I'm working on a location problem and I have an issue with the Benders decomposition. I'm using Cplex with Python. I coded a single cut and a multi-cut to compare.
The single-cut implementation takes a very long time to run. It requires huge amounts of time to add several cuts (~5000 sec for 7 cuts on a 50 node network). Meanwhile, the multi-cut takes less time (40 sec) to add 500-7000x the number of cuts.
1- Where do you think the problem is coming from?
2- Is there a way to know how many subproblems the code is creating and solving? and if there are any Cplex built-in functions to do this?