scispace - formally typeset
Search or ask a question
Topic

Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: This work presents a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems and finds provably near-optimal solutions to these difficult Stochastic programs using only a moderate amount of computation time.
Abstract: The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps. We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 21694 scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.

461 citations

Journal ArticleDOI
TL;DR: In this article, a stochastic security-constrained multi-period electricity market clearing problem with unit commitment is formulated, where reserve services are determined by economically penalizing the operation of the market by the expected load not served.
Abstract: The first of this two-paper series formulates a stochastic security-constrained multi-period electricity market-clearing problem with unit commitment. The stochastic security criterion accounts for a pre-selected set of random generator and line outages with known historical failure rates and involuntary load shedding as optimization variables. Unlike the classical deterministic reserve-constrained unit commitment, here the reserve services are determined by economically penalizing the operation of the market by the expected load not served. The proposed formulation is a stochastic programming problem that optimizes, concurrently with the pre-contingency social welfare, the expected operating costs associated with the deployment of the reserves following the contingencies. This stochastic programming formulation is solved in the second companion paper using mixed-integer linear programming methods. Two cases are presented: a small transmission-constrained three-bus network scheduled over a horizon of four hours and the IEEE Reliability Test System scheduled over 24 h. The impact on the resulting generation and reserve schedules of transmission constraints and generation ramp limits, of demand-side reserve, of the value of load not served, and of the constitution of the pre-selected set of contingencies are assessed.

459 citations

Journal ArticleDOI
TL;DR: A cutting plane algorithm for two-stage stochastic linear programs with recourse that uses randomly generated observations of random variables to construct statistical estimates of supports of the objective function and establishes the convergence of the algorithm under relatively mild assumptions.
Abstract: We present a cutting plane algorithm for two-stage stochastic linear programs with recourse. Motivated by Benders' decomposition, our method uses randomly generated observations of random variables to construct statistical estimates of supports of the objective function. In general, the resulting piecewise linear approximations do not agree with the objective function in finite time. However, certain subsequences of the estimated supports are shown to accumulate at supports of the objective function, with probability one. From this, we establish the convergence of the algorithm under relatively mild assumptions.

457 citations

Journal ArticleDOI
TL;DR: A stochastic management problem is reformulate as a highly e$cient robust optimization model capable of generating solutions that are progressively less sensitive to the data in the scenario set, and the method proposed herein to transform a robust model into a linear program only requires adding n#m variables.

452 citations

Journal ArticleDOI
TL;DR: A recently developed software tool executing on a computational grid is used to solve many large instances of these problems, allowing for high-quality solutions and to verify optimality and near-optimality of the computed solutions in various ways.
Abstract: We investigate the quality of solutions obtained from sample-average approximations to two-stage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain high-quality solutions and to verify optimality and near-optimality of the computed solutions in various ways.

449 citations


Network Information
Related Topics (5)
Optimization problem
96.4K papers, 2.1M citations
86% related
Scheduling (computing)
78.6K papers, 1.3M citations
85% related
Optimal control
68K papers, 1.2M citations
84% related
Supply chain
84.1K papers, 1.7M citations
83% related
Markov chain
51.9K papers, 1.3M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532