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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, the authors used stochastic dynamic programming (SDP) and statistical model for the streamflow prediction to determine the optimal monthly total hydrogeneration for a large hydroelectric power system in the Pacific Northwest.
Abstract: For a large hydroelectric power system, such as that of the Pacific Northwest, an important operational decision each month is the amount of hydrogeneration. This decision is important because the inflow of the water is uncertain while hydro, with zero marginal cost, can be used not only to satisfy firm load commitments, but also to displace other firm resources or to serve secondary loads. In such a case, the tradeoff between savings at the present and expected benefits in the future is determined mainly by the total hydrogeneration. The use of a composite representation of multireservoir hydroelectric power systems to determine the optimal monthly total hydrogeneration is described. The analytical tool employed is that of stochastic dynamic programming, and the statistical model for the streamflow prediction is based on previous flows and snowpack information. For the anticipated 1975 system in the Pacific Northwest, comparison between the optimal operation introduced here and the presently used rule-curve operation indicates that substantial savings may be obtained, mainly owing to the more uniform displacement of the high marginal cost thermal resources by hydrogeneration.

114 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed an algorithm for multistage stochastic linear programs with recourse where random quantities in different stages are independent. And they proved that the algorithm is convergent with probability one.
Abstract: We propose an algorithm for multistage stochastic linear programs with recourse where random quantities in different stages are independent. The algorithm approximates successively expected recourse functions by building up valid cutting planes to support these functions from below. In each iteration, for the expected recourse function in each stage, one cutting plane is generated using the dual extreme points of the next-stage problem that have been found so far. We prove that the algorithm is convergent with probability one.

114 citations

Journal ArticleDOI
TL;DR: Numerical results suggest that the persistency model is capable of obtaining estimates that perform as well, if not better, than classical methods, such as logit and cross-nested logit models, and can be used to obtain choice probability estimates for more complex choice problems.
Abstract: Given a discrete maximization problem with a linear objective function where the coefficients are chosen randomly from a distribution, we would like to evaluate the expected optimal value and the marginal distribution of the optimal solution. We call this the persistency problem for a discrete optimization problem under uncertain objective, and the marginal probability mass function of the optimal solution is named the persistence value. In general, this is a difficult problem to solve, even if the distribution of the objective coefficient is well specified. In this paper, we solve a subclass of this problem when the distribution is assumed to belong to the class of distributions defined by given marginal distributions, or given marginal moment conditions. Under this model, we show that the persistency problem maximizing the expected objective value over the set of distributions can be solved via a concave maximization model. The persistency model solved using this formulation can be used to obtain important qualitative insights to the behavior of stochastic discrete optimization problems. We demonstrate how the approach can be used to obtain insights to problems in discrete choice modeling. Using a set of survey data from a transport choice modeling study, we calibrate the random utility model with choice probabilities obtained from the persistency model. Numerical results suggest that our persistency model is capable of obtaining estimates that perform as well, if not better, than classical methods, such as logit and cross-nested logit models. We can also use the persistency model to obtain choice probability estimates for more complex choice problems. We illustrate this on a stochastic knapsack problem, which is essentially a discrete choice problem under budget constraint.

114 citations

Book
01 Jan 1971

114 citations

Journal ArticleDOI
03 Mar 2007-Top
TL;DR: In this paper, the authors generalize the definition of the bounds for the optimal value of the objective function for various deterministic equivalent models in multistage stochastic programs and prove a similar chain of inequalities with the lower and upper bounds depending substantially on the structure of the problem.
Abstract: We generalize the definition of the bounds for the optimal value of the objective function for various deterministic equivalent models in multistage stochastic programs. The parameters EVPI and VSS were introduced for two-stage models. The parameter EVPI, the expected value of perfect information, measures how much it is reasonable to pay to obtain perfect information about the future. The parameter VSS, the value of the stochastic solution, allows us to obtain the goodness of the expected solution value when the expected values are replaced by the random values for the input variables. We extend the definition of these parameters to the multistage stochastic model and prove a similar chain of inequalities with the lower and upper bounds depending substantially on the structure of the problem.

113 citations


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