Polyhedral techniques in combinatorial optimization I: Theory

Statistica Neerlandica

Volumn 50, Issue 1, 1996, Pages 3-26

  Aardal, K ^a   Van Hoesel, C P M ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

Combinatorial optimization; Polyhedral combinatorics; Valid inequalities

Indexed keywords

EID: 0030560215     PISSN: 00390402     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9574.1996.tb01478.x     Document Type: Article

References (59)

1. AARDAL, K. (1994), Capacitated facility location: separation algorithms and computational experience, CentER Discussion Paper 9480, Tilburg (submitted for publication).
2. AARDAL, K., A. HIPOLITO, C. P. M. VAN HOESEL and B. JANSEN (1995), A branch-and-cut algorithm for the frequency assignment problem, Working Paper, Limburg University, Maastricht.
3. AARDAL, K. and C. P. M. VAN HOESEL (1995), Uncapacitated facility location: lifting, separation and computations (in preparation).
4. AARDAL, K., M. LABBÉ, J. LEUNG and M. QUEYRANNE (1994), On the two-level uncapacitated facility location problem, CentER Discussion Paper 9486, Tilburg (submitted for publication).
5. AARDAL, K., Y. POCHET and L. A. WOLSEY (1993), Capacitated facility location: valid inequalities and facets, CORE Discussion Paper 9323, Louvain-la-Neuve (to appear in Mathematics of Operations Research).
6. VAN DEN AKKER, J. M., C. P. M. VAN HOESEL and M. W. P. SAVELSBERGH (1993), A time-indexed formulation of single-machine scheduling problems part I: facets and characterizations, Memorandum COSOR 93-27. Eindhoven University of Technology, Eindhoven (submitted for publication).
7. VAN DEN AKKER, J. M., C. A. J. HURKENS and M. W. P. SAVELSBERGH (1995), A time-indexed formulation of single-machine scheduling problems II: branch-and-cut, Memorandum, Eindhoven University of Technology, Eindhoven.
8. APPLEGATE, D., R. E. BIXBY, V. CHVÁTAL and W. COOK (1994), Finding cuts in the TSP, Preliminary report, available through anonymous ftp from netlib.att.com in the directory netlib/att/math/applegate/TSP.
9. BALAS, E. (1975), Facets of the knapsack polytope, Mathematical Programming 8, 146-164.
10. BALAS, E., S. CERIA, G. CORNUÉJOLS and NATRAJ (1994), Gomory cuts revisited, Working Paper No. 1994-16, Carnegie Mellon University, Graduate School of Industrial Administration, Pittsburgh.
11. BARANY, I., T. J. VAN ROY and L. A. WOLSEY (1984), Uncapacitated lot-sizing: the convex hull of solutions, Mathematical Programming Study 22, 32-43.
12. CHVÁTAL, V. (1973), Edmonds polytopes and a hierarchy of combinatorial problems, Discrete Mathematics 4, 185-224.
13. CHVÁTAL, V. (1975), On certain polytopes associated with graphs, Journal of Combinatorial Theory B 18, 138-154.
14. COOK, W., C. COULLARD and GY. TURÁN (1987), On the complexity of cutting-plane proofs, Discrete Applied Mathematics 18, 25-38.
15. COOK, W., A. M. H. GERARDS, A. SCHRIJVER and É. TARDOS (1986), Sensitivity theorems in integer linear programming, Mathematical Programming 34, 251-264.
16. CRAMA, Y. and F. SPIEKSMA (1995), Scheduling jobs of equal length: complexity, facets and computational results, in: E. BALAS and J. CLAUSEN (eds.), Integer programming and combinatorial optimization, Lecture Notes in Computer Science 920, Springer, Berlin, 227-291.
17. CROWDER, H. P., E. L. JOHNSON and M. W. PADBERG (1983), Solving large-scale zero-one linear programming problems, Operations Research 31, 803-934.
18. CROWDER, H. and M. W. PADBERG (1980), Solving large-scale symmetric traveling salesman problems to optimality, Management Science 26, 459-509.
19. DANTZIG, G. B., D. R. FULKERSON and S. M. JOHNSON (1954), Solution of a large-scale traveling-salesman problem, Operations Research 2, 393-410.
20. EDMONDS, J. (1965), Maximum matching and a polyhedron with 0,1-vertices, Journal of Research of the National Bureau of Standards (B) 69, 67-72.
21. EDMONDS, J. and R. GILES (1977), A min-max relation for submodular functions on graphs, in: P. L. HAMMER, E. L. JOHNSON, B. H. KORTE and G. L. NEMHAUSER (eds.), Annals of Discrete Mathematics 1, 185-204.
22. VAN EIJL C. and C. P. M. VAN HOESEL (1995), Linear description of the discrete lot sizing problem with Wagner-Whitin costs. Research Report, Eindhoven University of Technology.
23. GAREY, M. R. and D. S. JOHNSON (1979), Computers and intractability: a guide to the theory of NP-completeness, Freeman, San Francisco.
24. 4, Journal of Combinatorial Theory, Series B 47, 330-348.
25. GERARDS, A. M. H. (1995), Matching, in: M. BALL, T. L. MAGNANTI, C. L. MONMA and G. L. NEMHAUSER (eds), Handbooks in operations research and management science: networks, North-Holland, Amsterdam.
26. GERARDS, A. M. H. and A. SCHRIJVER (1986), Matrices with the Edmonds-Johnson property, Combinatorica 6, 365-389.
27. GERARDS, A. M. H. and F. B. SHEPHERD (1995), Characterization of the graphs with all subgraphs t-perfect (in preparation).
28. GILES, R. and W. R. PULLEYBLANK (1979), Total dual integrality and integer polyhedra, Linear Algebra and Its Applications 25, 191-196.
29. GOEMANS, M. X. (1995). Worst-case comparison of valid inequalities for the TSP, Mathematical Programming 69, 335-349.
30. GOMORY, R. E. (1958), Outline of an algorithm for integer solutions to linear programs, Bulletin of the American Mathematical Society 64, 275-278.
31. GOMORY, R. E. (1960), Solving linear programming problems in integers, in: R. BELLMAN and M. HALL, Jr. (eds.), Combinatorial analysis, Proceedings of Symposia in Applied Mathematics X, American Mathematical Society, Providence, 211-215.
32. GOMORY, R. E. (1963), An algorithm for integer solutions to linear programs, in: R. L. GRAVES and P. WOLFE (eds.), Recent advances in mathematical programming, McGraw-Hill, New York, 269-302.
33. GRÖTSCHEL, M. (1980), On the symmetric traveling salesman problem: solution of a 120 city problem, Mathematical Programming Studies 12, 61-77.
34. GRÓTSCHEL, M. and O. HOLLAND (1991), Solution of large-scale symmetric traveling salesman problems, Mathematical Programming 51, 141-202.
35. GRÓTSCHEL, M., L. LOVÁSZ and A. SCHRIJVER (1981), The ellipsoid method and its consequences in combinatorial optimization, Combinatorica 1, 169-197, corrigendum: 4, 291-295.
36. GRÓTSCHEL, M. and M. W. PADBERG (1979), On the symmetric traveling salesman problem I: inequalities, Mathematical Programming 16, 265-280.
37. GRÓTSCHEL, M. and W. R. PULLEYBLANK (1986), Clique tree inequalities and the symmetric traveling salesman problem, Mathematics of Operations Research 11, 537-569.
38. GU, Z., G. L. NEMHAUSER and M. W. P. SAVELSBERGH (1995), Sequence independent lifting of cover inequalities, in: E. BALAS and J. CLAUSEN (eds.), Integer programming and combinatorial optimization, Lecture Notes in Computer Science 920, Springer, Berlin, 452-462.
39. HAMMER, P. L., E. L. JOHNSON and U. N. PELED (1975), Facets of regular 0-1 polytopes, Mathematical Programming 8, 179-206.
40. VAN HOESEL, C. P. M. and A. KOLEN (1994), A linear description of the discrete lot sizing and scheduling problem, European Journal of Operational Research 75, 342-353.
41. VAN HOESEL, C. P. M., A. KOLEN and VAN EIJL (1995), A class of valid inequalities for the discrete lot sizing and scheduling problem (in preparation).
42. VAN HOESEL, C. P. M., A. P. M. WAGELMANS and L. A. WOLSEY (1994), Economic lot sizing with start-up costs: the convex hull, SIAM Journal of Discrete Mathematics 7, 141-151.
43. JÜNGER, M., G. REINELT and S. THIENEL (1995), Practical problem solving with cutting plane algorithms in combinatorial optimization, in: W. COOK, L. LOVÁSZ and P. SEYMOUR (eds.), DIMACS Series in discrete mathematics and theoretical computer science 20, AMS.
44. KARP, R. M. (1972), Reducibility among combinatorial problems, in: R. E. MILLER and J. W. THATCHER (eds.), Complexity of computer computations, Plenum Press, New York, 85-103.
45. KARP, R. M. and C. H. PAPADIMITRIOU (1980), On linear characterizations of combinatorial optimization problems, Proceedings of the 21st Annual Symposium on Foundation of Computer Science, IEEE, New York, 1-9.
46. LENSTRA, JR., H. W. (1983), Integer programming with a fixed number of variables, Mathematics of Operations Research 8, 538-548.
47. NEMHAUSER, G. L. and M. W. P. SAVELSBERGH (1992), A cutting plane algorithm for the single-machine scheduling problem with release times, in: M. AKGÜL, H. HAMACHER and S. TUFECKI (eds.), Combinatorial optimization: new frontiers in the theory and practice, NATO ASI Series F: Computer and System Sciences 82, Springer, Berlin, 63-84.
48. NEMHAUSER, G. L. and L. A. WOLSEY (1988), Integer and combinatorial optimization, Wiley, New York.
49. PADBERG, M. W. (1980), (1,k)-configurations and facets for packing problems, Mathematical Programming 18, 94-99.
50. PADBERG, M. W. and M. GRÖTSCHEL (1985), Polyhedral computations, in: E. LAWLER, J. K. LENSTRA, A. H. G. RINNOOY KAN and D. B. SHMOYS (eds.), The traveling salesman problem: a guided tour of combinatorial optimization, John Wiley and Sons.
51. PADBERG, M. W. and G. RINALDI (1987), Optimization of a 532-city symmetric traveling salesman polytope by branch and cut, Operations Research Letters 6, 1-7. Addendum 9, (1990), 353.
52. PADBERG, M. W. and G. RINALDI (1990), Facet identification for the symmetric traveling salesman problem, Mathematical Programming 47, 219-257.
53. SAVELSBERGH, M. W. P., G. C. SIGISMONDI and G. L. NEMHAUSER (1994), Functional description of MINTO, a Mixed INTeger Optimizer, Operations Research Letters 15, 47-58.
54. SCHRIJVER, A. (1980), On cutting planes, in: M. DEZA and I. G. ROSENBERG (eds), Combinatorics 79 part II, Annals of Discrete Mathematics 9, 291-296.
55. SCHRIJVER, A. (1981), On total dual integrality, Linear Algebra and Its Applications 38, 27-32.
56. SCHRIJVER, A. (1986), Theory of linear and integer programming, Wiley, Chichester.
57. SEYMOUR, P. D. (1980), Decomposition of regular matroids, Journal of Combinatorial Theory (B) 28, 305-359.
58. WAGELMANS, A. P. M., C. P. M. VAN HOESEL and A. W. J. KOLEN (1992), Economic lot-sizing: an script O sign(n log n) algorithm that runs in linear time in the Wagner-Whitin case, Operations Research 40S, S145-S156.
59. WOLSEY, L. A. (1975), Faces for a linear inequality in 0-1 variables, Mathematical Programming 8, 165-178.