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].