Approximations in stochastic and robust programming problems

Optimization procedures are very useful tools in many economic decision-making problems. We deal with the case of optimization problems where uncertainties in parameters occur. The stochastic programming approach considers the probability distribution of uncertain parameters and seeks for a solution that is feasible up to a certain level of probability (chance-constrained programming). Robust programming techniques search for such a solution that satisfies simultaneously all possible realizations of the parameters. Both methods require some kind of approximation because of computational difficulties. The paper deals with such approximations and illustrates the essential difference between the two above-mentioned methods. Even if a variety of economic problems lead to the same optimization program, one is required to choose a correct method to solve it; the economic background of the problem is crucial for such decision.