Bi-objective mean-variance method based on Chebyshev inequality bounds for multi-objective stochastic problems.

Multi-objective programming became more and more popular in real world decision making problems in recent decades. There is an underlying and fundamental uncertainty in almost all of these problems. Among different frameworks of dealing with uncertainty, probability and statistic-based schemes are well-known. In this paper, a method is developed to find some efficient solutions of a multi-objective stochastic programming problem. The method composed a process of transforming the stochastic multi-objective problem to a bi-objective equivalent using the concept of Chebyshev inequality bounds and then solving the obtained problem with a fuzzy set based approach. Application of the proposed method is examined on two numerical examples and the results are compared with different methods. These comparisons illustrated that the results are satisfying.