Start with the LP Relaxation: Begin by solving the linear programming (LP) relaxation of the ILP, which allows decision variables to take on continuous values.

Identify Non-Integer Solutions: If the optimal solution to the LP relaxation has non-integer values for the decision variables, it indicates that the solution is not feasible for the ILP.

Generate Cuts: Create a "cut," which is a new linear constraint that excludes the current non-integer solution from the feasible region while still including all feasible integer solutions. This cut is derived from the properties of the problem and helps refine the feasible set.

Add Cuts to the Model: Incorporate the new constraint into the existing model and resolve the LP relaxation with the added cut.

Iterate: Repeat the process—checking for non-integer solutions and generating additional cuts—until an optimal integer solution is found or no further cuts can be generated.