Metode Pencarian Langsung untuk Model Pemrograman Nonlinier Stochastic Campuran

Abstract

Stochastic programming is a tool for optimal planning and decision making in the presence of uncertainty in the data. The type of study object is a random optimization problem where the results (outcomes) of random data are not re- vealed at run time, and the decisions to be optimized do not have to anticipate future results. This provides a close link to the ”real time” optimization required for optimal decisions ”here and now” in an uncertain data environment. In this research, a new approach is proposed to obtain global optimization of nonlinear mixed-count stochastic programming problem models. The research focuses on two-stage stochastic problems with non-linearity in the objective function and con- straints. The variables in the first stage have a whole value while the variables in the second stage are a mixture of whole and continuous. Problems are formulated using scenario-based representation. The basic idea for solving this non-linear mixed-mixed stochastic programming problem is to transform the model into an equivalent model in the form of a deterministic non-linear mixed-mixed program. This is possible because the uncertainties, which are assumed to be discrete in distribution, can be modeled as a finite number of scenarios. However, the size of the equivalent model will grow rapidly as a consequence of the number of sce- narios and the number of time horizons. The concept of filtered probability space combined with data mining will be used to create scenarios. The approach used to solve large-scale non-linear mixed-count programs is to lift the value of the non- basis variable from its boundaries so as to force a base variable to have a count value. Then the reduced problem is processed in which the calculated variables are kept constant and changes are made to these variables in discrete steps to obtain a global optimal solution.