A branch-and-cut algorithm for capacitated network design problems

Mathematical Programming, Series B

Volumn 86, Issue 1, 1999, Pages 17-39

  Günlük, Oktay ^a,b  

^a School of Operations Research and Industrial Engineering   (United States)

^b AT AND T LABS RESEARCH   (United States)

Author keywords

Branch and cut; Computing; Mixed integer programming

Indexed keywords

EID: 0001774148     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070050077     Document Type: Article

References (29)

1. Applegate, D., Bixby, R., Chvátal, V., Cook, W. (1995): The traveling salesman problem. Manuscript
2. Barahona, F. (1996): Network design using cut inequalities. SIAM J. Optim. 6, 823-837
3. Brockmüller, B., Günlük, O., Wolsey, L.A. (1996): Designing private line networks - Polyhedral analysis and computation. CORE Discussion Paper
4. Bienstock, D. (1996): Private communication
5. Bienstock, D., Chopra, S., Günlük, O., Tsai, C.-Y. (1998): Minimum cost capacity installation for multicommodity network flows. Math. Program. 81, 177-199
6. Bienstock, D., Günlük, O. (1996): Capacitated network design - Polyhedral structure and computation. INFORMS J. Comput. 8, 243-259
7. Bienstock, D., Günlük, O. (1995): Computational experience with a difficult multicommodity flow problem. Math. Program. 68, 213-238
8. Cunningham, W. (1985): Optimal attack and reinforcement of a network. J. ACM 32, 549-561
9. Dahl, G., Martin, A., Stoer, M. (1995): Routing through virtual paths in layered telecommunication networks. Preprint, to appear in Oper. Res.
10. Dahl, G., Stoer, M. (1994): A polyhedral approach to multicommodity survivable network design. Numer. Math. 68, 149-167
11. Dribeek, N. (1966): An algorithm for the solution of mixed integer programming problems. Manage. Sci. 12, 576-587
12. Garfinkel, R.S., Nemhauser, G.L. (1972): Integer Programming. Wiley, New York
13. Günlük, O. (1996): A branch-and-cut algorithm for capacitated network design problems. Working paper, Dept. of ORIE, Cornell University
14. Günlük, O. (1994): Computational problems in telecommunication networks. PhD thesis, Dept. of IEOR, Columbia University
15. Günlük , O., Pochet, Y. (1996): Mixing mixed-integer inequalities. CORE discussion paper
16. Iri, M. (1971): On an extension of the max-flow min-cut theorem to multicommodity flows. J. Oper. Res. Soc. Jpn. 13, 129-135
17. Linderoth, J., Savalsbergh, M. (1997): A computational study of search strategies for mixed integer programming. Preprint, to appear in INFORMS J. Comput.
18. Lund, C., Phillips, S., Reingold, N. (1996): Private communication
19. Magnanti, T.L., Mirchandani, P. (1993): Shortest paths, single origin-destination network design and associated polyhedra. Networks 23, 103-121
20. Magnanti, T.L., Mirchandani, P., Vachani, R. (1993): The convex hull of two core capacitated network design problems. Math. Program. 60, 233-250
21. Magnanti, T.L., Mirchandani, P., Vachani, R. (1995): Modeling and solving the two-facility network loading problem. Oper. Res. 43, 142-157
22. Nash-Williams, C.S.J.A. (1961): Edge-disjoint spanning trees of finite graphs. J. Lond. Math. Soc. 36, 199-208
23. Nemhauser, G.L., Wolsey, L.A. (1988): Integer and Combinatorial Optimization. Wiley, New York
24. Onaga, K., Kakusho, O. (1971): On feasibility conditions of multicommodity flows in networks. IEEE Trans. Circuit Theory CT-18, 4, 425-129
25. Padberg, M., Rinaldi, G. (1987): Optimization of a 532-city traveling salesman problem by branch-and-cut. Oper. Res. Lett. 6, 1-7
26. Padberg, M., Rinaldi, G. (1991): A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev. 33, 60-100
27. Pochet, Y., Wolsey, L.A. (1993): Lot-sizing with constant batches: Formulation and valid inequalities. Math. Oper. Res. 18, 767-785
28. Tomlin, J. (1971): An improved branch-and-bound method for integer programming. Oper. Res. 19, 1070-1075
29. Tutte, W.T. (1961): On the problem of decomposing a graph into n connected factors. J. Lond. Math. Soc. 36, 221-230