Originally posted by: YavuzD

Hi, I am working on a large scale MIP and try to implement Benders Decomposition to solve the problem effectively. As a general practice, the integer variables are handled in the master problem and linear variables are assigned to a set of sub-problems. I want to know if it is possible  to have integer sub-problem in Benders Algorithm implemented in IBM ILOG CPLEX Optimization Studio  Version: 12.8.

Originally posted by: open_ball

The answer should be No. The point of creating a sub problem is to generate a feasibility or optimality cut. To do so, you take advantage of the duality. The strong duality is guaranteed to hold for LPs. What you can do is that you can relax the integer variables in the sub problem. If they are binary variables, I'd recommend you changing your framework. 

However, I guess Alex might give you a better explanation. Hope this helps. 

Open ball's answer is correct. Subproblems cannot have integer variables since the theory of Benders algorithm requires taking the dual of the subproblem.