Computation of some stochastic linear programming problems with Cauchy and extreme value distributions

Abstract

Stochastic programming is concerned with optimization problems in which some or all parameters are treated as random variables in order to capture the uncertainty which is almost always an inherent feature of the system being modelled. It is a methodology for allocating today’s resources to meet tomorrow’s unknown demands. A general approach to deal with uncertainty is to assign a probability distribution to the unknown parameters. The basic idea used in stochastic optimization is to convert the probabilistic model to an equivalent deterministic model. The resulting model is then solved by standard linear or non-linear programming methods. In this paper two probability distributions, the Cauchy distribution and the extreme value distribution, are introduced for stochastic programming. Two different approaches are applied to transform the probabilistic multi-objective linear programming problem into deterministic models. The computational procedures of the models are discussed.