I have tried to understand the method of relaxing an integer program. I am in the process of implementing and solving a MIP for the FJSSP. For this I use the python-MIP package to solve it. From my understanding, one does relax an integer program, solve it through a branch and bound algorithm which branches on specific fractional variables and possibly get an integer solution. I have tried to do this by relaxing my original integer model and solving it, which gives me an optimal solution with fractional values for my decision variable.
But how do I get the integer values from my fractional solution now?
Do I need to perform a Branch and Bound algorithm on the fractional solution?
I am a little bit confused because in the description of python-MIP, it said that the solver already uses an Branch and Cut Algorithm to solve it, so I thought the relaxed model would give me an integer solution by branching through the tree.