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Advances in Operations Research
Volume 2012 (2012), Article ID 279181, 21 pages
http://dx.doi.org/10.1155/2012/279181
Research Article

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

1Department of Mathematics, Indian Institute of Technology, Kharagpur 721 302, India
2Department of Mining Engineering, Indian Institute of Technology, Kharagpur 721 302, India

Received 17 March 2012; Accepted 14 June 2012

Academic Editor: Albert P. M. Wagelmans

Copyright © 2012 S. K. Barik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.