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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 article, a decision-making framework based on stochastic programming is proposed for a retailer to determine the sale price of electricity to the customers based on time-of-use (TOU) rates, and manage a portfolio of different contracts in order to procure its demand and to hedge against risks, within a medium-term period.
Abstract: This paper proposes a decision-making framework, based on stochastic programming, for a retailer: 1) to determine the sale price of electricity to the customers based on time-of-use (TOU) rates, and 2) to manage a portfolio of different contracts in order to procure its demand and to hedge against risks, within a medium-term period. Supply sources include the pool, self-production facilities and several instruments such as forward contracts, call options, and interruptible contracts. The objective is to maximize the profit and simultaneously to minimize the risks in terms of a multi-period risk measure. Moreover, the risks are measured using conditional value at risk (CVaR) methodology. The reaction of the customers to the retailers' selling prices as well as the competition between the retailers is modeled through a market share function. The problem is formulated as a mixed-integer stochastic programming. It is solved by a decomposition technique, and the decomposed parts are solved by a branch-and-bound algorithm.

176 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extend the theory of stochastic programs with recourse to the general case when essentially all the parameters involved are random, and show that without restriction, the equivalent deterministic form of a deterministic program with recourse is a convex program for which we obtain some additional properties when some of the parameters of the original problem are constant.
Abstract: : So far the study of stochastic programs with recourse has been limited to the case (called by G. Dantzig programming under uncertainty) when only the right-hand sides or resources of the problem are random. In this paper the authors extend the theory to the general case when essentially all the parameters involved are random. This generalization immediately raises the problem of attributing a precise meaning to the stochastic constraints. They examine a probability formulation (satisfying the constraints almost surely) and a possibility formulation (satisfying the constraints for all values of the random parameters in the support of their joint distribution) and show them equivalent under a rather weak but curious W-condition. Finally, they prove that without restriction the equivalent deterministic form of a stochastic program with recourse is a convex program for which we obtain some additional properties when some of the parameters of the original problem are constant. The applications of the theoretical results of this paper to certain classes of stochastic programs which have arisen from practical problems will be presented in a separate paper: 'Stochastic Programs with Recourse: Special Forms.' (Author)

176 citations

Proceedings ArticleDOI
04 Nov 1991
TL;DR: The authors address incorporating a meta-level evolutionary programming that can simultaneously evolve optimal settings for these parameters while a search for the appropriate extrema is being conducted, and indicate the suitability of such a procedure.
Abstract: A brief review of efforts is simulated evolution is given. Evolutionary programming is a stochastic optimization technique that is useful for discovering the extrema of a nonlinear function. To implement such a search, several high-level parameters must be chosen, such as the amount of mutational noise, the severity of the mutation noise, and so forth. The authors address incorporating a meta-level evolutionary programming that can simultaneously evolve optimal settings for these parameters while a search for the appropriate extrema is being conducted. The preliminary experiments reported indicate the suitability of such a procedure. Meta-evolutionary programming was able to converge to points on each of two response surfaces that were close to the global optimum. >

175 citations

Journal ArticleDOI
TL;DR: This paper model the network retrofit problem as a two-stage stochastic programming problem that optimizes a mean-risk objective of the system loss and develops an efficient algorithm to efficiently handle the binary integer variables in the first stage and the nonlinear recourse in the second stage of the model formulation.

175 citations

Journal ArticleDOI
TL;DR: This work solves the stochastic Darcy flow problem in primal formulation via the spectral SFEM and focuses on its efficient iterative solution, and bases the block-diagonal preconditioner on algebraic multigrid to achieve optimal computational complexity.
Abstract: Deterministic models of fluid flow and the transport of chemicals in flows in heterogeneous porous media incorporate partial differential equations (PDEs) whose material parameters are assumed to be known exactly. To tackle more realistic stochastic flow problems, it is fitting to represent the permeability coefficients as random fields with prescribed statistics. Traditionally, large numbers of deterministic problems are solved in a Monte Carlo framework and the solutions are averaged to obtain statistical properties of the solution variables. Alternatively, so-called stochastic finite-element methods (SFEMs) discretize the probabilistic dimension of the PDE directly leading to a single structured linear system. The latter approach is becoming extremely popular but its computational cost is still perceived to be problematic as this system is orders of magnitude larger than for the corresponding deterministic problem. A simple block-diagonal preconditioning strategy incorporating only the mean component of the random field coefficient and based on incomplete factorizations has been employed in the literature and observed to be robust, for problems of moderate variance, but without theoretical analysis. We solve the stochastic Darcy flow problem in primal formulation via the spectral SFEM and focus on its efficient iterative solution. To achieve optimal computational complexity, we base our block-diagonal preconditioner on algebraic multigrid. In addition, we provide new theoretical eigenvalue bounds for the preconditioned system matrix. By highlighting the dependence of these bounds on all the SFEM parameters, we illustrate, in particular, why enriching the stochastic approximation space leads to indefinite system matrices when unbounded random variables are employed.

175 citations


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