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Showing papers on "Stochastic programming published in 2007"


Book
01 Feb 2007
TL;DR: This research monograph is the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including thetreatment of the intricate measure-theoretic issues.
Abstract: This research monograph is the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including the treatment of the intricate measure-theoretic issues.

1,811 citations


Journal ArticleDOI
TL;DR: The main focus will be on the different approaches to perform robust optimization in practice including the methods of mathematical programming, deterministic nonlinear optimization, and direct search methods such as stochastic approximation and evolutionary computation.

1,435 citations


Journal ArticleDOI
TL;DR: In this article, the authors developed a decision-making tool that can be used by government agencies in planning for flood emergency logistics. But the decision variables include the structure of rescue organizations, locations of rescue resource storehouses, allocations of rescue resources under capacity restrictions, and distributions of resources.
Abstract: This paper aims to develop a decision-making tool that can be used by government agencies in planning for flood emergency logistics. In this article, the flood emergency logistics problem with uncertainty is formulated as two stochastic programming models that allow for the determination of a rescue resource distribution system for urban flood disasters. The decision variables include the structure of rescue organizations, locations of rescue resource storehouses, allocations of rescue resources under capacity restrictions, and distributions of rescue resources. By applying the data processing and network analysis functions of the geographic information system, flooding potential maps can estimate the possible locations of rescue demand points and the required amount of rescue equipment. The proposed models are solved using a sample average approximation scheme. Finally, a real example of planning for flood emergency logistics is presented to highlight the significance of the proposed model as well as the efficacy of the proposed solution strategy.

516 citations


DOI
01 Jan 2007
TL;DR: This paper formulate minimal requirements that should be imposed on a scenario generation method before it can be used for solving the stochastic programming model and shows how the requirements can be tested.
Abstract: Stochastic programs can only be solved with discrete distributions of limited cardinality. Input, however, normally comes in the form of continuous distributions or large data sets. Creating a limited discrete distribution from input is called scenario generation. In this paper, we discuss how to evaluate the quality or suitability of scenario generation methods for a given stochastic programming model. We formulate minimal requirements that should be imposed on a scenario generation method before it can be used for solving the stochastic programming model. We also show how the requirements can be tested. The procedures for testing a scenario generation method is illustrated on a case from portfolio management.

500 citations


Book ChapterDOI
05 Mar 2007
TL;DR: This systematic study is able to find a minimum frequency of change allowed in a problem for two dynamic EMO procedures to adequately track Pareto-optimal frontiers on-line and suggest an automatic decision-making procedure for arriving at a dynamic single optimal solution on- line.
Abstract: Most real-world optimization problems involve objectives, constraints, and parameters which constantly change with time Treating such problems as a stationary optimization problem demand the knowledge of the pattern of change a priori and even then the procedure can be computationally expensive Although dynamic consideration using evolutionary algorithms has been made for single-objective optimization problems, there has been a lukewarm interest in formulating and solving dynamic multi-objective optimization problems In this paper, we modify the commonly-used NSGA-II procedure in tracking a new Pareto-optimal front, as soon as there is a change in the problem Introduction of a few random solutions or a few mutated solutions are investigated in detail The approaches are tested and compared on a test problem and a real-world optimization of a hydro-thermal power scheduling problem This systematic study is able to find a minimum frequency of change allowed in a problem for two dynamic EMO procedures to adequately track Pareto-optimal frontiers on-line Based on these results, this paper also suggests an automatic decision-making procedure for arriving at a dynamic single optimal solution on-line

434 citations


Journal ArticleDOI
TL;DR: This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption, and provides a new solution methodology using the Moreau–Yosida regularization.

388 citations


Book
01 Jan 2007
TL;DR: In this paper, the authors present a general framework for portfolio allocation based on mean-variance analysis and modern portfolio theory, with a focus on portfolio selection with higher moments through expansions of utility functions.
Abstract: Preface. About the Authors. CHAPTER 1. Introduction. Quantitative Techniques in the Investment Management Industry. Central Themes of This Book. Overview of This Book. PART ONE. Portfolio Allocation: Classical Theory and Extensions. CHAPTER 2. Mean-Variance Analysis and Modern Portfolio Theory. The Benefits of Diversification. Mean-Variance Analysis: Overview. Classical Framework for Mean-Variance Optimization. The Capital Market Line. Selection of the Optimal Portfolio When There Is a Risk-Free Asset. More on Utility Functions: A General Framework for Portfolio Choice. Summary. CHAPTER 3. Advances in the Theory of Portfolio Risk Measures. Dispersion and Downside Measures. Portfolio Selection with Higher Moments through Expansions of Utility. Polynomial Goal Programming for Portfolio Optimization with Higher Moments. Some Remarks on the Estimation of Higher Moments. The Approach of Malevergne and Sornette. Summary. CHAPTER 4. Portfolio Selection in Practice. Portfolio Constraints Commonly Used in Practice. Incorporating Transaction Costs in Asset-Allocation Models. Multiaccount Optimization. Summary. PART TWO. Robust Parameter Estimation. CHAPTER 5. Classical Asset Pricing. Definitions. Theoretical and Econometric Models. Random Walk Models. General Equilibrium Theories. Capital Asset Pricing Model (CAPM). Arbitrage Pricing Theory (APT). Summary. CHAPTER 6. Forecasting Expected Return and Risk. Dividend Discount and Residual Income Valuation Models. The Sample Mean and Covariance Estimators. Random Matrices. Arbitrage Pricing Theory and Factor Models. Factor Models in Practice. Other Approaches to Volatility Estimation. Application to Investment Strategies and Proprietary Trading. Summary. CHAPTER 7. Robust Estimation. The Intuition behind Robust Statistics. Robust Statistics. Robust Estimators of Regressions. Confidence Intervals. Summary. CHAPTER 8. Robust Frameworks for Estimation: Shrinkage, Bayesian Approaches, and the Black-Litterman Model. Practical Problems Encountered in Mean-Variance Optimization. Shrinkage Estimation. Bayesian Approaches. Summary. PART THREE. Optimization Techniques. CHAPTER 9. Mathematical and Numerical Optimization. Mathematical Programming. Necessary Conditions for Optimality for Continuous Optimization Problems. Optimization Duality Theory. How Do Optimization Algorithms Work? Summary. CHAPTER 10. Optimization under Uncertainty. Stochastic Programming. Dynamic Programming. Robust Optimization. Summary. CHAPTER 11. Implementing and Solving Optimization Problems in Practice. Optimization Software. Practical Considerations When Using Optimization Software. Implementation Examples. Specialized Software for Optimization Under Uncertainty. Summary. PART FOUR. Robust Portfolio Optimization. CHAPTER 12. Robust Modeling of Uncertain Parameters in Classical Mean-Variance Portfolio Optimization. Portfolio Resampling Techniques. Robust Portfolio Allocation. Some Practical Remarks on Robust Portfolio Allocation Models. Summary. CHAPTER 13. The Practice of Robust Portfolio Management: Recent Trends and New Directions. Some Issues in Robust Asset Allocation. Portfolio Rebalancing. Understanding and Modeling Transaction Costs. Rebalancing Using an Optimizer. Summary. CHAPTER 14. Quantitative Investment Management Today and Tomorrow. Using Derivatives in Portfolio Management. Currency Management. Benchmarks. Quantitative Return-Forecasting Techniques and Model-Based Trading Strategies. Trade Execution and Algorithmic Trading. Summary. APPENDIX A. Data Description: The MSCI World Index. INDEX.

375 citations


Journal ArticleDOI
TL;DR: In this article, a meta-heuristic of ant colony optimization (ACO) for solving the logistics problem arising in disaster relief activities is presented. But, the problem is not solved in an iterative manner and the results indicate that this algorithm performs well in terms of solution quality and run time.
Abstract: This paper presents a meta-heuristic of ant colony optimization (ACO) for solving the logistics problem arising in disaster relief activities The logistics planning involves dispatching commodities to distribution centers in the affected areas and evacuating the wounded people to medical centers The proposed method decomposes the original emergency logistics problem into two phases of decision making, ie, the vehicle route construction, and the multi-commodity dispatch The sub-problems are solved in an iterative manner The first phase builds stochastic vehicle paths under the guidance of pheromone trails while a network flow based solver is developed in the second phase for the assignment between different types of vehicle flows and commodities The performance of the algorithm is tested on a number of randomly generated networks and the results indicate that this algorithm performs well in terms of solution quality and run time

365 citations


Journal ArticleDOI
TL;DR: An approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations is introduced, which converts the original model into a second-order cone program, which is computationally tractable both in theory and in practice.
Abstract: In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. Using a linear decision rule, we also propose a tractable approximation approach for solving a class of multistage chance-constrained stochastic linear optimization problems. An attractive feature of the framework is that we convert the original model into a second-order cone program, which is computationally tractable both in theory and in practice. We demonstrate the framework through an application of a project management problem with uncertain activity completion time.

358 citations


Journal ArticleDOI
TL;DR: A two-stage robust optimization approach for solving network flow and design problems with uncertain demand is described and an upper bound on the probability of infeasibility of a robust solution for a random demand vector is provided.
Abstract: We describe a two-stage robust optimization approach for solving network flow and design problems with uncertain demand. In two-stage network optimization, one defers a subset of the flow decisions until after the realization of the uncertain demand. Availability of such a recourse action allows one to come up with less conservative solutions compared to single-stage optimization. However, this advantage often comes at a price: two-stage optimization is, in general, significantly harder than single-stage optimization. For network flow and design under demand uncertainty, we give a characterization of the first-stage robust decisions with an exponential number of constraints and prove that the corresponding separation problem is NP-hard even for a network flow problem on a bipartite graph. We show, however, that if the second-stage network topology is totally ordered or an arborescence, then the separation problem is tractable. Unlike single-stage robust optimization under demand uncertainty, two-stage robust optimization allows one to control conservatism of the solutions by means of an allowed “budget for demand uncertainty.” Using a budget of uncertainty, we provide an upper bound on the probability of infeasibility of a robust solution for a random demand vector. We generalize the approach to multicommodity network flow and design, and give applications to lot-sizing and location-transportation problems. By projecting out second-stage flow variables, we define an upper bounding problem for the two-stage min-max-min optimization problem. Finally, we present computational results comparing the proposed two-stage robust optimization approach with single-stage robust optimization as well as scenario-based two-stage stochastic optimization.

349 citations


Journal ArticleDOI
TL;DR: This paper overviews several selected topics in this popular area, specifically, recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data, tractability of robust counterparts, links between RO and traditional chance constrained settings of problems with stochastic data, and a novel generic application of the RO methodology in Robust Linear Control.
Abstract: Robust Optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic “uncertain-but- bounded” data perturbations. In this paper, we overview several selected topics in this popular area, specifically, (1) recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data, (2) tractability of robust counterparts, (3) links between RO and traditional chance constrained settings of problems with stochastic data, and (4) a novel generic application of the RO methodology in Robust Linear Control.

Journal ArticleDOI
TL;DR: In this paper, a combined power management/design optimization problem for the performance optimization of FCHVs is formulated, which includes subsystem scaling models to predict the characteristics of components of different sizes, and a parameterizable and near-optimal controller for power management optimization.

Journal ArticleDOI
TL;DR: This work used Bayesian updating of the probability of success of the two options and stochastic dynamic programming to determine the optimal strategy over a specified number of years to manage ecological systems in the face of uncertainty.
Abstract: Active adaptive management balances the requirements of management with the need to learn about the system being managed, which leads to better decisions It is difficult to judge the benefit of management actions that accelerate information gain, relative to the benefit of making the best management decision given what is known at the time We present a first step in developing methods to optimize management decisions that incorporate both uncertainty and learning via adaptive management We assumed a manager can allocate effort to discrete units (eg, areas for revegetation or animals for reintroduction), the outcome can be measured as success or failure (eg, the revegetation in an area is successful or the animal survives and breeds), and the manager has two possible management options from which to choose We further assumed that there is an annual budget that may be allocated to one or both of the two options and that the manager must decide on the allocation We used Bayesian updating of the probability of success of the two options and stochastic dynamic programming to determine the optimal strategy over a specified number of years, The costs, level of certainty about the success of the two options, and the timeframe of management all influenced the optimal allocation of the annual budget In addition, the choice of management objective had a large influence on the optimal decision In a case study of Merri Creek, Melbourne, Australia, we applied the approach to determining revegetation strategies Our approach can be used to determine how best to manage ecological systems in the face of uncertainty

Journal ArticleDOI
TL;DR: A chance constrained compromise programming model (CCCP) is proposed as a deterministic transformation to multi-objective stochastic programming portfolio model based on CP and chance constrained programming (CCP) models.

Book
08 Jan 2007
TL;DR: In this article, the authors propose a simplex method for robust optimization in finance, using linear programming, nonlinear programming, and Quadratic programming, with the use of robust optimization tools.
Abstract: 1. Introduction 2. Linear programming: theory and algorithms 3. LP models: asset/liability cash flow matching 4. LP models: asset pricing and arbitrage 5. Nonlinear programming: theory and algorithms 6. NLP volatility estimation 7. Quadratic programming: theory and algorithms 8. QP models: portfolio optimization 9. Conic optimization tools 10. Conic optimization models in finance 11. Integer programming: theory and algorithms 12. IP models: constructing an index fund 13. Dynamic programming methods 14. DP models: option pricing 15. DP models: structuring asset backed securities 16. Stochastic programming: theory and algorithms 17. SP models: value-at-risk 18. SP models: asset/liability management 19. Robust optimization: theory and tools 20. Robust optimization models in finance Appendix A. Convexity Appendix B. Cones Appendix C. A probability primer Appendix D. The revised simplex method Bibliography Index.

Journal ArticleDOI
Ioana Popescu1
TL;DR: It is proved that for a general class of objective functions, the robust solutions amount to solving a certain deterministic parametric quadratic program, and a general projection property for multivariate distributions with given means and covariances is proved.
Abstract: We provide a method for deriving robust solutions to certain stochastic optimization problems, based on mean-covariance information about the distributions underlying the uncertain vector of returns. We prove that for a general class of objective functions, the robust solutions amount to solving a certain deterministic parametric quadratic program. We first prove a general projection property for multivariate distributions with given means and covariances, which reduces our problem to optimizing a univariate mean-variance robust objective. This allows us to use known univariate results in the multidimensional setting, and to add new results in this direction. In particular, we characterize a general class of objective functions (the so-called one- or two-point support functions), for which the robust objective is reduced to a deterministic optimization problem in one variable. Finally, we adapt a result from Geoffrion (1967a) to reduce the main problem to a parametric quadratic program. In particular, our results are true for increasing concave utilities with convex or concave-convex derivatives. Closed-form solutions are obtained for special discontinuous criteria, motivated by bonus- and commission-based incentive schemes for portfolio management. We also investigate a multiproduct pricing application, which motivates extensions of our results for the case of nonnegative and decision-dependent returns.

Journal ArticleDOI
TL;DR: A generic stochastic model for the design of networks comprising both supply and return channels, organized in a closed loop system, based on the branch-and-cut procedure known as the integer L-shaped method is presented.

Journal Article
TL;DR: This book provides a unified framework based on a sensitivity point of view and introduces new approaches and proposes new research topics within this sensitivity-based framework.
Abstract: Performance optimization is vital in the design and operation of modern engineering systems, including communications, manufacturing, robotics, and logistics. Most engineering systems are too complicated to model, or the system parameters cannot be easily identified, so learning techniques have to be applied. This book provides a unified framework based on a sensitivity point of view. It also introduces new approaches and proposes new research topics within this sensitivity-based framework. This new perspective on a popular topic is presented by a well respected expert in the field.

Journal ArticleDOI
TL;DR: In this paper, a technique based on stochastic programming is proposed to optimally solve the electricity procurement problem faced by a large consumer, where risk aversion is explicitly modeled using the conditional value-at-risk methodology.
Abstract: This paper provides a technique based on stochastic programming to optimally solve the electricity procurement problem faced by a large consumer. Supply sources include bilateral contracts, a limited amount of self-production and the pool. Risk aversion is explicitly modeled using the conditional value-at-risk methodology. Results from a realistic case study are provided and analyzed

Journal ArticleDOI
TL;DR: It is argued that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages.
Abstract: In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.

Journal ArticleDOI
TL;DR: A stochastic mixed-integer linear programming model that involves both hydropower production and physical trading aspects is developed and the effects of including uncertainty explicitly into optimization by comparing the Stochastic approach to a deterministic approach are explored.

01 Jan 2007
TL;DR: Within the framework of multi-stage mixed-integer linear stochastic programming, a short-term production plan for a price-taking hydropower plant operating under uncertainty is developed.

Journal ArticleDOI
TL;DR: The CVRPSD can be formulated as a set partitioning problem and it is shown that the associated column generation subproblem can be solved using a dynamic programming scheme.

Journal ArticleDOI
TL;DR: A probabilistic bi-level linear multi-objective programming problem and its application in enterprise-wide supply chain planning problem where (1) market demand, (2) production capacity of each plant and (3) resource available to all plants for each product are random variables and the constraints may consist of joint probability distributions or not.

Journal ArticleDOI
01 Jan 2007
TL;DR: Experimental results show that the proposed stochastic beam search is more accurate and efficient than both the state-of-the-art meta-heuristic and the traditional determinist beam search.
Abstract: In this paper, the optimization of the Berth Allocation Problem (BAP) is transformed into a multiple stage decision making procedure and a new multiple stage search method, namely stochastic beam search algorithm, is proposed to solve it. New techniques such as an improved beam search scheme, a two-phase node goodness estimation, and a stochastic node selection criteria are proposed. Real-life information provided by Singapore Port was collected as our test data. Experimental results show that the proposed stochastic beam search is more accurate and efficient than both the state-of-the-art meta-heuristic and the traditional determinist beam search.

Journal ArticleDOI
TL;DR: Extensions of the classical Markowitz mean-variance portfolio optimization model are studied, which considers that the expected asset returns are stochastic by introducing a probabilistic constraint, and proposes an exact solution approach, which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time.
Abstract: In this paper, we study extensions of the classical Markowitz' mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint imposing that the expected return of the constructed portfolio must exceed a prescribed return level with a high confidence level. We study the deterministic equivalents of these models. In particular, we define under which types of probability distributions the deterministic equivalents are second-order cone programs, and give exact or approximate closed-form formulations. Second, we account for real-world trading constraints, such as the need to diversify the investments in a number of industrial sectors, the non-profitability of holding small positions and the constraint of buying stocks by lots, modeled with integer variables. To solve the resulting problems, we propose an exact solution approach in which the uncertainty in the estimate of the expected returns and the integer trading restrictions are simultaneously considered. The proposed algorithmic approach rests on a non-linear branch-and-bound algorithm which features two new branching rules. The first one is a static rule, called idiosyncratic risk branching, while the second one is dynamic and called portfolio risk branching. The proposed branching rules are implemented and tested using the open-source framework of the solver Bonmin. The comparison of the computational results obtained with standard MINLP solvers and with the proposed approach shows the effectiveness of this latter which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time.

Journal ArticleDOI
TL;DR: The proposed model, which is called Stochastic Varying Chromosome Length Genetic Algorithm with water Quality constraints (SVLGAQ), is applied to the Ghomrud Reservoir–River system in the central part of Iran and shows, the proposed model for reservoir operation and waste load allocation can reduce theSalinity of the allocated water demands as well as the salinity build-up in the reservoir.

Journal ArticleDOI
TL;DR: The problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function and it is shown that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance.
Abstract: The quality of multi-stage stochastic optimization models as they appear in asset liability management, energy planning, transportation, supply chain management, and other applications depends heavily on the quality of the underlying scenario model, describing the uncertain processes influencing the profit/cost function, such as asset prices and liabilities, the energy demand process, demand for transportation, and the like. A common approach to generate scenarios is based on estimating an unknown distribution and matching its moments with moments of a discrete scenario model. This paper demonstrates that the problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function. We show that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance. The resulting optimization problem can be viewed as a multi-dimensional facility location problem, for which at least good heuristic algorithms exist. For multi-stage problems, a scenario tree is constructed as a nested facility location problem. Numerical convergence results for financial mean-risk portfolio selection conclude the paper.

Journal ArticleDOI
TL;DR: This new model considers as random events the demand, the equivalent availability of the generating plants, and the transmission capacity factor of the transmission lines and introduces a risk factor by means of the mean-variance Markowitz theory.
Abstract: In this paper, a new model for generation and transmission expansion is presented. This new model considers as random events the demand, the equivalent availability of the generating plants, and the transmission capacity factor of the transmission lines. In order to incorporate these random events into an optimization model, stochastic programming and probabilistic constraints are used. A risk factor is introduced in the objective function by means of the mean-variance Markowitz theory. The solved optimization problem is a mixed integer nonlinear program. The expected value of perfect information is obtained in order to show the cost of ignoring uncertainty. The proposed model is illustrated by a six- and a 21-node network using a dc approximation.

Journal ArticleDOI
TL;DR: Earlier work on scenario reduction is extended by relying directly on Fortet-Mourier metrics instead of using upper bounds given in terms of mass transportation problems, and some numerical results are provided.