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Showing papers on "Stochastic programming published in 1998"


Journal ArticleDOI
TL;DR: In this paper, an introduction to stochastic programming is presented, which is based on the idea of Stochastic Programming (SPP) and is used in our work.
Abstract: (1998). Introduction to Stochastic Programming. Journal of the Operational Research Society: Vol. 49, No. 8, pp. 897-898.

1,274 citations


Journal ArticleDOI
TL;DR: A fuzzy simulation based genetic algorithm is designed for solving chance constrained programming from stochastic to fuzzy environments and some numerical examples are discussed.

624 citations


Book
30 Sep 1998
TL;DR: In this paper, the average cost optimization theory for countable state spaces is presented, as well as an inventory model for finite state spaces and a cost minimization theory for continuous time processes.
Abstract: Optimization Criteria. Finite Horizon Optimization. Infinite Horizon Discounted Cost Optimization. An Inventory Model. Average Cost Optimization for Finite State Spaces. Average Cost Optimization Theory for Countable State Spaces. Computation of Average Cost Optimal Policies for Infinite State Spaces. Optimization Under Actions at Selected Epochs. Average Cost Optimization of Continuous Time Processes. Appendices. Bibliography. Index.

475 citations


Journal ArticleDOI
TL;DR: A stochastic version of the interdictor's problem: Minimize the expected maximum flow through the network when interdiction successes are binary random variables is formulated and solved.
Abstract: Using limited assets, an interdictor attempts to destroy parts of a capacitated network through which an adversary will subsequently maximize flow. We formulate and solve a stochastic version of the interdictor's problem: Minimize the expected maximum flow through the network when interdiction successes are binary random variables. Extensions are made to handle uncertain arc capacities and other realistic variations. These two-stage stochastic integer programs have applications to interdicting illegal drugs and to reducing the effectiveness of a military force moving materiel, troops, information, etc., through a network in wartime. Two equivalent model formulations allow Jensen's inequality to be used to compute both lower and upper bounds on the objective, and these bounds are improved within a sequential approximation algorithm. Successful computational results are reported on networks with over 100 nodes, 80 interdictable arcs, and 180 total arcs.

367 citations


Journal ArticleDOI
TL;DR: A stochastic branch and bound method for solving Stochastic global optimization problems is proposed and random accuracy estimates derived.
Abstract: A stochastic branch and bound method for solving stochastic global optimization problems is proposed. As in the deterministic case, the feasible set is partitioned into compact subsets. To guide the partitioning process the method uses stochastic upper and lower estimates of the optimal value of the objective function in each subset. Convergence of the method is proved and random accuracy estimates derived. Methods for constructing stochastic upper and lower bounds are discussed. The theoretical considerations are illustrated with an example of a facility location problem.

340 citations


Journal ArticleDOI
TL;DR: The model is based on an inexact chance-constrained programming method, which improves upon the existing inexact and stochastic programming approaches by allowing both distribution information in B and uncertainties in A and C to be effectively incorporated within its optimization process.

324 citations


01 Jan 1998
TL;DR: A COMPREHENSIVE approach called the decision support problem technique is being developed and implemented at the University of Houston to provide support for human judgment in designing an artifact that can be manufactured and maintained.
Abstract: 1. Our Frame of Reference A COMPREHENSIVE approach called the decision support problem technique" is being developed and implemented at the University of Houston to provide support for human judgment in designing an artifact that can be manufactured and maintained. Decision support problems (DSPs) provide a means for modeling decisions encountered in design, manufacture, and maintenance. Multiple objectives that are quantified using analysis-based "hard" and insight-based "soft" information can be modeled in the DSPs. For real-world, practical systems, not all of the information will be available for modeling systems comprehensively and correctly in the early stages of the project. Therefore, the solution to the problem, even if it is obtained using optimization techniques, cannot be the optimum with respect to the real world. However, this solution can be used to support a designer's quest for a superior solution. In a computerassisted environment, this support is provided in the form of optimal solutions for decision support problems. Formulation and solution of DSPs provide a means for making the following types of decisions:

289 citations


Journal ArticleDOI
TL;DR: In this paper, a statistical inference is developed and applied to estimation of the error, validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm for two-stage stochastic programming with recourse where the random data have a continuous distribution.
Abstract: In this paper we consider stochastic programming problems where the objective function is given as an expected value function. We discuss Monte Carlo simulation based approaches to a numerical solution of such problems. In particular, we discuss in detail and present numerical results for two-stage stochastic programming with recourse where the random data have a continuous (multivariate normal) distribution. We think that the novelty of the numerical approach developed in this paper is twofold. First, various variance reduction techniques are applied in order to enhance the rate of convergence. Successful application of those techniques is what makes the whole approach numerically feasible. Second, a statistical inference is developed and applied to estimation of the error, validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

287 citations


Proceedings ArticleDOI
01 May 1998
TL;DR: It is shown that the fundamental problem of finding an optimal policy which maximizes the average performance level of a system, subject to a constraint on the power consumption, can be formulated as a stochastic optimization problem called policy optimization.
Abstract: Dynamic power management schemes (also called policies) can be used to control the power consumption levels of electronic systems, by setting their components in different states, each characterized by a performance level and a power consumption. In this paper, we describe power-managed systems using a finite-state, stochastic model. Furthermore, we show that the fundamental problem of finding an optimal policy which maximizes the average performance level of a system, subject to a constraint on the power consumption, can be formulated as a stochastic optimization problem called policy optimization. Policy optimization can be solved exactly in polynomial time (in the number of states of the model). We implemented a policy optimization tool and tested the quality of the optimal policies on a realistic case study.

278 citations


Proceedings ArticleDOI
01 Dec 1998
TL;DR: This work presents a review of methods for optimizing stochastic systems using simulation and focuses on gradient based techniques for optimization with respect to continuous decision parameters and on random search methods for optimizationWith respect to discrete decision parameters.
Abstract: We present a review of methods for optimizing stochastic systems using simulation. The focus is on gradient based techniques for optimization with respect to continuous decision parameters and on random search methods for optimization with respect to discrete decision parameters.

254 citations


Journal ArticleDOI
TL;DR: This paper develops and analyzes a model of an oil property, where production rates and oil prices both vary stochastically over time and the decision maker may terminate production or accelerate production by drilling additional wells.
Abstract: There are two major competing procedures for evaluating risky projects where managerial flexibility plays an important role: one is decision analytic, based on stochastic dynamic programming, and the other is option pricing theory (or contingent claims analysis), based on the no-arbitrage theory of financial markets. In this paper, we show how these two approaches can be profitably integrated to evaluate oil properties. We develop and analyze a model of an oil property-either a developed property or a proven but undeveloped reserve-where production rates and oil prices both vary stochastically over time and, at any time, the decision maker may terminate production or accelerate production by drilling additional wells. The decision maker is assumed to be risk averse and can hedge price risks by trading oil futures contracts. We also describe extensions of this model that incorporate additional uncertainties and options, discuss its use in exploration decisions and in evaluating a portfolio of properties rather than a single property, and briefly describe other potential applications of this integrated methodology.

Journal ArticleDOI
TL;DR: The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition and finite convergence of the method is established when Gomory’s fractional cutting plane algorithm or a branch-and-bound algorithm is applied.
Abstract: We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of the method is established when Gomory’s fractional cutting plane algorithm or a branch-and-bound algorithm is applied.

Journal ArticleDOI
TL;DR: A Historical Sketch on Sensitivity Analysis and Parametric Programming T.J. Greenberg and the Optimal Set and Optimal Partition Approach.
Abstract: Foreword. Preface. 1. A Historical Sketch on Sensitivity Analysis and Parametric Programming T. Gal. 2. A Systems Perspective: Entity Set Graphs H. Muller-Merbach. 3. Linear Programming 1: Basic Principles H.J. Greenberg. 4. Linear Programming 2: Degeneracy Graphs T. Gal. 5. Linear Programming 3: The Tolerance Approach R.E. Wendell. 6. The Optimal Set and Optimal Partition Approach A.B. Berkelaar, et al. 7. Network Models G.L. Thompson. 8. Qualitative Sensitivity Analysis A. Gautier, et al. 9. Integer and Mixed-Integer Programming C. Blair. 10. Nonlinear Programming A.S. Drud, L. Lasdon. 11. Multi-Criteria and Goal Programming J. Dauer, Yi-Hsin Liu. 12. Stochastic Programming and Robust Optimization H. Vladimirou, S.A. Zenios. 13. Redundancy R.J. Caron, et al. 14. Feasibility and Viability J.W. Chinneck. 15. Fuzzy Mathematical Programming H.-J. Zimmermann. Subject Index.

Journal ArticleDOI
TL;DR: In this article, a robustness measure that penalizes second-stage costs that are above the expected cost is introduced, thus making possible the solution of large-scale problems through linear programming techniques.
Abstract: The need to model uncertainty in process design and operations has long been recognized. A frequently taken approach, the two-stage paradigm, involves partitioning the problem variables into two stages: those that have to be decided before and those that can be decided after the uncertain parameters reveal themselves. The resulting two-stage stochastic optimization models minimize the sum of the costs of the first stage and the expected cost of the second stage. A potential limitation of this approach is that it does not account for the variability of the second-stage costs and might lead to solutions where the actual second-stage costs are unacceptably high. In order to resolve this difficulty, we introduce a robustness measure that penalizes second-stage costs that are above the expected cost. Incorporating this measure into stochastic programming formulations does not introduce nonlinearlities, thus making possible the solution of large-scale problems through linear programming techniques. The propose...

Journal ArticleDOI
TL;DR: In this paper, the authors present the CALM model which has been designed to deal with uncertainty affecting both assets (in either the portfolio or the market) and liabilities (in the form of scenario dependent payments or borrowing costs).
Abstract: Multistage stochastic programming (in contrast to stochastic control) has found wide application in the formulation and solution of financial problems characterized by a large number of state variables and a generally low number of possible decision stages. The literature on the use of multistage recourse modelling to formalize complex portfolio optimization problems dates back to the early seventies, when the technique was first adopted to solve a fixed interest security portfolio problem. We present here the CALM model which has been designed to deal with uncertainty affecting both assets (in either the portfolio or the market) and liabilities (in the form of scenario dependent payments or borrowing costs). We consider as an instance a pension fund problem in which portfolio rebalancing is allowed over a long-term horizon at discrete time points and where liabilities refer to five different classes of pension contracts. The portfolio manager, given an initial wealth, seeks the maximization of terminal wealth at the horizon, with investment returns modelled as discrete state random vectors. Decision vectors represent possible investments in the market and holding or selling assets in the portfolio, as well as borrowing decisions from a credit line or deposits with a bank. Computational results are presented for a set of 10-stage portfolio problems using different solution methods and libraries (OSL,CPLEX,OB1). The portfolio problem with an underlying vector data process which allows up to 2688 realizations at the 10 year horizon is solved on an IBM RS6000/590 for a set of twenty four large scale test problems using the simplex and barrier methods provided by CPLEX (the latter for either linear or quadratic objective), the predictor/corrector interior point method provided in OB1, the simplex method of OSL, the MSLiP-OSL code instantiating nested Benders decomposition with subproblem solution using OSL simplex and the current version of MSLiP.

Journal ArticleDOI
TL;DR: The CALM model, designed to deal with uncertainty affecting both assets and liabilities (in the form of scenario dependent payments or borrowing costs) is presented, which is based on the current version of MSLiP.
Abstract: Multistage stochastic programming - in contrast to stochastic control - has found wideapplication in the formulation and solution of financial problems characterized by a largenumber of state variables and a generally low number of possible decision stages. Theliterature on the use of multistage recourse modelling to formalize complex portfolio optimizationproblems dates back to the early seventies, when the technique was first adopted tosolve a fixed income security portfolio problem. We present here the CALM model, whichhas been designed to deal with uncertainty affecting both assets (in either the portfolio orthe market) and liabilities (in the form of scenario dependent payments or borrowing costs).We consider as an instance a pension fund problem in which portfolio rebalancing is allowedover a long-term horizon at discrete time points and where liabilities refer to five differentclasses of pension contracts. The portfolio manager, given an initial wealth, seeks the maximizationof terminal wealth at the horizon, with investment returns modelled as discretestate random vectors. Decision vectors represent possible investments in the market andholding or selling assets in the portfolio, as well as borrowing decisions from a credit lineor deposits with a bank. Computational results are presented for a set of 10-stage portfolioproblems using different solution methods and libraries (OSL, CPLEX, OB1). The portfolioproblem, with an underlying vector data process which allows up to 2688 realizations at the10-year horizon, is solved on an IBM RS6000y590 for a set of twenty-four large-scale testproblems using the simplex and barrier methods provided by CPLEX (the latter for eitherlinear or quadratic objective), the predictorycorrector interior point method provided in OB1,the simplex method of OSL, the MSLiP-OSL code instantiating nested Benders decompositionwith subproblem solution using OSL simplex, and the current version of MSLiP.

Journal ArticleDOI
TL;DR: Technical aspects of the Russell-Yasuda Kasai financial planning model are discussed, including the models for the discrete distribution scenario generation processes for the uncertain parameters of the model, and a comparison of algorithms used in the model's solution.
Abstract: This paper discusses technical aspects of the Russell-Yasuda Kasai financial planning model. These include the models for the discrete distribution scenario generation processes for the uncertain parameters of the model, the mathematical approach used to develop the infinite-horizon end-effects part of the model, a comparison of algorithms used in the model's solution, and a comparison of the multistage stochastic linear programming model with the previous technology, static mean-variance analysis. Experience and benefits of the model in Yasuda-Kasai's financial planning process is also discussed.

Journal ArticleDOI
TL;DR: Borders and algorithms are given for the case where the distributions and the variables controllinginformation discovery are discrete and an algorithmic procedure for solving problems of this type is proposed.
Abstract: In the “standard” formulation of a stochastic program with recourse, the distribution ofthe random parameters is independent of the decisions. When this is not the case, the problemis significantly more difficult to solve. This paper identifies a class of problems that are“manageable” and proposes an algorithmic procedure for solving problems of this type. Wegive bounds and algorithms for the case where the distributions and the variables controllinginformation discovery are discrete. Computational experience is reported.

Journal ArticleDOI
TL;DR: The framework is based on a two-state stochastic MINLP formulation for the maximization of a function comprising the expected value of the profit, operating and fixed costs of the plant to address process synthesis problems under uncertainty.

Journal ArticleDOI
TL;DR: A general stochastic search procedure is proposed, which develops the concept of the branch-and-bound method, and the main idea is to process large collections of possible solutions and to devote more attention to the most promising groups.
Abstract: The optimal allocation of indivisible resources is formalized as a stochastic optimization problem involving discrete decision variables. A general stochastic search procedure is proposed, which develops the concept of the branch-and-bound method. The main idea is to process large collections of possible solutions and to devote more attention to the most promising groups. By gathering more information to reduce the uncertainty and by narrowing the search area, the optimal solution can be found with probability one. Special techniques for calculating stochastic lower and upper bounds are discussed. The results are illustrated by a computational experiment.

Journal ArticleDOI
TL;DR: A multi-stage stochastic programming approach to formulate a flexible energy plan that incorporates multiple future scenarios and provides for mid-course corrections depending upon the actual realizations of future uncertainties can give insights beyond the scope of an analysis based on deterministic scenarios.

Journal ArticleDOI
TL;DR: This paper discusses three classes of dynamic optimization problems with discontinuities: path-constrained problems, hybrid discrete/continuous problems, and mixed-integer dynamic optimize problems.
Abstract: Many engineering tasks can be formulated as dynamic optimization or open-loop optimal control problems, where we search a priori for the input profiles to a dynamic system that optimize a given performance measure over a certain time period. Further, many systems of interest in the chemical processing industries experience significant discontinuities during transients of interest in process design and operation. This paper discusses three classes of dynamic optimization problems with discontinuities: path-constrained problems, hybrid discrete/continuous problems, and mixed-integer dynamic optimization problems. In particular, progress toward a general numerical technology for the solution of large-scale discontinuous dynamic optimization problems is discussed.

Journal ArticleDOI
TL;DR: This paper gives an overview of some stochastic optimization strategies, namely, evolution strategies, genetic algorithms, and simulated annealing, and how these methods can be applied to problems in electrical engineering.
Abstract: This paper gives an overview of some stochastic optimization strategies, namely, evolution strategies, genetic algorithms, and simulated annealing, and how these methods can be applied to problems in electrical engineering. Since these methods usually require a careful tuning of the parameters which control the behavior of the strategies (strategy parameters), significant features of the algorithms implemented by the authors are presented. An analytical comparison among them is performed. Finally, results are discussed on three optimization problems.

Book ChapterDOI
01 Jan 1998
TL;DR: In this paper, two kinds of models for the cost-optimal generation of electric power under uncertain load are introduced: (i) a dynamic model for the short-term operation and (ii) a power production planning model.
Abstract: A power generation system comprising thermal and pumpedstorage hydro plants is considered. Two kinds of models for the cost-optimal generation of electric power under uncertain load are introduced: (i) a dynamic model for the short-term operation and (ii) a power production planning model. In both cases the presence of stochastic data in the optimization model leads to multi-stage and two-stage stochastic programs respectively. Both stochastic programming problems involve a large number of mixed-integer (stochastic) decisions but their constraints are loosely coupled across operating power units. This is used to design Lagrangian relaxation methods for both models which lead to a decomposition into stochastic single unit subproblems. For the dynamic model a Lagrangian decomposition based algorithm is described in more detail. Special emphasis is put on a discussion of the duality gap the efficient solution of the multi-stage single unit subproblems and on solving the dual problem by bundle methods for convex nondifferentiable optimization.

Journal Article
TL;DR: It is proved that under mild conditions an optimal solution is contained in a finite set and a basic scheme to enumerate this set is presented and improvements are suggested to reduce the number of function evaluations needed.
Abstract: In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Grobner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.

BookDOI
01 Jan 1998
TL;DR: In this article, the authors proposed a multicriteria approach for the analysis and prediction of business failure in Greece and a new Rough Set approach to evaluation of bank bankruptcy risk.
Abstract: I: Multivariate Data Analysis and Multicriteria Analysis in Portfolio Selection Proposal for the Composition of a Solvent Portfolio with Chaos Theory and Data Analysis D Karapistolis, et al An Entropy Risk Aversion in Portfolio Selection A Scarelli Multicriteria Decision Making and Portfolio Management with Arbitrage Pricing Theory Ch Hurson, N Ricci-Xella II: Multivariate Data Analysis and Multicriteria Analysis in Business Failure, Corporate Performance and Bank Bankruptcy The Application of the Multi-Factor Model in the Analysis of Corporate Failure EM Vermeulen, et al Multivariate Analysis for the Assessment of Corporate Performance: The Case of Greece Y Caloghirou, et al Stable Set Internally Maximal: A Classification Method with Overlapping A Couturier, B Fioleau A Multicriteria Approach for the Analysis and Prediction of Business Failure in Greece C Zopounidis, et al A New Rough Set Approach to Evaluation of Bankruptcy Risk S Greco, et al FINCLAS: A Multicriteria Decision Support System for Financial Classification Problems C Zopounidis, M Doumpos A Mathematical Approach of Determining Bank Risks Premium J Gupta, Ph Spieser III: Linear and Stochastic Programming in Portfolio Management Designing Callable Bonds Using Simulated Annealing MR Holmer, et al Towards Sequential Sampling Algorithms for Dynamic Portfolio Management Z Chen, et al The Defeasance in the Framework of Finite Convergence in Stochastic Programming Ph Spieser, A Chevalier Mathematical Programming and Risk Management of Derivative Securities L Clewlow, et al IV: Fuzzy Sets and Artificial Intelligence Techniques in Financial Decisions Financial Risk in Investment J Gil-Aluja The Selection of a Portfolio Through a Fuzzy Genetic Algorithm: The POFUGENA Model E Lopez-Gonzalez, et al Predicting Interest Rates Using Artificial Neural Networks Th Politof, D Ulmer V: Multicriteria Analysis in Country Risk Evaluation Assessing Country Risk Using Multicriteria Analysis M Doumpos, et al Author Index

Proceedings ArticleDOI
16 Dec 1998
TL;DR: This work delineates circumstances under which the rollout algorithms are guaranteed to perform better than the heuristics on which they are based, and shows computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better thanThe performance of their underlying heuristic.
Abstract: Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. We focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, with considerable savings in computation over optimal algorithms. We delineate circumstances under which the rollout algorithms are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics.

Journal ArticleDOI
TL;DR: A discussion of methodologies for nonlinear geophysical inverse problems is presented in this paper, where a new class of method is presented which offers potential in both the optimization and the error analysis stage of the inversion.
Abstract: A discussion of methodologies for nonlinear geophysical inverse problems is presented Geophysical inverse problems are often posed as optimization problems in a finite-dimensional parameter space An Earth model is usually described by a set of parameters representing one or more geophysical properties (eg the speed with which seismic waves travel through the Earth's interior) Earth models are sought by minimizing the discrepancies between observation and predictions from the model, possibly, together with some regularizing constraint The resulting optimization problem is usually nonlinear and often highly so, which may lead to multiple minima in the misfit landscape Global (stochastic) optimization methods have become popular in the past decade A discussion of simulated annealing, genetic algorithms and evolutionary programming methods is presented in the geophysical context Less attention has been paid to assessing how well constrained, or resolved, individual parameters are Often this problem is poorly posed A new class of method is presented which offers potential in both the optimization and the `error analysis' stage of the inversion This approach uses concepts from the field of computational geometry The search algorithm described here does not appear to be practical in problems with dimension much greater than 10

Journal ArticleDOI
TL;DR: In this paper, the authors developed multi-period dynamic models for fixed-income portfolio management under uncertainty, using multi-stage stochastic programming with recourse, and evaluated their performance vis-a-vis single-period models.

Book ChapterDOI
01 Jan 1998
TL;DR: The solution method uses the concept of a p-Ievel efficient point (pLEP) intoduced by the first author (1990) and works in such a way that first all pLEP's are enumerated, then a cutting plane method does the rest of the job.
Abstract: The most important static stochastic programming models, that can be formulated in connection with a linear programming problem, where some of the right-hand side values are random variables, are: the simple recourse model, the probabilistic constrained model and the combination of the two. In this paper we present algorithmic solution to the second and third models under the assumption that the random variables have a discrete joint distribution. The solution method uses the concept of a p-level efficient point (pLEP) intoduced by the first author (1990) and works in such a way that first all pLEP’s are enumerated, then a cutting plane method does the rest of the job.