Two-stage stochastic programming problems involving interval discrete random variables

Abstract

In this paper, we propose a two-stage stochastic linear programming problem considering some of the left hand side and right hand side of linear constraints parameters as interval discrete random variables with known probability distribution and rest of the parameters are precisely known. Both the randomness and discrete intervals are simultaneously considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are studied in two-stage stochastic programming. To solve the stated problem, first we remove the randomness from the problem and formulate an equivalent deterministic linear programming model with interval coefficients. Then the deterministic model is solved using the solution procedure of linear programming with interval coefficients. We obtain the upper bound 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 process. A numerical example is presented to demonstrate the usefulness of the proposed methodology.