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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: Reoptimizing the policy when a decision is made within the simulation resulted in better system performance, particularly when severe penalties were incurred for water and power shortages and coarse discretizations were employed in the SDP.
Abstract: This paper compares two approaches for implementing reservoir operating policies derived using stochastic dynamic programming (SDP) models. In particular, operating policies for the Shasta-Trinity system in Northern California are generated using SDP algorithms that employ either multilinear or multidimensional piecewise cubic functions to approximate the cost-to-go function. Release decisions in the simulations are then determined by either (1) interpolating in the policy tables or (2) reoptimizing the policy within the simulation, using the cost-to-go function generated by the SDP. The impact on simulated system performance of several discretization and interpolation schemes in the SDP is also evaluated. Reoptimizing the policy when a decision is made within the simulation resulted in better system performance, particularly when severe penalties were incurred for water and power shortages and coarse discretizations were employed in the SDP.

113 citations

Journal ArticleDOI
TL;DR: In this article, the authors formulate a generation expansion planning problem to determine the type and quantity of power plants to be constructed over each year of an extended planning horizon, considering uncertainty regarding future demand and fuel prices.
Abstract: We formulate a generation expansion planning problem to determine the type and quantity of power plants to be constructed over each year of an extended planning horizon, considering uncertainty regarding future demand and fuel prices. Our model is expressed as a two-stage stochastic mixed-integer program, which we use to compute solutions independently minimizing the expected cost and the Conditional Value-at-Risk; i.e., the risk of significantly larger-than-expected operational costs. We introduce stochastic process models to capture demand and fuel price uncertainty, which are in turn used to generate trees that accurately represent the uncertainty space. Using a realistic problem instance based on the Midwest US, we explore two fundamental, unexplored issues that arise when solving any stochastic generation expansion model. First, we introduce and discuss the use of an algorithm for computing confidence intervals on obtained solution costs, to account for the fact that a finite sample of scenarios was used to obtain a particular solution. Second, we analyze the nature of solutions obtained under different parameterizations of this method, to assess whether the recommended solutions themselves are invariant to changes in costs. The issues are critical for decision makers who seek truly robust recommendations for generation expansion planning.

113 citations

Journal ArticleDOI
TL;DR: An approach for modeling two-stage stochastic programs that yields a form suitable for interior point algorithms by replacing first stage variables with sparse "split variables" in conjunction with side-constraints is described.
Abstract: This paper describes an approach for modeling two-stage stochastic programs that yields a form suitable for interior point algorithms. A staircase constraint structure is created by replacing first stage variables with sparse "split variables" in conjunction with side-constraints. Dense columns are thereby eliminated. The resulting model is larger than traditional stochastic programs, but computational savings are substantial-over a tenfold improvement for the problems tested. A series of experiments with stochastic networks drawn from financial planning demonstrates the attained efficiencies. Comparisons with MINOS and the dual block angular stochastic programming model are provided as benchmarks. The split variable approach is applicable to general two-stage stochastic programs and other dual block angular models.

113 citations

Journal ArticleDOI
TL;DR: In this article, a two-stage stochastic programming approach is applied to efficiently optimize microgrid operations while satisfying a time-varying request and operation constraints, which aims at minimizing the expected cost of correction actions.

113 citations


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