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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 paper, a Bayesian stochastic dynamic programming (BSDP) model is proposed to generate optimal reservoir operating rules, which includes inflow, storage, and forecast as state variables, and describes streamflows with a discrete lag 1 Markov process.
Abstract: Operation of reservoir systems using stochastic dynamic programming (SDP) and Bayesian decision theory (BDT) is investigated in this study. The proposed model, called Bayesian stochastic dynamic programming (BSDP), which includes inflow, storage, and forecast as state variables, describes streamflows with a discrete lag 1 Markov process, and uses BDT to incorporate new information by updating the prior probabilities to posterior probabilities, is used to generate optimal reservoir operating rules. This continuous updating can significantly reduce the effects of natural and forecast uncertainties in the model. In order to test the value of the BSDP model for generating optimal operating rules, real-time reservoir operation simulation models are constructed using 95 years of monthly historical inflows of the Gunpowder River to Loch Raven reservoir in Maryland. The rules generated by the BSDP model are applied in an operation simulation model and their performance is compared with an alternative stochastic dynamic programming (ASDP) model and a classical stochastic dynamic programming (SDP) model. BSDP differs from the other two models in the selection of state variables and the way the transition probabilities are formed and updated.

147 citations

Book
01 Jan 1976

147 citations

Journal ArticleDOI
TL;DR: A method is presented to obtain sharp lower and upper bounds for the probability that at least one out of a number of events in an arbitrary probability space will occur, utilizing only the first few terms in the inclusion-exclusion formula.
Abstract: We present a method to obtain sharp lower and upper bounds for the probability that at least one out of a number of events in an arbitrary probability space will occur. The input data are some of the binomial moments of the occurrences, such as the sum of the probabilities of the individual events, or the sum of the joint probabilities of all pairs of events. We develop a special, very simple linear programming algorithm to obtain these bounds. The method allows us to compute good bounds in an optimal way, utilizing only the first few terms in the inclusion-exclusion formula. Possible applications include obtaining bounds for the reliability of a stochastic system, solving algorithmically some stochastic programming problems, and approximating multivariate probabilities in statistics. In a numerical example we approximate the probability that a Gaussian process runs below a given level in a number of consecutive epochs.

147 citations

Journal ArticleDOI
TL;DR: In this article, a two-stage integer stochastic program with recourse where the first stage variables determine which products to produce and how much to produce, and the second stage variables decide how the products are allocated to satisfy the realized demand is considered.
Abstract: In this paper we consider a single period multi-product inventory problem with stochastic demand, setup cost for production, and one-way product substitution in the downward direction. We model the problem as a two-stage integer stochastic program with recourse where the first stage variables determine which products to produce and how much to produce, and the second stage variables determine how the products are allocated to satisfy the realized demand. We exploit structural properties of the model and utilize a combination of optimization techniques including network flow, dynamic programming, and simulation-based optimization to develop effective heuristics. Through a computational study, we evaluate the performance of our heuristics by comparison with the corresponding optimal solution obtained from a large scale mixed integer linear program. The computational study indicates that our solution methodology can be very effective (98.8% on average) and can handle industrial-sized problems efficiently. We...

146 citations

Journal ArticleDOI
TL;DR: A general stochastic search procedure is proposed, which develops the concept of the branch-and-bound method, and the main idea is to process large collections of possible solutions and to devote more attention to the most promising groups.
Abstract: The optimal allocation of indivisible resources is formalized as a stochastic optimization problem involving discrete decision variables. A general stochastic search procedure is proposed, which develops the concept of the branch-and-bound method. The main idea is to process large collections of possible solutions and to devote more attention to the most promising groups. By gathering more information to reduce the uncertainty and by narrowing the search area, the optimal solution can be found with probability one. Special techniques for calculating stochastic lower and upper bounds are discussed. The results are illustrated by a computational experiment.

146 citations


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