We investigate the use of cutting planes for integer programs with general integer variables. We show how cutting planes arising from knapsack inequalities can be generated and lifted as in the case of 0-1 variables. We also explore the use of Gomory's mixed integer cuts. We address both...

A separation heuristic for mixed integer programs is presented that theoretically allows one to derive several families of "strong" valid inequalities for specific models and computationally gives results as good as or better than those obtained from several existing separation routines...

A branch-and-cut mixed integer programming system, called bc-opt, is described, incorporating most of the valid inequalities that have been used or suggested for such systems, namely lifted 0-1 knapsack inequalities, 0-1 gub knapsack and integer knapsack inequalities, flow cover and continuous...

Constraints arising in practice often contain many 0-1 variables and one or a small number of continuous variables. Existing knapsack separation routines cannot be used on such constraints. Here we study such constraint sets, and derive valid inequalities that can be used as cuts for such sets,...