Operations Research - Ph.D. / Sc.D.
https://hdl.handle.net/1721.1/7719
2020-05-29T03:35:39ZInference and decision models for regulatory and business challenges in low-Income countries
https://hdl.handle.net/1721.1/123732
Inference and decision models for regulatory and business challenges in low-Income countries
Beeler, Michael Francis.
This thesis develops inference and decision models to address challenges of particular relevance in low-income countries (LICs). The areas studied include intelligent tutoring systems (ITS), network infrastructure pricing, and anti-counterfeiting. The ITS chapter identifies previously unknown and serious limitations to Bayesian Knowledge Tracing and Deep Knowledge Tracing, which are two highly-cited methods designed to aid adaptive educational software. The work on Deep Knowledge Tracing led to new data augmentation methods for training recurrent neural networks to be robust in the face of unseen input sequences. We propose a statistically consistent, efficient, and unbiased alternative inference method for questions engaging one skill at a time. The network infrastructure pricing chapters examine how to allocate the cost of a future infrastructure network whose structure depends on the price-taking decisions of potential users. In a multi-period setting, strategic joining delay by users typically leads to lower utility. We develop a cost-allocation rule that uses rebates to prevent strategic delay. In the single-period setting, we derive closed-form solutions to the expected value of offering to build a simple 1D network and use the 1D solution to establish a lower-bound estimate for more complex 2D networks. The anti-counterfeiting chapter investigates the strategic procurement of counterfeits by retailers and the effects of shared retailer reputation on equilibrium procurement decisions using models that are more flexible and tractable than those previously appearing in the literature.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2019; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 207-213).
2019-01-01T00:00:00ZDistributionally robust optimization with marginals : theory and applications
https://hdl.handle.net/1721.1/123731
Distributionally robust optimization with marginals : theory and applications
Chen, Louis Lester.
In this thesis, we consider distributionally robust optimization (DRO) problems in which the ambiguity sets are designed from marginal distribution information - more specifically, when the ambiguity set includes any distribution whose marginals are consistent with given prescribed distributions that have been estimated from data. In the first chapter, we study the class of linear and discrete optimization problems in which the objective coefficients are chosen randomly from a distribution, and the goal is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to be specified up to only the marginal distributions. We generalize the primal-dual formulations for this problem from the set of joint distributions with absolutely continuous marginal distributions to arbitrary marginal distributions using techniques from optimal transport theory.; While the robust bound is shown to be NP-hard to compute for linear optimization problems, we identify multiple sufficient conditions for polynomial time solvability - one using extended formulations, another exploiting the interaction of combinatorial structure and optimal transport. This generalizes the known tractability results under marginal information from 0-1 polytopes to a class of integral polytopes and has implications on the solvability of distributionally robust optimization problems in areas such as scheduling, which we discuss. In the second chapter, we extend the primal-dual analysis of the previous chapter to the problem of distributionally robust network design. In this problem, the decision maker is to decide on the prepositioning of resources on arcs in a given s-t flow network in anticipation of an adversarys selection of a probability distribution for the arc capacities, aimed to minimize the expected max flow.; Again, the adversarys selection is limited to those distributions that are couplings of given are capacity distributions, one for each arc. We show that we can efficiently solve the distributionally robust network design problem in the case of finite-supported marginals. Further, we take advantage of the network setting to efficiently solve for the distribution the adversary responds with. The primal-dual formulation of our previous work takes on a striking form in this study. As one might expect, the form relates to the well-known Max Flow, Min-Cut theorem. And this leads to the intriguing interpretation as a 2-player, zero-sum game wherein player 1 chooses what to set the arc capacities to and player 2 chooses an s-t cut.; Essential to our analysis is the finding that the problem of finding the worst-case coupling of the stochastic arc capacities amounts to finding a distribution over the set of s-t cuts- this distribution being among the mixed strategies that player 2 would play in a Nash equilibrium. Furthermore, the support of such a distribution is a nested collection of s-t cuts, which implies an efficiently sized solution. Finally, the third chapter involves work inspired by the daily operations of HEMA supermarket, which is a recently established new retail model by Alibaba Group, China. In a HEMA supermarket store, a single SKU may be presented with demand in the form of multiple channels. The challenge facing HEMA is the question of how many units to stock in total between the warehouse and the store-front in advance of uncertain demand that arises in several consecutive time frames, each 30 minutes long.; In this work, we provide the first distributionally robust optimization study in the setting of omnichannel inventory management, wherein we are to make a stocking decision robust to an adversarys choice of coupling of available (marginal) demand distributions by channel and by time frame. The adversarys coupling decision amounts to designing a random mathematical program with equilibrium constraints (MPEC). And we provide both a structural analysis of the adversarys choice of coupling as well as an efficient procedure to find this coupling. In general, the overall distributionally robust stocking problem is non-concave. We provide sufficient conditions on the cost parameters under which this problem becomes concave, and hence tractable. Finally, we conduct experiments with HEMAs data.; In these experiments, we compare and contrast the performance of our distributionally robust solution with the performance of a naive Newsvendor-like solution on various SKUs of varying sales volume and number of channels on a 5-hour time window from 2pm - 7pm on weekends. Numerical experiments show that the distributionally robust solutions generally outperform the stochastic Newsvendor-like solution in SKUs exhibiting low-medium sales volume. Furthermore, and interestingly, in all of our experiments, the distributionally robust inventory decision problems presented by the historical data provided by HEMA are in fact concave.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2019; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 121-125).
2019-01-01T00:00:00ZData-driven pricing and inventory management with applications in fashion retail
https://hdl.handle.net/1721.1/123720
Data-driven pricing and inventory management with applications in fashion retail
Nambiar, Mila.
Fashion retail is typically characterized by (1) high demand uncertainty and products with short life cycles, which complicates demand forecasting, and (2) low salvage values and long supply lead times, which penalizes for inaccurate demand forecasting. In this thesis, we are interested in the design of algorithms that leverage fashion retail data to improve demand forecasting, and that make revenue-maximizing or cost-minimizing pricing and inventory management decisions. First, we study a multi-period dynamic pricing problem with feature information. We are especially interested in demand model misspecification, and show that it can lead to price endogeneity, and hence inconsistent price elasticity estimates and suboptimal pricing decisions. We propose a "random price shock" (RPS) algorithm that combines instrumental variables, well known in econometrics, with online learning, in order to simultaneously estimate demand and optimize revenue.; We demonstrate strong theoretical guarantees on the regret of RPS for both IID and non ID features, and numerically validate the algorithm's performance on synthetic data. Next, we present a case study in collaboration with Oracle Retail. We extend RPS to incorporate common business constraints such as markdown pricing and inventory constraints. We then conduct a counterfactual analysis where we simulate the algorithm's performance using fashion retail data. Our analysis estimates that the RPS algorithm will increase by 2-7% relative to current practice. Finally, we study an inventory allocation problem in a single-warehouse multiple-retailer setting with lost sales. We show that under general conditions this problem is convex, and that a Lagrangian relaxation-based approach can be applied to solve it in a computationally tractable, and near-optimal way.; This analysis allows us to prove structural results that give insights into how the allocation policy should depend on factors such as the retailer demand distributions, and demand learning.
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2019; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 167-171).
2019-01-01T00:00:00ZPrescriptive analytics in operations problems : a tree ensemble approach
https://hdl.handle.net/1721.1/123709
Prescriptive analytics in operations problems : a tree ensemble approach
Biggs, Max(Max Ray)
The main contributions of this thesis concern addressing challenges in the field of prescriptive optimization, and how machine learning techniques can be incorporated into solving data-driven operational optimization problems. In chapter 2, we provide a data-driven study of the secondary ticket market. In particular we are primarily concerned with accurately estimating price sensitivity for listed tickets. We propose a semi-parametric model for measuring heterogeneous treatment effects using the concept of orthogonalization in the classification setting, and derive a novel loss function which can be solved using a range of off-the-shelf machine learning methods. Over a wide range of synthetic data experiments, we show how this approach beats state-of-the-art machine learning and causal inference methods for estimating treatment effects in classification tasks.; In chapter 3, we show how to solve optimization problems with random forest objective functions and general polyhedral constraints. We show how to formulate this problem using MIO techniques and show this formulation can be decomposed and solved iteratively using Pareto-optimal Benders cuts. We also provide analytical guarantees on an approach that approximates a large scale random forest optimization problem by optimizing over a smaller forest, and develop heuristics based on ideas from cross validation. In chapter 4, we study a new problem where nurse practitioners need to be dynamically routed to patients' houses as service requests are received. We show how to solve using Approximate Dynamic Programming and develop methods to solve ADP's with combinatorial action spaces and non-linear cost-to-go functions approximated using a tree or tree ensemble approximation.; In chapter 5, we propose a Markov Decision Process (MDP) model for the tramp shipping that captures the dynamic and stochastic nature of spot cargo availability. We propose a novel methodology for solving this MDP in a tractable way, by introducing a ranking algorithm which is equivalent to solving the DP. We show that our ranking algorithm outperforms several benchmarks and the average performance of ships operating on the spot market in practice by between 4% and 32%.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.; Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2019; Cataloged from student-submitted PDF version of thesis.; Includes bibliographical references (pages 227-241).
2019-01-01T00:00:00Z