3.Stochastic Programming

Stochastic programming is used in optimization problems to deal with uncertainty. The lack of reliable data for deterministic analysis can be seen in all branches of science including physics, engineering, economics and the like. This cannot eliminate the inevitable need for decision-making in the real world. Therefore, in order to approach a reliable decision for the outputs of stochastic renewable energy resources, carrying out analyses on uncertain data by the use of stochastic programming is encouraged [20, 21].
Most of the stochastic problems can be solved using optimization techniques. It is worth-mentioning that if input data is certain, the optimal solution is obtained by deterministic solving techniques. However, mostly, the input data is uncertain and characterized by probability functions. Accordingly, it is not clear how exactly stochastic problems need to be formulated. One approach is to replace the inconsistent input data with the approximated values that leads to a specific optimizing problem. Nevertheless, the obtained solution seems not to be the most appropriate one. As another approach, probability distribution of input data can be approximated using a series of possible input occurrences where for each, a relevant occurrence probability is considered. For instance, three sets of input data with three certain occurrence probability values that sum of them is unit [22-26], can be considered. Afterwards, a stochastic problem can be formulated using weighted solution for each set of input data based on its occurrence probability; then, the best solution is obtained by considering of all input data effects. Concerning the uncertain input data which is explained by different sets of input data, the objective function would be highly uncertain; therefore, random variables need to be described in order to solving the problem. It is notable that the current approach does not give the best result for each set of input data; but, the best answer can be obtained regarding the weighted probability of occurrence of each input data [27-30].