Cutting planes in integer and mixed integer programming
Discrete Applied Mathematics
Exponential Lower Bounds on the Lengths of Some Classes of Branch-and-Cut Proofs
Mathematics of Operations Research
A class of multi-level balanced Foundation-Penalty cuts for mixed-integer programs
International Journal of Computational Science and Engineering
On the Exact Separation of Mixed Integer Knapsack Cuts
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On the MIR Closure of Polyhedra
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Computers and Operations Research
On the relative strength of split, triangle and quadrilateral cuts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Minimal Valid Inequalities for Integer Constraints
Mathematics of Operations Research
Two-Step MIR Inequalities for Mixed Integer Programs
INFORMS Journal on Computing
Optimal Allocation of Surgery Blocks to Operating Rooms Under Uncertainty
Operations Research
Modeling and optimization of survivable P2P multicasting
Computer Communications
Lift-and-project cuts for mixed integer convex programs
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
An exact algorithm for the 0---1 linear knapsack problem with a single continuous variable
Journal of Global Optimization
Experiments with Two-Row Cuts from Degenerate Tableaux
INFORMS Journal on Computing
A note on the continuous mixing set
Operations Research Letters
On the complexity of cutting-plane proofs using split cuts
Operations Research Letters
Operations Research Letters
Description of 2-integer continuous knapsack polyhedra
Discrete Optimization
Chvatal-Gomory-tier cuts for general integer programs
Discrete Optimization
Foundation-penalty cuts for mixed-integer programs
Operations Research Letters
A computational analysis of lower bounds for big bucket production planning problems
Computational Optimization and Applications
Mixed Integer Formulations for a Short Sea Fuel Oil Distribution Problem
Transportation Science
Approximating the Split Closure
INFORMS Journal on Computing
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In this paper, we discuss the use of mixed integer rounding (MIR) inequalities to solve mixed integer programs. MIR inequalities are essentially Gomory mixed integer cuts. However, as we wish to use problem structure, we insist that MIR inequalities be generated from constraints or simple aggregations of constraints of the original problem. This idea is motivated by the observation that several strong valid inequalities based on specific problem structure can be derived as MIR inequalities.Here we present and test a separation routine for such MIR inequalities that includes a heuristic row aggregation procedure to generate a single knapsack plus continuous variables constraint, complementation of variables, and finally the generation of an MIR inequality. Inserted in a branch-and-cut system, the results suggest that such a routine is a useful additional tool for tackling a variety of mixed integer programming problems.