Download or read book Integer Programming Approaches to Risk averse Optimization written by Xiao Liu and published by . This book was released on 2016 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk-averse stochastic optimization problems widely exist in practice, but are generally challenging computationally. In this dissertation, we conduct both theoretical and computational research on these problems. First, we study chance-constrained two-stage stochastic optimization problems where second-stage feasible recourse decisions incur additional cost. We also propose a new model, where recovery decisions are made for the infeasible scenarios, and develop strong decomposition algorithms. Our computational results show the effectiveness of the proposed method. Second, we study the static probabilistic lot-sizing problem (SPLS), as an application of a two-stage chance-constrained problem in supply chains. We propose a new formulation that exploits the simple recourse structure, and give two classes of strong valid inequalities, which are shown to be computationally effective. Third, we study two-sided chance-constrained programs with a finite probability space. We reformulate this class of problems as a mixed-integer program. We study the polyhedral structure of the reformulation and propose a class of facet-defining inequalities. We propose a polynomial dynamic programming algorithm for the separation problem. Preliminary computational results are encouraging. Finally, we study risk-averse models for multicriteria stochastic optimization problems. We propose a new model that optimizes the worst-case multivariate conditional value-at-risk (CVaR), and develop a finitely convergent delayed cut generation algorithm.

Download or read book Linear and Mixed Integer Programming for Portfolio Optimization written by Renata Mansini and published by Springer. This book was released on 2015-06-10 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents solutions to the general problem of single period portfolio optimization. It introduces different linear models, arising from different performance measures, and the mixed integer linear models resulting from the introduction of real features. Other linear models, such as models for portfolio rebalancing and index tracking, are also covered. The book discusses computational issues and provides a theoretical framework, including the concepts of risk-averse preferences, stochastic dominance and coherent risk measures. The material is presented in a style that requires no background in finance or in portfolio optimization; some experience in linear and mixed integer models, however, is required. The book is thoroughly didactic, supplementing the concepts with comments and illustrative examples.

Download or read book Applied Integer Programming written by Der-San Chen and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems. Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book. Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems.

Download or read book Risk averse Optimization in Multicriteria and Multistage Decision Making written by Merve Merakli and published by . This book was released on 2018 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk-averse stochastic programming provides means to incorporate a wide range of risk attitudes into decision making. Pioneered by the advances in financial optimization, several risk measures such as Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) are employed in risk-averse stochastic programming for a variety of application areas. In this work, we consider risk-averse modeling approaches for stochastic multicriteria and stochastic sequential decision-making problems. First, we propose a new multivariate definition for CVaR as a set of vectors. We analyze its properties and establish that the new definition remedies some potential drawbacks of the existing definitions for discrete random variables. Motivated by the computational challenges in the optimization of vector-valued multivariate definitions of CVaR, next, we study two-stage stochastic programming problems with multivariate risk constraints utilizing a scalarization scheme. We formulate this problem as a mixed-integer program (MIP) and devise two delayed cut generation algorithms. The effectiveness of the proposed modeling approach and solution methods are demonstrated on a pre-disaster relief network design problem. Finally, we study the Markov Decision Processes (MDPs) under cost and transition probability uncertainty with the objective of optimizing the VaR associated with the expected performance of an MDP model. Based on a sampling approach, we provide an MIP formulation and a branch-and-cut algorithm, and demonstrate our proposed methods on an inventory management problem for long-term humanitarian relief operations.

Download or read book Risk Averse Optimization and Control written by Darinka Dentcheva and published by Springer Nature. This book was released on with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approaches to Integer Programming written by M. L. Balinski and published by . This book was released on 1974 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Branch and bound experiments in 0-1 programming; A subadditive approach to the group problem of integer programming; Two computationaly difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems; Lagrangean relaxation for integer programming; A heuristic algorithm for mixed-integer programming problems; On the group problem for mixed integer programming; Experiments in the formulation of integer programming problems.

Download or read book Stochastic Optimization written by Stanislav Uryasev and published by Springer Science & Business Media. This book was released on 2001-05-31 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics. Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering.

Download or read book Decision Making with Dominance Constraints in Two Stage Stochastic Integer Programming written by Uwe Gotzes and published by Springer Science & Business Media. This book was released on 2009-09-30 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uwe Gotzes analyzes an approach to account for risk aversion in two-stage models based upon partial orders on the set of real random variables. He illustrates the superiority of the proposed decomposition method over standard solvers for example with numerical experiments with instances from energy investment.

Download or read book Risk Neutral and Risk Averse Approaches to Multistage Stochastic Programming with Applications to Hydrothermal Operation Planning Problems written by Wajdi Tekaya and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this thesis is to investigate risk neutral and risk averse approaches to multistage stochastic programming with applications to hydrothermal operation planning problems. The purpose of hydrothermal system operation planning is to define an operation strategy which, for each stage of the planning period, given the system state at the beginning of the stage, produces generation targets for each plant. This problem can be formulated as a large scale multistage stochastic linear programming problem. The energy rationing that took place in Brazil in the period 2001/2002 raised the question of whether a policy that is based on a criterion of minimizing the expected cost (i.e. risk neutral approach) is a valid one when it comes to meet the day-to-day supply requirements and taking into account severe weather conditions that may occur. The risk averse methodology provides a suitable framework to remedy these deficiencies. This thesis attempts to provide a better understanding of the risk averse methodology from the practice perspective and suggests further possible alternatives using robust optimization techniques. The questions investigated and the contributions of this thesis are as follows. First, we suggest a multiplicative autoregressive time series model for the energy inflows that can be embedded into the optimization problem that we investigate. Then, computational aspects related to the stochastic dual dynamic programming (SDDP) algorithm are discussed. We investigate the stopping criteria of the algorithm and provide a framework for assessing the quality of the policy. The SDDP method works reasonably well when the number of state variables is relatively small while the number of stages can be large. However, as the number of state variables increases the convergence of the SDDP algorithm can become very slow. Afterwards, performance improvement techniques of the algorithm are discussed. We suggest a subroutine to eliminate the redundant cutting planes in the future cost functions description which allows a considerable speed up factor. Also, a design using high performance computing techniques is discussed. Moreover, an analysis of the obtained policy is outlined with focus on specific aspects of the long term operation planning problem. In the risk neutral framework, extreme events can occur and might cause considerable social costs. These costs can translate into blackouts or forced rationing similarly to what happened in 2001/2002 crisis. Finally, issues related to variability of the SAA problems and sensitivity to initial conditions are studied. No significant variability of the SAA problems is observed. Second, we analyze the risk averse approach and its application to the hydrothermal operation planning problem. A review of the methodology is suggested and a generic description of the SDDP method for coherent risk measures is presented. A detailed study of the risk averse policy is outlined for the hydrothermal operation planning problem using different risk measures. The adaptive risk averse approach is discussed under two different perspectives: one through the mean-AV@R and the other through the mean-upper-semideviation risk measures. Computational aspects for the hydrothermal system operation planning problem of the Brazilian interconnected power system are discussed and the contributions of the risk averse methodology when compared to the risk neutral approach are presented. We have seen that the risk averse approach ensures a reduction in the high quantile values of the individual stage costs. This protection comes with an increase of the average policy value - the price of risk aversion. Furthermore, both of the risk averse approaches come with practically no extra computational effort and, similarly to the risk neutral method, there was no significant variability of the SAA problems. Finally, a methodology that combines robust and stochastic programming approaches is investigated. In many situations, such as the operation planning problem, the involved uncertain parameters can be naturally divided into two groups, for one group the robust approach makes sense while for the other the stochastic programming approach is more appropriate. The basic ideas are discussed in the multistage setting and a formulation with the corresponding dynamic programming equations is presented. A variant of the SDDP algorithm for solving this class of problems is suggested. The contributions of this methodology are illustrated with computational experiments of the hydrothermal operation planning problem and a comparison with the risk neutral and risk averse approaches is presented. The worst-case-expectation approach constructs a policy that is less sensitive to unexpected demand increase with a reasonable loss on average when compared to the risk neutral method. Also, we comp are the suggested method with a risk averse approach based on coherent risk measures. On the one hand, the idea behind the risk averse method is to allow a trade off between loss on average and immunity against unexpected extreme scenarios. On the other hand, the worst-case-expectation approach consists in a trade off between a loss on average and immunity against unanticipated demand increase. In some sense, there is a certain equivalence between the policies constructed using each of these methods.

Download or read book Stochastic Programming written by Horand Gassmann and published by World Scientific. This book was released on 2013 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.

Download or read book Integer Programming Approaches for Some Non convex and Stochastic Optimization Problems written by James Luedtke and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation we study several non-convex and stochastic optimization problems. The common theme is the use of mixed-integer programming (MIP) techniques including valid inequalities and reformulation to solve these problems.

Download or read book Integer Programming Approaches for Semicontinuous and Stochastic Optimization written by Gustavo Angulo Olivares (I.) and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis concerns the application of mixed-integer programming techniques to solve special classes of network flow problems and stochastic integer programs. We draw tools from complexity and polyhedral theory to analyze these problems and propose improved solution methods. In the first part, we consider semi-continuous network flow problems, that is, a class of network flow problems where some of the variables are required to take values above a prespecified minimum threshold whenever they are not zero. These problems find applications in management and supply chain models where orders in small quantities are undesirable. We introduce the semi-continuous inflow set with variable upper bounds as a relaxation of general semi-continuous network flow problems. Two particular cases of this set are considered, for which we present complete descriptions of the convex hull in terms of linear inequalities and extended formulations. We also consider a class of semi-continuous transportation problems where inflow systems arise as substructures, for which we investigate complexity questions. Finally, we study the computational efficacy of the developed polyhedral results in solving randomly generated instances of semi-continuous transportation problems. In the second part, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of optimizing a linear function on the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear problem and finds applications in stochastic integer programming. We observe that the complexity of the problem depends on how P and X are specified. For instance, P can be explicitly given by its linear description, or implicitly by an oracle. Similarly, X can be explicitly given as a list of vectors, or implicitly as a face of P. While removing vertices turns to be hard in general, it is tractable for tractable 0-1 polytopes, and compact extended formulations can be obtained. Some extensions to integral polytopes are also presented. The third part is devoted to the integer L-shaped method for two-stage stochastic integer programs. A widely used model assumes that decisions are made in a two-step fashion, where first-stage decisions are followed by second-stage recourse actions after the uncertain parameters are observed, and we seek to minimize the expected overall cost. In the case of finitely many possible outcomes or scenarios, the integer L-shaped method proposes a decomposition scheme akin to Benders' decomposition for linear problems, but where a series of mixed-integer subproblems have to be solved at each iteration. To improve the performance of the method, we devise a simple modification that alternates between linear and mixed-integer subproblems, yielding significant time savings in instances from the literature. We also present a general framework to generate optimality cuts via a cut-generating problem. Using an extended formulation of the forbidden-vertices problem, we recast our cut-generating problem as a linear problem and embed it within the integer L-shaped method. Our numerical experiments suggest that this approach can prove beneficial when the first-stage set is relatively complicated.

Download or read book Supply Chain Disruption Management written by Tadeusz Sawik and published by Springer Nature. This book was released on 2020-05-29 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with stochastic combinatorial optimization problems in supply chain disruption management, with a particular focus on management of disrupted flows in customer-driven supply chains. The problems are modeled using a scenario based stochastic mixed integer programming to address riskneutral, risk-averse and mean-risk decision-making in the presence of supply chain disruption risks. The book focuses on integrated disruption mitigation and recovery decision-making and innovative, computationally efficient multi-portfolio approach to supply chain disruption management, e.g., selection of primary and recovery supply portfolios, demand portfolios, capacity portfolios, etc. Numerous computational examples throughout the book, modeled in part on realworld supply chain disruption management problems, illustrate the material presented and provide managerial insights. Many propositions formulated in the book lead to a deep understanding of the properties of developed stochastic mixed integer programs and optimal solutions. In the computational examples, the proposed mathematical programming models are solved using an advanced algebraic modeling language such as AMPL and CPLEX, GUROBI and XPRESS solvers. The knowledge and tools provided in the book allow the reader to model and solve supply chain disruption management problems using commercially available software for mixed integer programming. Using the end-of chapter problems and exercises, the monograph can also be used as a textbook for an advanced course in supply chain risk management. After an introductory chapter, the book is then divided into six main parts. Part I addresses selection of a supply portfolio; Part II considers integrated selection of supply portfolio and scheduling; Part III looks at integrated, equitably efficient selection of supply portfolio and scheduling; Part IV examines integrated selection of primary and recovery supply and demand portfolios and production and inventory scheduling, Part V deals with selection of resilient supply portfolio in multitier supply chain networks; and Part VI addresses selection of cybersecurity safequards portfolio for disruption management of information flows in supply chains.

Download or read book 50 Years of Integer Programming 1958 2008 written by Michael Jünger and published by Springer Science & Business Media. This book was released on 2009-11-06 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience.

Download or read book Dual Feasible Functions for Integer Programming and Combinatorial Optimization written by Cláudio Alves and published by Springer. This book was released on 2016-01-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a postgraduate audience the keys they need to understand and further develop a set of tools for the efficient computation of lower bounds and valid inequalities in integer programs and combinatorial optimization problems. After discussing the classical approaches described in the literature, the book addresses how to extend these tools to other non-standard formulations that may be applied to a broad set of applications. Examples are provided to illustrate the underlying concepts and to pave the way for future contributions.

Download or read book Optimization Methods in Finance written by Gerard Cornuejols and published by Cambridge University Press. This book was released on 2006-12-21 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

Download or read book Integer Programming and Combinatorial Optimization written by Jon Lee and published by Springer. This book was released on 2014-05-17 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014, held in Bonn, Germany, in June 2014. The 34 full papers presented were carefully reviewed and selected from 143 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.