Topic
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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TL;DR: In this paper, a method based on stochastic programming that explicitly incorporates uncertainty into the RTO problem is presented, which is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly.
145 citations
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TL;DR: This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions.
Abstract: Discrete-continuous optimization problems are commonly modeled in algebraic form as mixed-integer linear or nonlinear programming models. Since these models can be formulated in different ways, leading either to solvable or nonsolvable problems, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models. This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. An overview is provided of major research results that have emerged in this area. Basic concepts are emphasized as well as the major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixed-integer optimization models that exhibit strong continuous relaxations, which often translates into shorter computational times. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3276–3295, 2013
145 citations
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TL;DR: In this paper, a decentralized methodology to optimally schedule generating units while simultaneously determining the geographical allocation of the required reserve is proposed for an interconnected multi-area power system with cross-border trading in the presence of wind power uncertainty.
Abstract: This paper proposes a decentralized methodology to optimally schedule generating units while simultaneously determining the geographical allocation of the required reserve. We consider an interconnected multi-area power system with cross-border trading in the presence of wind power uncertainty. The multi-area market-clearing model is represented as a two-stage stochastic programming model. The proposed decentralized procedure relies on an augmented Lagrangian algorithm that requires no central operator intervention but just moderate interchanges of information among neighboring regions. The methodology proposed is illustrated using an example and a realistic case study.
145 citations
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TL;DR: In this paper, a stochastic programming-based tool is proposed to support adaptive transmission planning under market and regulatory uncertainties, where the objective is to minimize expected transmission and generation costs over the time horizon.
Abstract: We propose a stochastic programming-based tool to support adaptive transmission planning under market and regulatory uncertainties. We model investments in two stages, differentiating between commitments that must be made now and corrective actions that can be undertaken as new information becomes available. The objective is to minimize expected transmission and generation costs over the time horizon. Nonlinear constraints resulting from Kirchhoff's voltage law are included. We apply the tool to a 240-bus representation of the Western Electricity Coordinating Council and model uncertainty using three scenarios with distinct renewable electricity mandates, emissions policies, and fossil fuel prices. We conclude that the cost of ignoring uncertainty (the cost of using naive deterministic planning methods relative to explicitly modeling uncertainty) is of the same order of magnitude as the cost of first-stage transmission investments. Furthermore, we conclude that heuristic rules for constructing transmission plans based on scenario planning can be as suboptimal as deterministic plans.
144 citations
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TL;DR: A model for portfolio selection based on the semiabsolute deviation measure of risk, which can be transformed to a linear interval programming model studied in the paper, is proposed.
Abstract: This paper discusses a class of linear programming problems with interval coefficients in both the objective functions and constraints. The noninferior solutions to such problems are defined based on two order relations between intervals, and can be found by solving a parametric linear programming problem. Considering the uncertain returns of assets in capital markets as intervals, we propose a model for portfolio selection based on the semiabsolute deviation measure of risk, which can be transformed to a linear interval programming model studied in the paper. The method is illustrated by solving a simplified portfolio selection problem.
144 citations