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: It is shown that, under certain conditions, the presented model has a set of closed-form solutions, and the effects of random wind speed on the generated power can be readily assessed.
Abstract: In this paper a load dispatch model for the system consisting of both thermal generators and wind turbines is developed. The stochastic wind power is included in the model as a constraint. It is shown that, under certain conditions, the presented model has a set of closed-form solutions. The availability of closed-form solutions is helpful to gain more fundamental insights, such as the impact of a particular parameter on the optimal solution. Moreover, the feasible ranges of optimal solutions are given in the case that the output power of thermal turbines is restricted. Furthermore, the probability distribution and the average of solutions are derived. This is called the wait-and-see approach in the discipline of stochastic programming. The present work shows that the effects of random wind speed on the generated power can be readily assessed.
159 citations
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TL;DR: Extensions of the classical Markowitz mean-variance portfolio optimization model are studied, which considers that the expected asset returns are stochastic by introducing a probabilistic constraint, and proposes an exact solution approach, which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time.
Abstract: In this paper, we study extensions of the classical Markowitz' mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint imposing that the expected return of the constructed portfolio must exceed a prescribed return level with a high confidence level. We study the deterministic equivalents of these models. In particular, we define under which types of probability distributions the deterministic equivalents are second-order cone programs, and give exact or approximate closed-form formulations. Second, we account for real-world trading constraints, such as the need to diversify the investments in a number of industrial sectors, the non-profitability of holding small positions and the constraint of buying stocks by lots, modeled with integer variables. To solve the resulting problems, we propose an exact solution approach in which the uncertainty in the estimate of the expected returns and the integer trading restrictions are simultaneously considered. The proposed algorithmic approach rests on a non-linear branch-and-bound algorithm which features two new branching rules. The first one is a static rule, called idiosyncratic risk branching, while the second one is dynamic and called portfolio risk branching. The proposed branching rules are implemented and tested using the open-source framework of the solver Bonmin. The comparison of the computational results obtained with standard MINLP solvers and with the proposed approach shows the effectiveness of this latter which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time.
159 citations
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TL;DR: A stochastic programming model with probabilistic constraints aimed to solve both the location and the dimensioning problems in order to achieve a reliable level of service and minimize the overall costs is developed.
159 citations
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TL;DR: Recent advances that have addressed some of the barriers that have prevented optimization under uncertainty for mostly linear models are described.
159 citations
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TL;DR: This paper approximate two-stage robust binary programs by their corresponding K -adaptability problems, in which the decision maker precommits to K second-stage policies, here -and-now, and implements the best of these policies once the uncertain parameters are observed.
Abstract: Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multistage problems with continuous recourse. This paper takes a step toward extending the robust optimization methodology to problems with integer recourse, which have largely resisted solution so far. To this end, we approximate two-stage robust binary programs by their corresponding K-adaptability problems, in which the decision maker precommits to K second-stage policies, here -and-now, and implements the best of these policies once the uncertain parameters are observed. We study the approximation quality and the computational complexity of the K-adaptability problem, and we propose two mixed-integer linear programming reformulations that can be solved with off-the-shelf software. We demonstrate the effectiveness of our reformulations for stylized instances o...
158 citations