimization (MIO) and robust optimization (RO) methodologies in order to design new efficient online algorithms that outperform state-of-the-art methods for many important practical applications. We empirically demonstrate that RO-based algorithms are computationally tractable for instances of practical size, generate more cost-effective decisions and can simultaneously model a large class of similar online problems due to exceptional modeling power of MIO. In Part I, we consider the well-known K-server problem from the perspective of robust adaptive optimization. We propose a new tractable mixed integer linear formulation of the K-server problem that incorporates both information from the past and uncertainty about the future. By combining ideas from classical online algorithms developed in the computer science literature and robust and adaptive optimization developed in the operations research literature we propose a new method that (a) is computationally tractable, (b) almost always outperforms all other methods in numerical experiments, and (c) is stable with respect to potential errors in the assumptions about the future. In Part II, we consider several extensions of the asset-based weapon-to-target assignment problem whose objective is to protect ships in a fleet from incoming threats. We demonstrate that the new highly nonlinear MIO formulation (a) can be combined with lazy constraints techniques allowing the system designer to find optimal solutions in real time, (b) can be extended to the multi-period setting, and (c) admits a decentralized solution with limited loss of optimality. In Part III, we present a novel covariate-adaptive optimization algorithm for online allocation in clinical trials. The new approach leveraging MIO and RO techniques (a) guarantees a better between-group covariate balance in comparison with state-of- the-art methods, (b) yields statistical power at least as high as, and sometimes significantly higher than, randomization-based algorithms, and (c) is well protected against selection, investigator and accidental bias.
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 149-155).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/1721.1/1120132017-01-01T00:00:00Z