Computation of multi-objective two-stage fuzzy probabilistic programming problem

This paper presents a mathematical model that combines the mathematical models of stochastic programming (SP), namely two-stage stochastic (TSS) programming and chance-constrained programming in fuzzy environment. The complexity of the proposed model is due to multiple objective functions and presence of fuzzy random variables. Since it is difficult to solve the proposed model directly, the mathematical model is converted into an equivalent multi-objective TSS programming crisp model using alpha-cut technique. Then, using the concept of epsilon-constraint method, multi-objective deterministic TSS programming problem is converted into single objective deterministic mathematical model. The transformed model is solved using the existing methodology. Lastly, a numerical example is provided for illustrating the methodology.