Originally posted by: lbr33

I am dealing with a mathematical formulation, in which flow variables and route variables are present.

I implemented a column generation approach to solve the formulation (the route variables are generated as needed). This first version here, I called as complete version.

As the flow variables have 10 indexes, I can not go so far if all flow variables are added since the begin in the master problem.

Then, I implemented a version in which the flow variables are also added on demand (accordingly with their reduced costs). This second version, I called as incomplete version.
Do both versions necessarily need to converge to the same bound? Because, that is not what is happening. I have a difference of less than 1% between the bounds of the two versions. Is that ok or does it mean that I am doing something wrong?

Thanks a lot!

Are you solving both problems with the absolute and relative gap tolerance parameter set to 0? if not then CPLEX may stop prematurely because the solutions are close to optimal and the solutions in the two approaches may differ. Are there other parameter settings (time, node, iteration limits, ...) that may stop CPLEX prematurely? Is the solution for the incomplete problem better or worse than that for the complete one? If the incomplete solution is worse than the complete one, can you check whether the incomplete version contains all routes that selected in the optimal solution to the complete version? If there are missing routes you will have to figure out why they are missing and not added by your algorithm.