Static Stochastic Programming Models

Abstract

When formulating a stochastic programming problem, we usually start from a deterministic problem that we call underlying deterministic problem. Then, observing that some of the parameters are random, we formulate another problem, the stochastic programming problem, by taking into account the probability distribution of the random elements in the underlying problem. When decision can or has to be made in the presence of randomness, at one single step, i.e., we do not wait for the occurrence of any event or realization of some random variable(s), then we say that the stochastic programming model is static. The two words: model and problem are used as synonyms. In the strict sense, the model specifies the assumptions made concerning the system in mathematical terms and identifies system parameters with mathematical objects. Having these, we formulate a problem to be solved and use the obtained result for descriptive or operative purposes.