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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 describe and compare stochastic network optimization models for investment planning under uncertainty, focusing on multi-period a sset allocation and active portfolio management problems.
Abstract: We describe and compare stochastic network optimization models for investment planning under uncertainty. Emphasis is placed on multiperiod a sset allocation and active portfolio management problems. Myopic as well as multiple period models are considered. In the case of multiperiod models, the uncertainty in asset returns filters into the constraint coefficient matrix, yielding a multi-scenario program formulation. Different scenario generation procedures are examined. The use of utility functions to reflect risk bearing attitudes results in nonlinear stochastic network models. We adopt a newly proposed decomposition procedure for solving these multiperiod stochastic programs. The performance of the models in simulations based on historical data is discussed.

123 citations

Journal ArticleDOI
TL;DR: It is concluded that the presented SDP approach can provide operation policy highly adaptive to uncertainties arising from wind and price, and can help the wind company optimally manage its generation with ESS.
Abstract: This paper proposes an adaptive optimal policy for hourly operation of an energy storage system (ESS) in a grid-connected wind power company. The purpose is to time shift wind energy to maximize the expected daily profit following uncertainties in wind generation and electricity price. A stochastic dynamic programming (SDP) framework is adopted to formulate this problem, and an objective function approximation method is applied to improve the SDP computational efficiency. Case studies on the Electric Reliability Council of Texas demonstrate that the resultant profits from SDP-based operation policy are considerably higher than those from deterministic policy, and comparable to those from the perfect information model. It is concluded that the presented SDP approach can provide operation policy highly adaptive to uncertainties arising from wind and price. The proposed framework can help the wind company optimally manage its generation with ESS.

123 citations

Journal ArticleDOI
TL;DR: In this article, a class of stochastic optimization problems characterized by non-differentiability of the objective function is examined and it is shown that, in many cases, the expected value of the target function is differentiable and thus the resulting optimization problem can be solved by using classical analytical or numerical methods.
Abstract: In this paper, we examine a class of stochastic optimization problems characterized by nondifferentiability of the objective function. It is shown that, in many cases, the expected value of the objective function is differentiable and, thus, the resulting optimization problem can be solved by using classical analytical or numerical methods. The results are subsequently applied to the solution of a problem of economic resource allocation.

122 citations

Journal ArticleDOI
TL;DR: The authors propose several algorithmic and implementation advances in their parallel solver PIPS-IPM for stochastic optimization problems, including a novel, incomplete, augmented, multicore, sparse factorization implemented within the PARDISO linear solver and new multicore- and GPU-based dense matrix implementations.
Abstract: A scalable approach computes in operationally-compatible time the energy dispatch under uncertainty for electrical power grid systems of realistic size with thousands of scenarios. The authors propose several algorithmic and implementation advances in their parallel solver PIPS-IPM for stochastic optimization problems. New developments include a novel, incomplete, augmented, multicore, sparse factorization implemented within the PARDISO linear solver and new multicore- and GPU-based dense matrix implementations. They show improvement on the interprocess communication on Cray XK7 and XC30 systems. PIPS-IPM is used to solve 24-hour horizon power grid problems with up to 1.95 billion decision variables and 1.94 billion constraints on Cray XK7 and Cray XC30, with observed parallel efficiencies and solution times within an operationally defined time interval. To the authors' knowledge, "real-time"-compatible performance on a broad range of architectures for this class of problems hasn't been possible prior to this work.

122 citations

Journal ArticleDOI
TL;DR: This paper studies a problem, common to a wide variety of manufacturing companies, of determining the production schedule of style goods, such as clothing and consumer durables, under capacity constraints, by exploiting the problem's two-level hierarchical structure.
Abstract: In this paper we study a problem, common to a wide variety of manufacturing companies, of determining the production schedule of style goods, such as clothing and consumer durables, under capacity constraints. Demand for items is stochastic and occurs in the last season of the planning horizon. Demand estimates are revised in each period. We exploit the problem's two-level hierarchical structure, which is characterized by families and items. Production changeover costs from one family to another are high, compared to other costs. However, changeover costs between items in the same family are negligible. We first formulate this problem as a difficult-to-solve stochastic mixed integer programming problem. Then, exploiting the problem's hierarchical structure, we formulate a deterministic, mixed integer programming problem and solve it by means of an algorithm that provides an approximate solution. A lower bound is obtained by applying generalized linear programming to the approximate problem. We illustrate the procedure using the disguised data of a consumer electronics company. The computational results demonstrate the effectiveness of the proposed approach in a practical setting.

122 citations


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