Scenario Construction
In practice it might be possible to construct scenarios by eliciting expert's opinions on the future. The number of constructed scenarios should be relatively modest so that the obtained deterministic equivalent can be solved with reasonable computational effort. It is often claimed that a solution that is optimal using only a few scenarios provides more adaptable plans than one that assumes a single scenario only. In some cases such a claim could be verified by a simulation. In theory some measures of guarantee that an obtained solution solves the original problem with reasonable accuracy. Typically in applications only the first stage optimal solution has a practical value since almost always a "true" realization of the random data will be different from the set of constructed (generated) scenarios.
Suppose contains independent random components, each of which has three possible realizations (for example, future realizations of each random parameters are classified as low, medium and high), then the total number of scenarios is . Such exponential growth of the number of scenarios makes model development using expert opinion very difficult even for reasonable size . The situation becomes every worse if some random components of have continuous distributions.
Read more about this topic: Stochastic Programming
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