The Solving Method And Application Of Dependent Chance Programming

Stochastic programming is a class of mathematical programming, which deals with data containing stochastic information. It is different from common mathematical programming, because of its random coefficients. It makes stochastic programming fitter for the realistic problem and has a wide application in many fields, such as management, operation, economy and optimization control.There are two main ways to solve stochastic programming. The first one is transformation, i.e. transforming stochastic programming into its equivalent deterministic programming and then solving it by using the theory of the deterministic programming. The other one is approaching method, i.e. getting the approximate optimal value and solution of stochastic programming through genetic algorithm based on stochastic simulation. The methods of transformation are summarized in the paper, and it is generalized the type of the coefficients satisfying polynomial normal distribution.Dependent chance programming (DCP) is the method of optimizing the chance function of the event under uncertain surrounding. In this paper some deterministic equivalences are attained according to some different constrained conditions and distributions. Some corresponding properties are discussed, and a genetic algorithm based on stochastic simulation is given. Then DCP is applied to transportation problem, in order to avoid that that the solution given by common methods can't be used in reality.Transportation problem based on DCP is a multiobjective stochastic programming. A new evaluating function is given according to characteristicof chance function, to transform it to a single objective stochastic programming. At last transportation problem based on DCP is generalized by introducing goal programming, and transportation problem based on dependent chance goal programming is modeled.