Two-stage Stochastic Programming Problem with fuzzy random variables
Subject Areas : Stochastics ProblemsSuresh__Kumar__Barik Suresh__Kumar__Barik 1 * , Sarbeswar Mohanty 2
1 - Utkal University
2 - KIIT Deemed to be University
Keywords: Stochastic programming, Fuzzy stochastic programming, Fuzzy two-stage stochastic non-linear programming, Fuzzy random variables, Triangular fuzzy number.,
Abstract :
The objective of the present work is to develop a fuzzy random two-stage stochastic programming problem by considering some of the right hand side parameters of the constraints as fuzzy random variables with known fuzzy probability distributions along with known parameters as positive triangular fuzzy number. Both randomness and fuzziness are simultaneously considered in the present model. The recommended mathematical programming model can not be solved directly due to presence of fuzzy-randomness in the model parameters. Therefore, the problem has been first transformed into a crisp equivalent nonlinear programming model by removing the fuzziness and randomness from the proposed model. Therefore the crisp equivalent model is solved using the standard nonlinear programming technique. A numerical example is presented to demonstrate the usefulness of the suggested methodology.
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