Operations Research Center
http://hdl.handle.net/1721.1/5066
2017-02-18T04:39:53ZMethods for convex optimization and statistical learning
http://hdl.handle.net/1721.1/106683
Methods for convex optimization and statistical learning
Grigas, Paul (Paul Edward)
We present several contributions at the interface of first-order methods for convex optimization and problems in statistical machine learning. In the first part of this thesis, we present new results for the Frank-Wolfe method, with a particular focus on: (i) novel computational guarantees that apply for any step-size sequence, (ii) a novel adjustment to the basic algorithm to better account for warm-start information, and (iii) extensions of the computational guarantees that hold in the presence of approximate subproblem and/or gradient computations. In the second part of the thesis, we present a unifying framework for interpreting "greedy" first-order methods -- namely Frank-Wolfe and greedy coordinate descent -- as instantiations of the dual averaging method of Nesterov, and we discuss the implications thereof. In the third part of the thesis, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal low-rank solutions for nuclear norm regularized matrix completion and, for more general problems, induces near-optimal "well-structured" solutions. We establish computational guarantees that trade off efficiency in computing near-optimal solutions with upper bounds on the rank of iterates. We then present extensive computational results that show significant computational advantages over existing related approaches, in terms of delivering low rank and low run-time to compute a target optimality gap. In the fourth part of the thesis, we analyze boosting algorithms in linear regression from the perspective modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression can be viewed as subgradient descent to minimize the maximum absolute correlation between features and residuals. We also propose a slightly modified boosting algorithm that yields an algorithm for the Lasso, and that computes the Lasso path. Our perspective leads to first-ever comprehensive computational guarantees for all of these boosting algorithms, which provide a precise theoretical description of the amount of data-fidelity and regularization imparted by running a boosting algorithm, for any dataset. In the fifth and final part of the thesis, we present several related results in the contexts of boosting algorithms for logistic regression and the AdaBoost algorithm.
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 219-225).
2016-01-01T00:00:00ZVelocity-based storage and stowage decisions in a semi-automated fulfillment system
http://hdl.handle.net/1721.1/106682
Velocity-based storage and stowage decisions in a semi-automated fulfillment system
Yuan, Rong, Ph. D. Massachusetts Institute of Technology
The supply chain management for an online retailing business is centered around the operations of its fulfillment centers. A fulfillment center receives and holds inventory from vendors, and then uses this inventory to fill customer orders. Our research focuses on a new operating architecture of an order fulfillment system, enabled by new technology. We refer to it as the Semi-automated Fulfillment System. Different from the person-to-goods model in traditional warehouses, the semi-automated fulfillment system adopts a goods-to-person model for stowing and picking items from a storage field. In a semi-automated fulfillment system the inventory is stored on mobile storage pods; those mobile pods are then carried by robotic drives to static stations at which the operators conduct pick or stow operations. In the first chapter, we describe and identify three key operational decisions in the semiautomated fulfillment system, namely from which pods to pick the inventory needed (picking decision), where to return the pod to the storage field upon the completion of a pick or stow operation (storage decision), and to which pods to replenish the received inventory (stowage decision). We present a high-level capacity planning model for determining the number of robotic drives needed to achieve a given throughput level. This model highlights how the operational efficiency in this system depends on two key parameters, namely the travel time for an entire drive trip and the number of unit picks or stows per pod trip. In the second chapter, we focus on the storage decisions. The storage decision is to decide to which storage location to return a pod upon the completion of a pick or stow operation. We extend the academic results on the benefits of adopting velocity-based and class-based storage policies to the context of the semi-automated fulfillment system. We associate with each storage pod a velocity measure that represents an expectation of the number of picks from that pod in the near future. We then show that by assigning the high velocity pods to the most desirable storage locations, we can significantly reduce the drive travel time, compared to the random storage policy that returns the pod to a randomly-chosen storage location. We show that class-based storage policies with two or three classes, can achieve most of the benefits from the idealized velocity-based policy. Furthermore, we characterize how the performance of the velocity-based and class-based storage policies depend on the velocity variability across the storage pods; in particular we model how the benefits from velocity-based storage policies increase with increased variation in the pod velocities. In the third chapter, we build a discrete-time simulator to validate the theoretical models in the second chapter with real industry data. We observe a 6% to 11% reduction in the travel distance with 2-class or 3-class system, depending on the parameter settings. From a sensitivity analysis we establish the robustness of the class-based storage policies as they continue to perform well under a broad range of warehouse settings including different zoning strategies, resource utilization levels and space utilization levels. In the fourth chapter, we examine two stowage decisions, one at the zone level and the other at the pod level. The zone-level decision is to decide how to allocate the received inventory to multiple storage zones. The objective is to assure that the resulting picking workload for each zone is within its capacity. We show by simulation that a chaining-based allocation can be effective to balance the picking workload across different storage zones. The pod-level stowage decision is to decide on which pods to stow the inventory. We formulate a mixedinteger program (MIP) to find the optimal stowage profile that maximizes the number of unit picks per pod trip. We solve the MIP for a set of test cases to gain insight into the structure of optimal stowage policy. Motivated by these insights, we further propose a class-based stowage process that induces variability across the pod velocities.
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 153-156).
2016-01-01T00:00:00ZExploration vs. exploitation : reducing uncertainty in operational problems
http://hdl.handle.net/1721.1/106681
Exploration vs. exploitation : reducing uncertainty in operational problems
Shaposhnik, Yaron
Motivated by several core operational applications, we introduce a class of multistage stochastic optimization models that capture a fundamental tradeoff between performing work under uncertainty (exploitation) and investing resources to reduce the uncertainty in the decision making (exploration/testing). Unlike existing models, in which the exploration-exploitation tradeoffs typically relate to learning the underlying distributions, the models we introduce assume a known probabilistic characterization of the uncertainty, and focus on the tradeoff of learning exact realizations. In the first part of the thesis (Chapter 2), we study a class of scheduling problems that capture common settings in service environments in which the service provider must serve a collection of jobs that have a-priori uncertain processing times and priorities (modeled as weights). In addition, the service provider must decide how to dynamically allocate capacity between processing jobs and testing jobs to learn more about their respective processing times and weights. We obtain structural results of optimal policies that provide managerial insights, efficient optimal and near-optimal algorithms, and quantification of the value of testing. In the second part of the thesis (Chapter 3), we generalize the model introduced in the first part by studying how to prioritize testing when jobs have different uncertainties. We model difference in uncertainties using the convex order, a general relation between distributions, which implies that the variance of one distribution is higher than the variance of the other distribution. Using an analysis based on the concept of mean preserving local spread, we show that the structure of the optimal policy generalizes that of the initial model where jobs were homogeneous and had equal weights. Finally, in the third part of the thesis (Chapter 4), we study a broad class of stochastic combinatorial optimization that can be formulated as Linear Programs whose objective coefficients are random variables that can be tested, and whose constraint polyhedron has the structure of a polymatroid. We characterize the optimal policy and show that similar types of policies optimally govern testing decisions in this setting as well.
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 205-207).
2016-01-01T00:00:00ZDynamic learning and optimization for operations management problems
http://hdl.handle.net/1721.1/105087
Dynamic learning and optimization for operations management problems
Wang, He, Ph. D. Massachusetts Institute of Technology
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.
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).
2016-01-01T00:00:00Z