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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.


Papers
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Proceedings ArticleDOI
11 Jun 2006
TL;DR: In this paper, a stochastic bottom-up electricity market model is presented to optimise the unit commitment considering five kinds of markets and taking explicitly into account the stochastically behavior of the wind power generation and the prediction error.
Abstract: A large share of integrated wind power causes technical and financial impacts on the operation of the existing electricity system due to the fluctuating behaviour and unpredictability of wind power. The presented stochastic bottom-up electricity market model optimises the unit commitment considering five kinds of markets and taking explicitly into account the stochastic behaviour of the wind power generation and of the prediction error. It can be used for the evaluation of varying electricity prices and system costs due to wind power integration and for the investigation of integration measures.

169 citations

Journal ArticleDOI
TL;DR: A new decomposition method for multistage stochastic linear programming problems is proposed and it is shown that for large problems the authors can obtain substantial gains in efficiency with moderate numbers of processors.
Abstract: A new decomposition method for multistage stochastic linear programming problems is proposed. A multistage stochastic problem is represented in a tree-like form and with each node of the decision tree a certain linear or quadratic subproblem is associated. The subproblems generate proposals for their successors and some backward information for their predecessors. The subproblems can be solved in parallel and exchange information in an asynchronous way through special buffers. After a finite time the method either finds an optimal solution to the problem or discovers its inconsistency. An analytical illustrative example shows that parallelization can speed up computation over every sequential method. Computational experiments indicate that for large problems we can obtain substantial gains in efficiency with moderate numbers of processors.

169 citations

Journal ArticleDOI
TL;DR: This work studies two optimization criteria for the transmission expansion planning problem under the robust optimization paradigm, where the maximum cost and maximum regret of the expansion plan over all uncertainties are minimized, respectively.
Abstract: Due to the long planning horizon, transmission expansion planning is typically subjected to a lot of uncertainties including load growth, renewable energy penetration, policy changes, etc. In addition, deregulation of the power industry and pressure from climate change introduced new sources of uncertainties on the generation side of the system. Generation expansion and retirement become highly uncertain as well. Some of the uncertainties do not have probability distributions, making it difficult to use stochastic programming. Techniques like robust optimization that do not require a probability distribution became desirable. To address these challenges, we study two optimization criteria for the transmission expansion planning problem under the robust optimization paradigm, where the maximum cost and maximum regret of the expansion plan over all uncertainties are minimized, respectively. With these models, our objective is to make planning decisions that are robust against all scenarios. We use a two-layer algorithm to solve the resulting tri-level optimization problems. Then, in our case studies, we compare the performance of the minimax cost approach and the minimax regret approach under different characterizations of uncertainties.

169 citations

Journal ArticleDOI
TL;DR: In this paper, a multi-period supply chain network design problem is addressed, where a target is set for the return on investment and the risk of falling below it is measured and accounted for.
Abstract: In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these types of problems.

168 citations

Journal ArticleDOI
TL;DR: New valid inequalities for these mixed integer programming problems with probabilistic constraints involving random variables with discrete distributions are developed using specific properties of stochastic programming problems and bounds on the probability of the union of events.
Abstract: We consider stochastic programming problems with probabilistic constraints involving random variables with discrete distributions. They can be reformulated as large scale mixed integer programming problems with knapsack constraints. Using specific properties of stochastic programming problems and bounds on the probability of the union of events we develop new valid inequalities for these mixed integer programming problems. We also develop methods for lifting these inequalities. These procedures are used in a general iterative algorithm for solving probabilistically constrained problems. The results are illustrated with a numerical example.

168 citations


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