Software Complex for the Analysis of the Stochastic Programming Problems With Probability Criterion

Abstract

This paper describes the software complex for the construction of a smooth approximation of the probability function and its derivatives. The structural parts of the complex, its functionality and mathematical background are described. The software complex constructs an approximation of the probability that some loss function does not exceed a certain level of loss. The program supports lossfunctions defined in a LaTeX format and contains predefined standard functions, variables and mathematical signs. The software supports different variable types, such as constants, control variables, stochastic variables with known distribution and parameters and samples of stochastic variables with unknown distribution. The software complex supports a variety of predefined random distributions and allows to tune the result by setting other service parameters. The implemented approximation is based on the replacement of the Heaviside function inside the probability function expression with the sigmoid function. Next, the approximated probability function and its derivatives are represented as volume integrals. These integrals can be calculated numerically using the Monte-Carlo method. This approach provides a relatively quick and universal method of approximate calculation of the probability function and its derivatives. The software complex has a graphical user interface and produces a graphical representation of approximated functions along with their points data. The program also supports the construction of the surface approximations for the case of the loss function having two control variables. Obtained graphical and point data can be used in the solution of stochastic programming problems with probability criteria. Examples using the software complex as a tool for analyzing stochastic programming problems are given.