Generating facets for finite master cyclic group polyhedra using n-step mixed integer rounding functions

European Journal of Operational Research

Volumn 207, Issue 1, 2010, Pages 105-109

  Kianfar, Kiavash ^a   Fathi, Yahya ^b  

^a Department of Electrical and Computer Engineering   (United States)

^b North Carolina State University   (United States)

Author keywords

Facet; Group problem; Integer programming; Mixed integer rounding; Polyhedra

Indexed keywords

BREAK-POINTS; CYCLIC GROUP; GROUP PROBLEM; INFINITE GROUPS; LINEAR INTERPOLATION; MIXED-INTEGER ROUNDING;

DYNAMIC PROGRAMMING; GEOMETRY;

INTEGER PROGRAMMING;

EID: 77953870417     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2010.04.021     Document Type: Article

References (16)

1. Aráoz J., Evans L., Gomory R.E., and Johnson E.L. Cyclic group and knapsack facets. Mathematical Programming 96 (2003) 377-408
2. Atamtürk, A., Kianfar, K., 2010. n-Step mingling inequalities: New facets for the mixed integer knapsack set. Mathematical Programming, submitted for publication.
3. Dash S., and Günlük O. Valid inequalities based on simple mixed-integer sets. Mathematical Programming 105 (2006) 29-53
4. Dash S., and Günlük O. Valid inequalities based on the interpolation procedure. Mathematical Programming 106 (2006) 111-136
5. Dash S., Goycoolea M., and Günlük O. Two-step MIR inequalities for mixed integer programs. INFORMS Journal on Computing (2009) in press. doi:10.1287/ijoc.1090.0337
6. Dey S., and Richard J. Sequential-merge facets for two-dimensional group problems. In: Fischetti M., and Williamson D.P. (Eds). 12th International IPCO Conference: Integer Programming and Combinatorial Optimization (2007), Springer 30-42
7. Gomory R.E. Some polyhedra related to combinatorial problems. Linear Algebra and its Applications 2 (1969) 451-558
8. Gomory R.E., and Johnson E.L. Some continuous functions related to corner polyhedra. Mathematical Programming 3 (1972) 23-85
9. Gomory R.E., and Johnson E.L. Some continuous functions related to corner polyhedra, II. Mathematical Programming 3 (1972) 359-389
10. Gomory R.E., and Johnson E.L. T-space and cutting planes. Mathematical Programming 96 (2003) 341-375
11. Gomory R.E., Johnson E.L., and Evans L. Corner polyhedra and their connection with cutting planes. Mathematical Programming 96 (2003) 321-339
12. Kianfar, K., 2010. On n-step MIR and partition inequalities for integer knapsack/flow cover problems with divisible coefficients. Manuscript.
13. Kianfar K., and Fathi Y. Generalized mixed integer rounding inequalities: Facets for infinite group polyhedra. Mathematical Programming 120 (2009) 313-346
14. Klabjan D. Subadditive approaches in integer programming. European Journal of Operational Research 183 2 (2007) 525-545
15. Marchand H., and Wolsey L.A. Aggregation and mixed integer rounding to solve MIPs. Operations Research 49 (2001) 363-371
16. Richard J., Li Y., and Miller L. Valid inequalities for MIPs and group polyhedra from approximate liftings. Mathematical Programming 118 (2009) 253-277