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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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28 Feb 1985
TL;DR: A slide comprising a pair of telescopically related track members, ball bearings supporting the track members for relative longitudinal movement, a cage or retainer for the ball bearings longitudinally movable relative to the trackMembers, and a device for locking the retainer against movement from a predetermined locking position relative to one of the track Members when the other of theTrack members is moved longitudally out of engagement with the said one track member.
Abstract: A slide comprising a pair of telescopically related track members, ball bearings supporting the track members for relative longitudinal movement, a cage or retainer for the ball bearings longitudinally movable relative to the track members, and a device for locking the retainer against movement from a predetermined locking position relative to one of the track members when the other of the track members is moved longitudinally out of engagement with the said one track member. The locking device includes a locking member carried on the retainer and a cooperating locking member carried on the said one track member, the locking members being engageable when the retainer is in its said locking position and the said other track member is disengaged from the said one track member.

193 citations

Journal ArticleDOI
TL;DR: In this paper, a mixed integer linear programming (MILP) formulation for stochastic unit commitment is proposed to optimize system operation by simultaneously scheduling energy production, standing/spinning reserves and inertia-dependent fast frequency response in light of uncertainties associated with wind production and generation outages.
Abstract: High penetration of wind generation will increase the requirement for fast frequency response services as currently wind plants do not provide inertial response. Although the importance of inertia reduction has been widely recognized, its impact on the system scheduling has not been fully investigated. In this context, this paper proposes a novel mixed integer linear programming (MILP) formulation for stochastic unit commitment that optimizes system operation by simultaneously scheduling energy production, standing/spinning reserves and inertia-dependent fast frequency response in light of uncertainties associated with wind production and generation outages. Post-fault dynamic frequency requirements, 1) rate of change of frequency, 2) frequency nadir and 3) quasi-steady-state frequency are formulated as MILP constraints by using the simplified model of system dynamics. Moreover the proposed methodology enables the impact of wind uncertainty on system inertia to be considered. Case studies are carried out on the 2030 Great Britain system to demonstrate the importance of incorporating inertia-dependent fast frequency response in the stochastic scheduling and to indicate the potential for the proposed model to inform reviews of grid codes associated with fast frequency response and future development of inertia-related market.

193 citations

Journal ArticleDOI
TL;DR: It is proved that the classical mean-variance criterion leads to computational intractability even in the simplest stochastic programs, and a number of alternative mean-risk functions are shown to be computationally tractable using slight variants of existing stochastically programming decomposition algorithms.
Abstract: Traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criterion. A common approach to addressing risk in decision making problems is to consider a weighted mean-risk objective, where some dispersion statistic is used as a measure of risk. We investigate the computational suitability of various mean-risk objective functions in addressing risk in stochastic programming models. We prove that the classical mean-variance criterion leads to computational intractability even in the simplest stochastic programs. On the other hand, a number of alternative mean-risk functions are shown to be computationally tractable using slight variants of existing stochastic programming decomposition algorithms. We propose decomposition-based parametric cutting plane algorithms to generate mean-risk efficient frontiers for two particular classes of mean-risk objectives.

191 citations

Journal ArticleDOI
TL;DR: This short paper considers a discretization procedure often employed in practice and shows that the solution of the discretized algorithm converges to the Solution of the continuous algorithm, as theDiscretization grids become finer and finer.
Abstract: The computational solution of discrete-time stochastic optimal control problems by dynamic programming requires, in most cases, discretization of the state and control spaces whenever these spaces are infinite. In this short paper we consider a discretization procedure often employed in practice. Under certain compactness and Lipschitz continuity assumptions we show that the solution of the discretized algorithm converges to the solution of the continuous algorithm, as the discretization grids become finer and finer. Furthermore, any control law obtained from the discretized algorithm results in a value of the cost functional which converges to the optimal value of the problem.

191 citations

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...

190 citations


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