Stochastic programming is an approach in mathematical programming that allows one to take into account the uncertainty in optimization models.
While deterministic optimization problems are formulated using given parameters, real applications usually contain some unknown parameters. When parameters are known only within certain boundaries, one approach to solving such problems is called robust optimization . This approach is to find a solution that is acceptable for all such data and, in a sense, optimal.
Stochastic programming models have a similar form, but use knowledge of probability distributions for data or their estimates. The goal here is to find some solution that is valid for all (or almost all) possible data values and maximize the mathematical expectation of some function of solutions and random variables. In general, such models are formulated, solved analytically or numerically, their results are analyzed to provide useful information for decision makers.
Two-stage linear models of stochastic programming are most widely used and well studied. Here, the decision maker takes some action in the first stage, after which a random event occurs that affects the outcome of the first stage decision. In the second step, a corrective decision can then be made that compensates for any undesirable effects resulting from the decision of the first step.
The optimal solution to this model is the only solution to the first stage and many corrective decisions (decision rules) that determine what action should be taken at the second stage in response to each random result.