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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, the authors propose an offering strategy for a wind power producer with market power that participates in the day-ahead market as a price-maker, and in the balancing market as an deviator.
Abstract: As a result of subsidies and technological maturity, renewable electricity producers have grown in some jurisdictions to clearly dominant positions in the market. Under this context, we propose an offering strategy for a wind power producer with market power that participates in the day-ahead market as a price-maker, and in the balancing market as a deviator. Uncertainty pertaining to wind power production and balancing market price is represented through a set of correlated scenarios. The proposed model is a stochastic mathematical program with equilibrium constraints (MPEC) that can be recast as a tractable mixed-integer linear programming (MILP) problem, which is solvable using available optimization software. Results from an illustrative example and two case studies show the effectiveness of the proposed model.

178 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered nonlinear programming problems with stochastic constraints and showed that the deterministic surrogate problem CE-P contains a penalty function which penalizes violation of the constraints in the mean.
Abstract: We consider nonlinear programming problem P with stochastic constraints. The Lagrangean corresponding to such problems has a stochastic part, which in this work is replaced by its certainty equivalent in the sense of expected utility theory. It is shown that the deterministic surrogate problem CE-P thus obtained, contains a penalty function which penalizes violation of the constraints in the mean. The approach is related to several known methods in stochastic programming such as: chance constraints, stochastic goal programming, reliability programming and mean-variance analysis. The dual problem of CE-P is studied for problems with stochastic righthand sides in the constraints and a comprehensive duality theory is developed by introducing a new certainty equivalent NCE concept. Motivation for the NCE and its potential role in Decision Theory are discussed, as well as mean-variance approximations.

178 citations

Journal ArticleDOI
TL;DR: The developed TISP model provides a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken and furnishes the reflection of uncertainties presented as both probabilities and intervals.
Abstract: This study introduces a two-stage interval-stochastic programming (TISP) model for the planning of solid-waste management systems under uncertainty. The model is derived by incorporating the concept of two-stage stochastic programming within an interval-parameter optimization framework. The approach has the advantage that policy determined by the authorities, and uncertain information expressed as intervals and probability distributions, can be effectively communicated into the optimization processes and resulting solutions. In the modeling formulation, penalties are imposed when policies expressed as allowable waste-loading levels are violated. In its solution algorithm, the TISP model is converted into two deterministic submodels, which correspond to the lower and upper bounds for the desired objective-function value. Interval solutions, which are stable in the given decision space with associated levels of system-failure risk, can then be obtained by solving the two submodels sequentially. Two special characteristics of the proposed approach make it unique compared with other optimization techniques that deal with uncertainties. First, the TISP model provides a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken; second, it furnishes the reflection of uncertainties presented as both probabilities and intervals. The developed model is applied to a hypothetical case study of regional solid-waste management. The results indicate that reasonable solutions have been generated. They provide desired waste-flow patterns with minimized system costs and maximized system feasibility. The solutions present as stable interval solutions with different risk levels in violating the waste-loading criterion and can be used for generating decision alternatives.

177 citations

Journal ArticleDOI
TL;DR: Estimates of the sample sizes required to solve a multistage stochastic programming problem with a given accuracy by the (conditional sampling) sample average approximation method are derived based on Cramer's Large Deviations Theorem.

177 citations

Journal ArticleDOI
TL;DR: The CALM model, designed to deal with uncertainty affecting both assets and liabilities (in the form of scenario dependent payments or borrowing costs) is presented, which is based on the current version of MSLiP.
Abstract: Multistage stochastic programming - in contrast to stochastic control - has found wideapplication in the formulation and solution of financial problems characterized by a largenumber of state variables and a generally low number of possible decision stages. Theliterature on the use of multistage recourse modelling to formalize complex portfolio optimizationproblems dates back to the early seventies, when the technique was first adopted tosolve a fixed income security portfolio problem. We present here the CALM model, whichhas been designed to deal with uncertainty affecting both assets (in either the portfolio orthe market) and liabilities (in the form of scenario dependent payments or borrowing costs).We consider as an instance a pension fund problem in which portfolio rebalancing is allowedover a long-term horizon at discrete time points and where liabilities refer to five differentclasses of pension contracts. The portfolio manager, given an initial wealth, seeks the maximizationof terminal wealth at the horizon, with investment returns modelled as discretestate random vectors. Decision vectors represent possible investments in the market andholding or selling assets in the portfolio, as well as borrowing decisions from a credit lineor deposits with a bank. Computational results are presented for a set of 10-stage portfolioproblems using different solution methods and libraries (OSL, CPLEX, OB1). The portfolioproblem, with an underlying vector data process which allows up to 2688 realizations at the10-year horizon, is solved on an IBM RS6000y590 for a set of twenty-four large-scale testproblems using the simplex and barrier methods provided by CPLEX (the latter for eitherlinear or quadratic objective), the predictorycorrector interior point method provided in OB1,the simplex method of OSL, the MSLiP-OSL code instantiating nested Benders decompositionwith subproblem solution using OSL simplex, and the current version of MSLiP.

177 citations


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