A note on splitting of variables in integer programming models

The splitting of variables in an integer programming model is a tool to obtain a more constrained (tighter) linear programming relaxation. A known general method for knapsack constraints, the partial network reformulation method, produces an equivalent set of constraints that has only integer solutions. We show how to modify this method to reduce substantially the number of split variables and in most cases, the number of disaggregated constraints. Further, the modified method can implicitly handle upper bounds on as well as fixed charges for at least two variables of the considered constraint.