Originally posted by: SystemAdmin
Hi everybody,
I am working on a deterministic equivalent of a two stage stochastic problem with multiple planning periods. Uncertainty is modelled by a set of demand scenarios. Possible outcomes are defined for every period (independently) by a histogram for the respective period. For complexity reasons it is not possible to combine all outcomes of each period against all others.
On the one hand I want to have a set of possible outcomes that represents the histograms (with their relative frequencies), on the other hand some “extreme scenarios” regarding the demand (not regarding the probability!) should be included. It has to be mentioned that these cases do not necessarily have a very low probability because the relative frequencies of the histograms do not have to be Gaussian distributed.
My question is, if there is “a common” methodology, because having these two properties should be somehow desired in a lot of applications?! Subsequently some of my “ideas” are added, but I am not sure if I am “on the right track”.
I considered using Monte Carlo sampling, but this method might fails when only few scenarios are generated and the relative frequencies are more or less equally distributed. In this case the extreme scenarios (regarding the amount) are usually missed out. I also thought about sorting all histograms by the amount (descending) and combining always the i-th entry. The weighting of a scenario results by multiplication of the corresponding frequencies. With this method I might miss the probable scenarios because in some histograms high frequencies belong to high amounts where in others high frequencies belong to low amounts. Finally I considered a combination of both, where each method provides 50% of the total weight of the scenario set.
It would be nice to get some advice or remarks.
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