Generating efficient solutions with reservation levels in Multiobjective Stochastic Integer Problems

Abstract

This paper considers a special class of multiobjective stochastic in- teger linear programming (MOSILP) problems involving random variable co- efficients in the constraints. The presumed constraints reliability levels are less than one, then chance constrained programming (CCP) is used to handle with the randomness. It is shown how these problems can be transformed into equiv- alent multiobjective nonlinear integer programming (EMONLIP) problem when the random variables are independent and normally distributed with mean and variance that are linear in the decision variables. The algorithm developed here is based on the notion of level sets and level curves. It finds the Pareto optimal solutions throughout a linear integer program defined by eigenvalue relaxation. keywords: Multiple objective programming, Stochastic Programming, Chance constrained programming, nonlinear programming, level sets, level curves.