Perturbation analysis of linear programming problems with random parameters

This paper presents a methodology for analyzing large scale engineering problems with uncertain parameters. The coefficients of the objective function, the coefficients of the decision variables and the right hand side of the constraints are functions of random variables. The optimization problem is solved using the traditional simplex method. The uncertain parameters in the equations are expanded in the Taylor series. It is shown that the resulting equations are actually a set of linear programming recursive equations. Upon solving these equations, the required probabilistic statements can be easily established. An engineering example is provided to demonstrate the use of this methodology.