I am dealing with a multi-stage mixed-integer stochastic global supply chain optimization problem.
In this regard, I want to determine a tolerance value for the gap between the lower bound and the estimated upper bound (in the case of minimization) that will guarantee the reliability of results and inferred findings.
This question doesn’t have an answer. Simulate the policy and see if you like the results.
Right, got it, thanks. I was just wondering about some objective way to show the reliability of results. But I understand that in most of the cases, its the results themselves that will suggest their reliability based on the domain knowledge.
I think the point is that “reliable” is not an easily quantifiable factor. Is a 1% gap reliable? 10%? 0.1%?
I’ve hinted at this a few times but: your true problem is intractable. You can never hope to find a globally optimal policy to the true large-scale infinite-horizon mixed-integer multistage stochastic problem. You need to make approximations to be able to compute a feasible policy. Now the question is: how good is the policy? Just because you solve the SDDP model to a very small gap does not mean that the policy performs well in practice, because the approximations you made to be able to solve it with SDDP.jl might mean that the resulting policy performs poorly in practice. The only way to analyze the quality of the policy is to simulate it and see if you like the results.
Got it. Thanks.