I have a question regarding the separation problem that comes up when using a cutting-plane method. The separation problem is solved with a greedy type algorithm. Let's say that the initial problem have one constraint and x is binary. (Knapsack problem).
Step 1: Solve LP relaxation of the problem. Step 2: Set up and solve the separation problem => Result is a new constraint to the LP-problem. Step 3: Solve the LP-problem with the new constraint.If not integer solution: Step 4: Solve the new separation problem.
The problem comes up in step 4 when I need to solve the separation problem for the second time. I'm suppose to keep the old constraint and the new constraint or do I replace the old constraint with the new one (which I got from solving the first separation problem)? /U