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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 Minimax Regret formulation suitable for large-scale linear programming models was proposed for Greenhouse Gas abatement in the Province of Quebec, where the minimax regret strategy depends only on the extremal scenarios and not on intermediate ones, thus making the approach computationally efficient.

121 citations

Journal ArticleDOI
TL;DR: A stochastic dynamic programming (SDP) approach to unit commitment and dispatch is proposed, minimizing operating costs by making optimal unit commitment, dispatch, and storage decisions in the face of uncertain wind generation.
Abstract: Fluctuating wind production over short time periods is balanced by adjusting generation from thermal plants to meet demand. Thermal ramp rates are limited, so increased variation in wind output as wind penetration increases can add to system operating costs because of the need for more thermal operating reserves. Traditional deterministic modeling techniques fail to fully capture these extra costs. We propose a stochastic dynamic programming (SDP) approach to unit commitment and dispatch, minimizing operating costs by making optimal unit commitment, dispatch, and storage decisions in the face of uncertain wind generation. The SDP solution is compared with two other solutions: 1) that of a deterministic dynamic program with perfect wind predictions to find the cost of imperfect information, and 2) that of a simulation model run under a decision rule, derived from Monte Carlo simulations of the deterministic model, to assess the cost of suboptimal stochastic decision making. An example Netherlands application shows that these costs can amount to several percent of total production costs, depending on installed wind capacity. These are the conclusions of a single simplified case study. Nonetheless, the results indicate that efforts to improve wind forecasting and to develop stochastic commitment models may be highly beneficial.

121 citations

Journal ArticleDOI
TL;DR: This paper shows that, under arbitrary measures for variability, the robust optimization approach might lead to suboptimal solutions to the second-stage planning problem, and proposes sufficient conditions on the variability measure to remedy this problem.
Abstract: Robust-optimization models belong to a special class of stochastic programs, where the traditional expected cost minimization objective is replaced by one that explicitly addresses cost variability. This paper explores robust optimization in the context of two-stage planning systems. We show that, under arbitrary measures for variability, the robust optimization approach might lead to suboptimal solutions to the second-stage planning problem. As a result, the variability of the second-stage costs may be underestimated, thereby defeating the intended purpose of the model. We propose sufficient conditions on the variability measure to remedy this problem. Under the proposed conditions, a robust optimization model can be efficiently solved using a variant of the L-shaped decomposition algorithm for traditional stochastic linear programs. We apply the proposed framework to standard stochastic-programming test problems and to an application that arises in auctioning excess electric power.

121 citations

Journal ArticleDOI
TL;DR: An efficient algorithm for the numerical solution of the stochastic differential equation is developed and interesting properties of the algorithm enable the treatment of problems with a large number of variables.
Abstract: We propose a new stochastic algorithm for the solution of unconstrained vector optimization problems, which is based on a special class of stochastic differential equations. An efficient algorithm for the numerical solution of the stochastic differential equation is developed. Interesting properties of the algorithm enable the treatment of problems with a large number of variables. Numerical results are given.

121 citations

Journal ArticleDOI
TL;DR: Quantitative stability of linear multistage stochastic programs is studied and it is shown that the infima of such programs behave (locally) Lipschitz continuous with respect to the sum of an $L_{r}$-distance and of a distance measure for the filtrations of the original and approximate Stochastic processes.
Abstract: Quantitative stability of linear multistage stochastic programs is studied. It is shown that the infima of such programs behave (locally) Lipschitz continuous with respect to the sum of an $L_{r}$-distance and of a distance measure for the filtrations of the original and approximate stochastic (input) processes. Various issues of the result are discussed and an illustrative example is given. Consequences for the reduction of scenario trees are also discussed.

121 citations


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