MIP: Theory and Practice - Closing the Gap
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
Aggregation and Mixed Integer Rounding to Solve MIPs
Operations Research
K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau
INFORMS Journal on Computing
Mathematical Programming: Series A and B
Valid inequalities based on simple mixed-integer sets
Mathematical Programming: Series A and B
Valid inequalities based on the interpolation procedure
Mathematical Programming: Series A and B
Mixed-Integer Cuts from Cyclic Groups
Mathematical Programming: Series A and B
Production design for plate products in the steel industry
IBM Journal of Research and Development - Business optimization
On the strength of Gomory mixed-integer cuts as group cuts
Mathematical Programming: Series A and B
On the Exact Separation of Mixed Integer Knapsack Cuts
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Operations Research Letters
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Two-step mixed integer rounding (MIR) inequalities are valid inequalities derived from a facet of a simple mixed integer set with three variables and one constraint. In this paper we investigate how to effectively use these inequalities as cutting planes for general mixed integer problems. We study the separation problem for single-constraint sets and show that it can be solved in polynomial time when the resulting inequality is required to be sufficiently different from the associated MIR inequalities. We discuss computational issues and present numerical results based on a number of data sets.