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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: Borders on the value of the stochastic solution are presented, that is, the potential benefit from solving the stoChastic program over solving a deterministic program in which expected values have replaced random parameters.
Abstract: Stochastic linear programs have been rarely used in practical situations largely because of their complexity. In evaluating these problems without finding the exact solution, a common method has been to find bounds on the expected value of perfect information. In this paper, we consider a different method. We present bounds on the value of the stochastic solution, that is, the potential benefit from solving the stochastic program over solving a deterministic program in which expected values have replaced random parameters. These bounds are calculated by solving smaller programs related to the stochastic recourse problem.

310 citations

Journal ArticleDOI
TL;DR: This paper presents a unit commitment model for studying the impact of large-scale wind integration in power systems with transmission constraints and system component failures, and presents a scenario selection algorithm for selecting and weighing wind power production scenarios and composite element failures.
Abstract: In this paper we present a unit commitment model for studying the impact of large-scale wind integration in power systems with transmission constraints and system component failures. The model is formulated as a two-stage stochastic program with uncertain wind production in various locations of the network as well as generator and transmission line failures. We present a scenario selection algorithm for selecting and weighing wind power production scenarios and composite element failures, and we provide a parallel dual decomposition algorithm for solving the resulting mixed-integer program. We validate the proposed scenario selection algorithm by demonstrating that it outperforms alternative reserve commitment approaches in a 225 bus model of California with 130 generators and 375 transmission lines. We use our model to quantify day-ahead generator capacity commitment, operating cost impacts, and renewable energy utilization levels for various degrees of wind power integration. We then demonstrate that failing to account for transmission constraints and contingencies can result in significant errors in assessing the economic impacts of renewable energy integration. Subject classifications: unit commitment; stochastic programming; wind power; transmission constraints. Area of review: Environment, Energy, and Sustainability.

308 citations

Journal ArticleDOI
TL;DR: This work used Bayesian updating of the probability of success of the two options and stochastic dynamic programming to determine the optimal strategy over a specified number of years to manage ecological systems in the face of uncertainty.
Abstract: Active adaptive management balances the requirements of management with the need to learn about the system being managed, which leads to better decisions It is difficult to judge the benefit of management actions that accelerate information gain, relative to the benefit of making the best management decision given what is known at the time We present a first step in developing methods to optimize management decisions that incorporate both uncertainty and learning via adaptive management We assumed a manager can allocate effort to discrete units (eg, areas for revegetation or animals for reintroduction), the outcome can be measured as success or failure (eg, the revegetation in an area is successful or the animal survives and breeds), and the manager has two possible management options from which to choose We further assumed that there is an annual budget that may be allocated to one or both of the two options and that the manager must decide on the allocation We used Bayesian updating of the probability of success of the two options and stochastic dynamic programming to determine the optimal strategy over a specified number of years, The costs, level of certainty about the success of the two options, and the timeframe of management all influenced the optimal allocation of the annual budget In addition, the choice of management objective had a large influence on the optimal decision In a case study of Merri Creek, Melbourne, Australia, we applied the approach to determining revegetation strategies Our approach can be used to determine how best to manage ecological systems in the face of uncertainty

307 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a methodology to characterize the stochastic processes pertaining to wind speed at different geographical locations via scenarios, where each one of these scenarios embodies time dependencies and is spatially dependent of the scenarios describing other wind processes.

305 citations

Journal ArticleDOI
TL;DR: A tabu search heuristic is developed for a version of the stochastic vehicle routing problem where customers are present at locations with some probabilities and have random demands and produces an optimal solution in 89.45% of cases.
Abstract: This paper considers a version of the stochastic vehicle routing problem where customers are present at locations with some probabilities and have random demands. A tabu search heuristic is developed for this problem. Comparisons with known optimal solutions on problems whose sizes vary from 6 to 46 customers indicate that the heuristic produces an optimal solution in 89.45% of cases, with an average deviation of 0.38% from optimality.

305 citations


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