Multi-cover inequalities for totally-ordered multiple knapsack sets: theory and computation

We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The may come different inequalities if the weights in form totally-ordered set. Thus, we introduce and study structure valid multi-cover derive for its convex hull have number interesting properties. First, they generalize well-known (1, k)-configuration inequalities. Second, are not aggregation cuts. Third, cannot be generated as rank-1 Chvátal-Gomory cuts inequality system consisting constraints all their minimal cover also provide conditions under which facets set, well those fully characterize hull. give an integer program solve separation numerical experiments that showcase strength these new