Essays in Large Scale Optimization Algorithm and Its Application in Revenue Management PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Essays in Large Scale Optimization Algorithm and Its Application in Revenue Management PDF full book. Access full book title Essays in Large Scale Optimization Algorithm and Its Application in Revenue Management by Mingxi Zhu (Researcher in optimization algorithms). Download full books in PDF and EPUB format.
Author: Mingxi Zhu (Researcher in optimization algorithms) Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This dissertation focuses on the large-scale optimization algorithm and its application in revenue management. It comprises three chapters. Chapter 1, Managing Randomization in the Multi-Block Alternating Direction Method of Multipliers for Quadratic Optimization, provides theoretical foundations for managing randomization in the multi-block alternating direction method of multipliers (ADMM) method for quadratic optimization. Chapter 2, How a Small Amount of Data Sharing Benefits Distributed Optimization and Learning, presents both the theoretical and practical evidences on sharing a small amount of data could hugely benefit distributed optimization and learning. Chapter 3, Dynamic Exploration and Exploitation: The Case of Online Lending, studies exploration/ exploitation trade-offs, and the value of dynamic extracting information in the context of online lending. The first chapter is a joint work with Kresimir Mihic and Yinyu Ye. The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical computational efficiency of the method, because one big matrix factorization is needed at least once even for linear and convex quadratic programming. This drawback may be overcome by enforcing a multi-block structure of the decision variables in the original optimization problem. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. On the other hand, two positive developments have been made: first, if in each cyclic loop one randomly permutes the updating order of the multiple blocks, then the method converges in expectation for solving any system of linear equations with any number of blocks. Secondly, such a randomly permuted ADMM also works for equality-constrained convex quadratic programming even when the objective function is not separable. The goal of this paper is twofold. First, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Secondly, using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM, with a variable-grouping strategy, could significantly improve the computation efficiency on solving most quadratic optimization problems. The second chapter is a joint work with Yinyu Ye. Distributed optimization algorithms have been widely used in machine learning and statistical estimation, especially under the context where multiple decentralized data centers exist and the decision maker is required to perform collaborative learning across those centers. While distributed optimization algorithms have the merits in parallel processing and protecting local data security, they often suffer from slow convergence compared with centralized optimization algorithms. This paper focuses on how small amount of data sharing could benefit distributed optimization and learning for more advanced optimization algorithms. Specifically, we consider how data sharing could benefit distributed multi-block alternating direction method of multipliers (ADMM) and preconditioned conjugate gradient method (PCG) with application in machine learning tasks of linear and logistic regression. These algorithms are commonly known as algorithms between the first and the second order methods, and we show that data share could hugely boost the convergence speed for this class of the algorithms. Theoretically, we prove that a small amount of data share leads to improvements from near-worst to near-optimal convergence rate when applying ADMM and PCG methods to machine learning tasks. A side theory product is the tight upper bound of linear convergence rate for distributed ADMM applied in linear regression. We further propose a meta randomized data-sharing scheme and provide its tailored applications in multi-block ADMM and PCG methods in order to enjoy both the benefit from data-sharing and from the efficiency of distributed computing. From the numerical evidences, we are convinced that our algorithms provide good quality of estimators in both the least square and the logistic regressions within much fewer iterations by only sharing 5% of pre-fixed data, while purely distributed optimization algorithms may take hundreds more times of iterations to converge. We hope that the discovery resulted from this paper would encourage even small amount of data sharing among different regions to combat difficult global learning problems. The third chapter is a joint work with Haim Mendelson. This paper studies exploration and exploitation tradeoffs in the context of online lending. Unlike traditional contexts where the cost of exploration is an opportunity cost of lost revenue or some other implicit cost, in the case of unsecured online lending, the lender effectively gives away money in order to learn about the borrower's ability to repay. In our model, the lender maximizes the expected net present value of the cash flow she receives by dynamically adjusting the loan amounts and the interest (discount) rate as she learns about the borrower's unknown income. The lender has to carefully balance the trade-offs between earning more interest when she lends more and the risk of default, and we provided the optimal dynamic policy for the lender. The optimal policy support the classic "lean experimentation" in certain regime, while challenge such concept in other regime. When the demand elasticity is zero (the discount rate is set exogenously), or the elasticity a decreasing function of the discount rate, the optimal policy is characterized by a large number of small experiments with increasing repayment amounts. When the demand elasticity is constant or when it is an increasing function of the discount rate, we obtain a two-step optimal policy: the lender performs a single experiment and then, if the borrower repays the loan, offers the same loan amount and discount rate in each subsequent period without any further experimentation. This result sheds light in how to take into account the market churn measured by elasticity, in the dynamic experiment design under uncertain environment. We further provide the implications under the optimal policies, including the impact of the income variability, the value of information and the consumer segmentation. Lastly, we extend the methodology to analyze the Buy-Now-Pay-Later business model and provide the policy suggestions.
Author: Mingxi Zhu (Researcher in optimization algorithms) Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This dissertation focuses on the large-scale optimization algorithm and its application in revenue management. It comprises three chapters. Chapter 1, Managing Randomization in the Multi-Block Alternating Direction Method of Multipliers for Quadratic Optimization, provides theoretical foundations for managing randomization in the multi-block alternating direction method of multipliers (ADMM) method for quadratic optimization. Chapter 2, How a Small Amount of Data Sharing Benefits Distributed Optimization and Learning, presents both the theoretical and practical evidences on sharing a small amount of data could hugely benefit distributed optimization and learning. Chapter 3, Dynamic Exploration and Exploitation: The Case of Online Lending, studies exploration/ exploitation trade-offs, and the value of dynamic extracting information in the context of online lending. The first chapter is a joint work with Kresimir Mihic and Yinyu Ye. The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical computational efficiency of the method, because one big matrix factorization is needed at least once even for linear and convex quadratic programming. This drawback may be overcome by enforcing a multi-block structure of the decision variables in the original optimization problem. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. On the other hand, two positive developments have been made: first, if in each cyclic loop one randomly permutes the updating order of the multiple blocks, then the method converges in expectation for solving any system of linear equations with any number of blocks. Secondly, such a randomly permuted ADMM also works for equality-constrained convex quadratic programming even when the objective function is not separable. The goal of this paper is twofold. First, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Secondly, using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM, with a variable-grouping strategy, could significantly improve the computation efficiency on solving most quadratic optimization problems. The second chapter is a joint work with Yinyu Ye. Distributed optimization algorithms have been widely used in machine learning and statistical estimation, especially under the context where multiple decentralized data centers exist and the decision maker is required to perform collaborative learning across those centers. While distributed optimization algorithms have the merits in parallel processing and protecting local data security, they often suffer from slow convergence compared with centralized optimization algorithms. This paper focuses on how small amount of data sharing could benefit distributed optimization and learning for more advanced optimization algorithms. Specifically, we consider how data sharing could benefit distributed multi-block alternating direction method of multipliers (ADMM) and preconditioned conjugate gradient method (PCG) with application in machine learning tasks of linear and logistic regression. These algorithms are commonly known as algorithms between the first and the second order methods, and we show that data share could hugely boost the convergence speed for this class of the algorithms. Theoretically, we prove that a small amount of data share leads to improvements from near-worst to near-optimal convergence rate when applying ADMM and PCG methods to machine learning tasks. A side theory product is the tight upper bound of linear convergence rate for distributed ADMM applied in linear regression. We further propose a meta randomized data-sharing scheme and provide its tailored applications in multi-block ADMM and PCG methods in order to enjoy both the benefit from data-sharing and from the efficiency of distributed computing. From the numerical evidences, we are convinced that our algorithms provide good quality of estimators in both the least square and the logistic regressions within much fewer iterations by only sharing 5% of pre-fixed data, while purely distributed optimization algorithms may take hundreds more times of iterations to converge. We hope that the discovery resulted from this paper would encourage even small amount of data sharing among different regions to combat difficult global learning problems. The third chapter is a joint work with Haim Mendelson. This paper studies exploration and exploitation tradeoffs in the context of online lending. Unlike traditional contexts where the cost of exploration is an opportunity cost of lost revenue or some other implicit cost, in the case of unsecured online lending, the lender effectively gives away money in order to learn about the borrower's ability to repay. In our model, the lender maximizes the expected net present value of the cash flow she receives by dynamically adjusting the loan amounts and the interest (discount) rate as she learns about the borrower's unknown income. The lender has to carefully balance the trade-offs between earning more interest when she lends more and the risk of default, and we provided the optimal dynamic policy for the lender. The optimal policy support the classic "lean experimentation" in certain regime, while challenge such concept in other regime. When the demand elasticity is zero (the discount rate is set exogenously), or the elasticity a decreasing function of the discount rate, the optimal policy is characterized by a large number of small experiments with increasing repayment amounts. When the demand elasticity is constant or when it is an increasing function of the discount rate, we obtain a two-step optimal policy: the lender performs a single experiment and then, if the borrower repays the loan, offers the same loan amount and discount rate in each subsequent period without any further experimentation. This result sheds light in how to take into account the market churn measured by elasticity, in the dynamic experiment design under uncertain environment. We further provide the implications under the optimal policies, including the impact of the income variability, the value of information and the consumer segmentation. Lastly, we extend the methodology to analyze the Buy-Now-Pay-Later business model and provide the policy suggestions.
Author: Vladimir Tsurkov Publisher: Springer Science & Business Media ISBN: 1475732430 Category : Computers Languages : en Pages : 322
Book Description
Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control.
Author: Lorenz T. Biegler Publisher: Springer Science & Business Media ISBN: 1461219604 Category : Mathematics Languages : en Pages : 339
Book Description
With contributions by specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics, the major themes include an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models.
Author: Pontus Giselsson Publisher: Springer ISBN: 3319974785 Category : Mathematics Languages : en Pages : 412
Book Description
This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific coverage of this active research field, the book serves as a powerful source of information for practitioners as well as theoreticians. Large-Scale and Distributed Optimization is a unique combination of contributions from leading experts in the field, who were speakers at the LCCC Focus Period on Large-Scale and Distributed Optimization, held in Lund, 14th–16th June 2017. A source of information and innovative ideas for current and future research, this book will appeal to researchers, academics, and students who are interested in large-scale optimization.
Author: Richard H. Byrd Publisher: ISBN: Category : Chemistry Languages : en Pages : 16
Book Description
Abstract: "We describe a new stochastic global optimization algorithm that is oriented towards solving large scale problems, and present the results of applying it to a class of problems in molecular chemistry. Our new algorithm incorporates some full-dimensional random sampling and local minimizations as in existing stochastic methods, but the keys to its success are two new phases that concentrate on selected small dimensional subproblems of the overall problem. These phases constitute a major portion of the computational effort of the new method, and represent a significant departure from existing stochastic methods.
Author: Donald C. Wood Publisher: Emerald Group Publishing ISBN: 1839096608 Category : Social Science Languages : en Pages : 285
Book Description
This volume explores current issues in national and international policy, business and capitalism and economic theory and behavior specifically pertaining to Brazil. The underlying theme running through the collection is the steady encroachment of neoliberalism into economic policy and practice, and the impact this has had on everyday ways of life.
Author: Rajpal Bobby Singh Nyotta Publisher: ISBN: Category : Languages : en Pages : 219
Book Description
The essays in this dissertation lie at the intersection of revenue management, urban mobility, and technology. Some of the most well-studied problems in operations management and operations research have been inspired by the transportation sector. For instance, the traveling salesman problem, the vehicle routing problem, freight logistics, airline fleet planning, port operations, and rail scheduling are set in the transportation industry. In this dissertation, we restrict our analysis to urban mobility, which focuses on transportation in metropolitan cities. Urban mobility has evolved dramatically over the past decade due to advances in technology, in particular, the mobile phone. Bike-sharing, ride-sharing, and vehicle sharing are possible today because of the growth and popularity of mobile phones. Because of this growth, users are able to access train and bus schedules in real-time, pay fares, and instantaneously reserve and check-out shared cars, bikes, electric scooters, and other types of shared vehicles. While this accessibility provides users with more flexibility, the systems are also increasingly difficult to operate and manage. One way to address this operational complexity involves using tools and methods from revenue management. More generally, using price and discounts as levers to shape customer behavior in a way that improves the system's service level, revenue, customer satisfaction, and other key performance metrics. This dissertation is made up of four essays across three chapters that address questions in operating systems in urban mobility, and we use techniques from revenue management to study how these systems can operate more effectively. In Chapter 1, we study free-ride policies as a mechanism to incentivize users of a "dockless" or "free-floating" electric vehicle sharing system (EVSS) to park vehicles at charging stations in order to maintain a charged fleet. A balanced system has a fleet that is adequately charged and evenly dispersed throughout the city. If left to unfold naturally, the system would fall out of balance, and revenue and customer experience might suffer. Most sharing systems use manual repositioning to achieve this balance, but we consider pricing incentives as an alternative method. We develop an infinite horizon dynamic program to analyze free-ride policies. We focus on an EVSS that offers free rides to customers if they return vehicles to charging stations. We build on this initial formulation to construct a mixed-integer program that outputs intuitive, battery-threshold rules for when to offer free rides. We also extend the model to accommodate more general discount-based policies. In a discrete-event simulation model using real data from an EVSS, we compare the performance of this simple policy against other sophisticated policies, including the commonly used fine-based policy, which fines users for street-parking vehicles with low battery. We first find that the simple threshold-based policy performs close to a more sophisticated, black-box policy in terms of revenue. We also discover that the free-ride policies generate customer utilities that are ten times higher than fine-based policies, but also generate less revenue. However, free-ride policies can be less costly to implement since they rely on manual repositioning up to 65-75% less than the benchmarking policies. Our simulation reveals this three-dimensional trade-off between customer satisfaction, revenue, and operational complexity. Our results are robust under many demand patterns and under a variety of network settings. In the remaining chapters, we are motivated by the claim that 30% of metropolitan traffic is a result of individuals searching or "cruising" for parking (Shoup, 2017). It is theorized that this cruising behavior causes superfluous traffic congestion that can be assuaged and mitigated with more effective pricing polices. In particular, pricing policies that ensure there is at least one open spot available on each block at all times under regular demand. With this in mind, Chapters 2 and 3 examine how to develop dynamic pricing policies that both maximize revenue and address traffic congestion, with Chapter 2 focusing on estimating key parameters that feed into the pricing models and Chapter 3 focusing on developing the price optimization models. In order to develop such pricing policies, one needs to know the price and spatial elasticity of parking, where price elasticity is a measure of the change in demand in response to a price change and the spatial elasticity is a measure of how much money a customer would require to park a mile or a block away from their destination. Using data from our industry partner, a venture-backed technology company that develops a software-as-a-service (SaaS) platform to manage parking, permitting, and micro-mobility for municipalities and organizations throughout the world, we are able to empirically estimate both of these values in Chapter 2. In this chapter, the context is parking-specific and the estimates are unique to the data from our partner city. However, we believe that our approach and the estimates can be used across urban mobility applications, and beyond, as these elasticities are often assumed to be known or given in many classic revenue management problems. In Chapter 2.1, the first essay of Chapter 2, we estimate the price elasticity after a 20% price increase in a mid-sized U.S. city and find the average price elasticity of parking demand is between -3.42 and -1.57, which is higher than existing estimates (Lehner and Peer, 2019). One reason our study could be producing higher estimates is because, as far as we know, our work is the first to use transactions data from a mobile phone application for parking payments, which is more accurate and detailed than the data used in the existing literature. With our model, we can also measure how long it takes for customers to learn about and respond to the price change. Despite the price change being publicly advertised, we find that customers do not respond to the price change until they experience it firsthand. In Chapter 2.2, the second essay of Chapter 2, we estimate the spatial elasticity. We perform our estimation using a panel dataset of parking transactions spanning 21 months in a large U.S. city. During this time frame, there was an unannounced pricing error where two neighboring blocks were discounted by 67% for 16 months. We find that customers require approximately $81 to walk an additional mile to their intended destination. This estimate increases 13% in the presence of rain and 36% during the morning rush hour. In Chapter 3, the final chapter of this dissertation, we study optimal, dynamic pricing policies for a system, or network, of reusable resources, where a parking spot on a city block can be interpreted as a resource that can be "reused" after it is vacated. We focus our analysis on a single reusable product (i.e., a single zone or block with a fixed number of parking spaces) and aim to set the price as a function of the number of occupied spaces. Our objective is to maximize the long-run average revenue under Markovian assumptions (i.e., Poisson arrival and exponential usage times). In queuing theory, such a model is known as an Erlang loss system. We reformulate this objective function using a metric that we term the "conditional entry-state distribution." There does not exist a method for computing this metric, so in Chapter 3, we develop an algorithm that converges to the metric's true value for any Erlang loss system. We also provide analysis on the performance and speed of the algorithm.
Author: Robert G. Cross Publisher: Crown Currency ISBN: 0307788989 Category : Business & Economics Languages : en Pages : 289
Book Description
From the man the Wall Street Journal hailed as "the guru of Revenue Management" comes revolutionary ways to recover from the after effects of downsizing and refocus your business on growth. Whatever happened to growth? In Revenue Management, Robert G. Cross answers this question with his ground-breaking approach to revitalizing businesses: focusing on the revenue side of the ledger instead of the cost side. The antithesis of slash-and-burn methods that left companies with empty profits and dissatisfied stockholders, Revenue Management overturns conventional thinking on marketing strategies and offers the key to initiating and sustaining growth. Using case studies from a variety of industries, small businesses, and nonprofit organizations, Cross describes no-tech, low-tech, and high-tech methods that managers can use to increase revenue without increasing products or promotions; predict consumer behavior; tap into new markets; and deliver products and services to customers effectively and efficiently. His proven tactics will help any business dramatically improve its bottom line by meeting the challenge of matching supply with demand.
Author: Mingxi Zhu (Researcher in optimization algorithms)
Author: Mingxi Zhu (Researcher in optimization algorithms)
Author: Vladimir Tsurkov
Author: Lorenz T. Biegler
Author: Pontus Giselsson
Author: Richard H. Byrd
Author: Donald C. Wood
Author: 
Author: Rajpal Bobby Singh Nyotta
Author: 
Author: Robert G. Cross