Originally posted by: VKV7_Anulark_Naber

I have cuts that involve new variables, so I need to add cuts and variables at the same time. Is it possible to do that in UserCutCallback? If not, is there any other way around it except adding those (new) variables to the original model? The problem is i I can generate all (new) variables, but not all of them are really needed in cuts. Thanks in advance.

No, it is not possible to add variables while a solve is in progress. It is possible to add variables to a model (before solving) even if those variables are not used anywhere in the original model. (It requires an explicit call to the appropriate add() method.) So enumerating the variables you might need in the cuts and adding them at the start is a possibility.

Another possibility it's to use a framework that supports branch-cut-and-price (Symphony comes to mind), and use CPLEX as the LP solver. I don't know how hard it would be to implement what you have in mind.

A third possibility would be to eliminate via algebra the new variables before adding the cuts, if possible.

Originally posted by: VKV7_Anulark_Naber

Thank you.