For two-stage integer stochastic problems with recourse, the Value of the Stochastic Solution is defined as:

VSS = EEV - RP

EEV = fix 1st stage, solve subproblems, take probability based weighted average (solved by N MIPs with N = number of scenarios )

RP = recourse problem (solved with e.g. L-shaped)

My question is: "Is the VSS still valid when both EEV and RP are solved by sampling techniques?"

I did not find any references on this issue.

asked 15 May '13, 08:17

cvhuele's gravatar image

cvhuele
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I don't think you can solve EEV and RP using sampling techniques. Whatever you get will be an estimation. My guess is that you can estimate VSS.

(15 May '13, 09:26) Austin Buchanan

Austin is right (see comment above). If you use a sampling method then you would have estimates of the EEV and the RP and you would therefore have an estimate of the VSS. But the concept is abstract, whatever the solution method used, so it remains valid, subject to some care around semantics.

Technically, you could use the fact that EEV and RP are likely to have strong positive covariance to get a very good estimate of the VSS.

Practically speaking, what the VSS provides is an estimate (that is being generous -- more like an eyeballing) of the "amount of recourse" available, subject to how you modeled your time series, how you built your scenarios, etc. This is why the VSS on academic SP problems tends to be very close to 0. If instances are the result of random sampling or contrived situations forced to be linear, there will be many ways around an early bad decision, and therefore the VSS is low.

In summary, unless there is something glaringly peculiar about the problem, I would not worry too much about the quality of the VSS, unless you want to demonstrate some property in a more rigorous setting.

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answered 15 May '13, 22:26

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Leo
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Asked: 15 May '13, 08:17

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