Computation of probabilistic linear programming problems involving normal and log-normal random variables with a joint constraint

Abstract

A method for solving single- and multi-objective probabilistic linear programming problems with a joint constraint is presented. It is assumed that the parameters in the probabilistic linear programming problems are random variables, and the probabilistic problem is converted to an equivalent deterministic mathematical programming problem. In this paper the parameters are generally considered as normal and log-normal random variables. A non-linear programming method is used to solve the single-objective deterministic problem, and a fuzzy programming method is used to solve the multi-objective deterministic problem. Finally, a numerical example is presented to illustrate the methodology.

Keywords:

• Probabilistic linear programming
• Joint constraints
• Single objective
• Multi-objective
• Normal random variable
• Log-normal random variable
• Fuzzy programming