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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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Journal ArticleDOI
TL;DR: In this paper, the authors compare stochastic and reserve methods and evaluate the benefits of a combined approach for the efficient management of uncertainty in the unit commitment problem and show that unit commitment solutions obtained for the combined approach are robust and superior with respect to the traditional approach in terms of both economics and reliability metrics.
Abstract: Uncertainty in power systems operations has been traditionally managed by multistage decision making and operating reserve requirements. A familiar example of multistage decisions is day-ahead unit commitment and real-time economic dispatch. An alternate approach for managing uncertainty is a stochastic formulation, which allows the explicit modeling of the sources of uncertainty. This paper compares stochastic and reserve methods and evaluates the benefits of a combined approach for the efficient management of uncertainty in the unit commitment problem. Numerical studies show that unit commitment solutions obtained for the combined approach are robust and superior with respect to the traditional approach in terms of both economics and reliability metrics.

415 citations

Book ChapterDOI
01 Jan 2003
TL;DR: This chapter starts with motivating examples and then proceeds to formulation of linear, and later nonlinear, two stage stochastic programming problems, and gives a functional description of two stage programs.
Abstract: In this introductory chapter we discuss some basic approaches to modeling of stochastic optimization problems. We start with motivating examples and then proceed to formulation of linear, and later nonlinear, two stage stochastic programming problems. We give a functional description of two stage programs. After that we proceed to a discussion of multistage stochastic programming and its connections with dynamic programming. We end this chapter by introducing robust and min–max approaches to stochastic programming. Finally, in the appendix, we introduce and briefly discuss some relevant concepts from probability and optimization theories.

410 citations

Journal ArticleDOI
01 Jan 1969-Tellus A
TL;DR: Stochastic dynamic prediction as mentioned in this paper assumes the laws governing atmospheric behavior are entirely deterministic, but seeks solutions corresponding to probabilistic statements of the initial conditions, thus recognizing the impossibility of exact or sufficiently dense observations.
Abstract: Stochastic dynamic prediction assumes the laws governing atmospheric behavior are entirely deterministic, but seeks solutions corresponding to probabilistic statements of the initial conditions, thus recognizing the impossibility of exact or sufficiently dense observations. The equation that must be solved is the continuity equation for probability. For practical reasons only approximate solutions to this equation are possible in general. Deterministic forecasts represent a very low order of approximation. More exact methods are developed and some of the attributes and advantages of stochastic dynamic predictions are illustrated by applying them to a low order set of dynamic equations. Stochastic dynamic predictions have significantly smaller mean square errors than deterministic procedures, and also give specific information on the nature and extent of the uncertainty of the forecast. Also the range of time over which useful forecasts can be obtained is extended. However, they also require considerably more extensive calculations. The question of analysis to obtain the initial stochastic statement of the atmospheric state is considered and one finds here too a promise of significant advantages over present deterministic methods. It is shown how the stochastic method can be used to assess the value of new or improved data by considering their influence on the decrease in the uncertainty of the forecast. Comparisons among physical-numerical models are also made more effectively by applying stochastic methods. Finally the implications of stochastic dynamic prediction on the question of predictability are briefly considered, with the conclusion that some earlier estimates have been too pessimistic. DOI: 10.1111/j.2153-3490.1969.tb00483.x

407 citations

Posted Content
TL;DR: In this article, a method for solving numerical dynamic stochastic optimization problems that avoids root-finding operations is introduced, which is applicable to many microeconomic and macroeconomic problems.
Abstract: This paper introduces a method for solving numerical dynamic stochastic optimization problems that avoids rootfinding operations. The idea is applicable to many microeconomic and macroeconomic problems, including life cycle, buffer-stock, and stochastic growth problems. Software is provided.

405 citations

Journal ArticleDOI
TL;DR: This work presents an algorithm that produces a discrete joint distribution consistent with specified values of the first four marginal moments and correlations, constructed by decomposing the multivariate problem into univariate ones, and using an iterative procedure that combines simulation, Cholesky decomposition and various transformations to achieve the correct correlations.
Abstract: In stochastic programming models we always face the problem of how to represent the random variables. This is particularly difficult with multidimensional distributions. We present an algorithm that produces a discrete joint distribution consistent with specified values of the first four marginal moments and correlations. The joint distribution is constructed by decomposing the multivariate problem into univariate ones, and using an iterative procedure that combines simulation, Cholesky decomposition and various transformations to achieve the correct correlations without changing the marginal moments. With the algorithm, we can generate 1000 one-period scenarios for 12 random variables in 16 seconds, and for 20 random variables in 48 seconds, on a Pentium III machine.

401 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532