Two-stage stochastic programming problems involving multi-choice parameters

In this paper, we propose a two-stage stochastic linear programming model considering some of the right hand side parameters of the first stage constraints as multi-choice parameters and rest of the right hand side parameters of the constraints as exponential random variables with known means. Both the randomness and multi-choiceness are simultaneously considered for the model parameters. Randomness is characterized by some random variables with its distribution and multi-choiceness is handled by using interpolating polynomials. To solve the proposed problem, first we remove the fuzziness and then for multi-choice parameters interpolating polynomials are established. After establishing the deterministic equivalent of the model, standard mathematical programming technique is applied to solve the problem. A numerical example is presented to demonstrate the usefulness of the proposed methodology.