Stochastic programming problems involving Pareto distribution

Abstract

Stochastic programming is a branch of mathematical programming that considers optimization in the presence of uncertainty. In this paper, both single-objective and multi-objective stochastic programming problems are considered, where the right hand side parameters follow Pareto distribution with known mean and variance. Both the stochastic programming methods namely, chance constrained programming and two-stage stochastic programming are used. In order to solve these stochastic programming problems; we convert these problems into some equivalent deterministic models. Then we use standard mathematical programming techniques for solving single-objective deterministic model. We use fuzzy programming technique to solve the multi-objective deterministic model. The solution procedures are illustrated with an example.