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Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables

Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highlights the possible risk involved in the decision-making tool. A numerical example is presented to demonstrate the proposed solution procedure. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Operations Research Hindawi Publishing Corporation

Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables

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Publisher
Hindawi Publishing Corporation
Copyright
Copyright © 2012 S. K. Barik et al.
ISSN
1687-9147
eISSN
1687-9155
Publisher site
See Article on Publisher Site

Abstract

Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highlights the possible risk involved in the decision-making tool. A numerical example is presented to demonstrate the proposed solution procedure.

Journal

Advances in Operations ResearchHindawi Publishing Corporation

Published: Dec 17, 2012

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