Free linearpart cutting optimizer
Abaffy and Allevi present a modified version of the L-shaped method in, used to solve two-stage stochastic linear programs with fixed recourse. This method is essentially an external approximation algorithm that can effectively solve the large-scale problems that occur after the stochastic programming is transformed into deterministic mathematical programming. It is based on the duality theory, and the algorithm converges to the optimal solution by determining the feasible cutting plane and optimal cutting, and solving the main problem step by step. In these methods, the dual decomposition L-shape algorithm established in the literature is the most effective algorithm for solving two-stage stochastic programming.
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With regard to the theory and methods of two-stage stochastic programming, a very systematic study has been conducted and many important solutions have been proposed. It is a method by making decisions before and after observing the value of a variable.
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Classic stochastic programming with recourse is a type of expected value problem, modeling based on a two-stage decision-making method. According to different research problems, stochastic programming mainly consists of three problems: distribution problem, expected value problem, and probabilistic constraint programming problem.
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Currently, the main method to solve the stochastic programming is to transform the stochastic programming into its own deterministic equivalence class and using the existing deterministic planning method to solve it. It was proposed by Dantzig, an American economist in 1956. Stochastic programming is an important method to solve decision problems in random environment.