Online Algorithms for Dynamic Resource Allocation Problems

Dynamic resource allocation problems are everywhere. Airlines reserve flight seats for those who purchase flight tickets. Healthcare facilities reserve appointment slots for patients who request them. Freight carriers such as motor carriers, railroad companies, and shipping companies pack containers with loads from specific origins to destinations. We focus on optimizing such allocation problems where resources need to be assigned to customers in real time. These problems are particularly difficult to solve because they depend on random external information that unfolds gradually over time, and the number of potential solutions is overwhelming to search through by conventional methods. In this dissertation, we propose viable allocation algorithms for industrial use, by fully leveraging data and technology to produce gains in efficiency, productivity, and usability of new systems. The first chapter presents a summary of major methodologies used in modeling and algorithm design, and how the methodologies are driven by the size of accessible data. Chapters 2 to 5 present genuine research results of resource allocation problems that are based on Wang and Truong (2017); Wang et al. (2015); Stein et al. (2017); Wang et al. (2016). The algorithms and models cover problems in multiple industries, from a small clinic that aims to better utilize its expensive medical devices, to a technology giant that needs a cost-effective, distributed resource-allocation algorithm in order to maintain the relevance of its advertisements to hundreds of millions of consumers

Near-Optimal Primal-Dual Algorithms for Quantity-Based Network Revenue Management

We study the canonical quantity-based network revenue management (NRM) problem where the decision-maker must irrevocably accept or reject each arriving customer request with the goal of maximizing the total revenue given limited resources. The exact solution to the problem by dynamic programming is computationally intractable due to the well-known curse of dimensionality. Existing works in the literature make use of the solution to the deterministic linear program (DLP) to design asymptotically optimal algorithms. Those algorithms rely on repeatedly solving DLPs to achieve near-optimal regret bounds. It is, however, time-consuming to repeatedly compute the DLP solutions in real time, especially in large-scale problems that may involve hundreds of millions of demand units. In this paper, we propose innovative algorithms for the NRM problem that are easy to implement and do not require solving any DLPs. Our algorithm achieves a regret bound of $O(\log k)$, where $k$ is the system size. To the best of our knowledge, this is the first NRM algorithm that (i) has an $o(\sqrt{k})$ asymptotic regret bound, and (ii) does not require solving any DLPs

Approximation algorithms for product framing and pricing

We propose one of the first models of “product framing” and pricing. Product framing refers to the way consumer choice is influenced by how the products are framed or displayed. We present a model in which a set of products is displayed or framed into a set of virtual web pages. We assume that consumers consider only products in the top pages with different consumers willing to see different numbers of pages. Consumers select a product, if any, from these pages following a general choice model. We show that the product-framing problem is NP-hard. We derive algorithms with guaranteed performance relative to an optimal algorithm under reasonable assumptions. Our algorithms are fast and easy to implement. We also present structural results and design algorithms for pricing under framing effects for the multinomial logit model. We show that, for profit maximization problems, at optimality, products are displayed in descending order of their value gap and in ascending order of their markups

Metabolomics reveals the response of hydroprimed maize to mitigate the impact of soil salinization

Soil salinization is a major environmental stressor hindering global crop production. Hydropriming has emerged as a promising approach to reduce salt stress and enhance crop yields on salinized land. However, a better mechanisitic understanding is required to improve salt stress tolerance. We used a biochemical and metabolomics approach to study the effect of salt stress of hydroprimed maize to identify the types and variation of differentially accumulated metabolites. Here we show that hydropriming significantly increased catalase (CAT) activity, soluble sugar and proline content, decreased superoxide dismutase (SOD) activity and peroxide (H2O2) content. Conversely, hydropriming had no significant effect on POD activity, soluble protein and MDA content under salt stress. The Metabolite analysis indicated that salt stress significantly increased the content of 1278 metabolites and decreased the content of 1044 metabolites. Ethisterone (progesterone) was the most important metabolite produced in the roots of unprimed samples in response to salt s tress. Pathway enrichment analysis indicated that flavone and flavonol biosynthesis, which relate to scavenging reactive oxygen species (ROS), was the most significant metabolic pathway related to salt stress. Hydropriming significantly increased the content of 873 metabolites and significantly decreased the content of 1313 metabolites. 5-Methyltetrahydrofolate, a methyl donor for methionine, was the most important metabolite produced in the roots of hydroprimed samples in response to salt stress. Plant growth regulator, such as melatonin, gibberellin A8, estrone, abscisic acid and brassinolide involved in both treatment. Our results not only verify the roles of key metabolites in resisting salt stress, but also further evidence that flavone and flavonol biosynthesis and plant growth regulator relate to salt tolerance