An optimal procedure for solving the hierarchical network design problem

IIE Transactions (Institute of Industrial Engineers)

Volumn 39, Issue 5, 2007, Pages 513-524

  Obreque, Carlos ^a,b   Marianov, Vladimir ^a  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b UNIVERSIDAD DEL BÍO BÍO   (Chile)

Author keywords

Hierarchical network design problem; Integer programming; Problem reduction; Shortest path containing a node or an arc

Indexed keywords

AD HOC NETWORKS; DESIGN; INTEGER PROGRAMMING; POLYNOMIALS;

LOOPLESS MAIN PATH; MULTICOMMODITY FLOWS; PROBLEM REDUCTION;

HIERARCHICAL SYSTEMS;

EID: 33847764947     PISSN: 0740817X     EISSN: 15458830     Source Type: Journal    
DOI: 10.1080/07408170600941615     Document Type: Article

References (19)

1. Balakrishnan, A.,.Magnanti, T. and Mirchandani, P. (1994) Modeling and heuristic worst-case performance analysis of the two-level network design problem. Management Science, 40:7, pp. 846-867.
2. Balakrishnan, A.,.Magnanti, T. and Mirchandani, P. (1994) A dual-based algorithm for multi-level network design. Management Science, 40:5, pp. 567-581.
3. Beasley, J. E. (2005)
4. Chopra, S. and Tsai, C. (2002) A branch-and-cut approach for minimum cost multi-level network design. Discrete Mathematics, 242, pp. 65-92.
5. Current, J. (1988) The design of a hierarchical transportation network with transshipment facilities. Transportation Science, 22:4, pp. 270-277.
6. Current, J. and Pirkul, H. (1991) The hierarchical network design problem with transshipment facilities. European Journal of Operational Research, 52, pp. 338-347.
7. Current, J.,.ReVelle, C. and Cohon, J. (1986) The hierarchical network design problem. European Journal of Operational Research, 27, pp. 57-66.
8. Current, J.,.ReVelle, C. and Cohon, J. (1987) The median shortest path problem: A multiobjective approach to analyze cost vs. accessibility in the design of networks. Transportation Science, 21:3, pp. 188-197.
9. Duin, C. and Volgenant, A. (1989) Reducing the hierarchical network design problem. European Journal of Operational Research, 39, pp. 332-344.
10. Duin, C. W. and Volgenant, A. (1990) Heuristics for the hierarchical network design problem. Twenty-Five Years of Operations Research in the Netherlands, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands
11. Duin, C. and Volgenant, A. (1991) The multi-weighted Steiner tree problem. Annals of Operations Research, 33, pp. 451-469.
12. Gouveia, L. and Telhada, J. (2001) An augmented arborescence formulation for the two-level network design problem. Annals of Operations Research, 106:1, pp. 47-61.
13. Koch, T. and Martin, A. (1998) Solving Steiner tree problems in graphs to optimality. Networks, 32, pp. 207-232.
14. Mirchandani, P. (1996) The multi-tier tree problem. INFORMS Journal on Computing, 8:3, pp. 202-218.
15. Obreque, C. and Marianov, V. (2004) A procedure for designing hierarchical path-tree networks and finding the optimal locations of the extremes of the main path, Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
16. Pirkul, H.,.Current, J. and Nagarajan, V. (1991) The hierarchical network design problem: A new formulation and solution procedures. Transportation Science, 25:3, pp. 175-182.
17. Pirkul, H. and Nagarajan, V. (1992) Locating concentrators in centralized computer networks. Annals of Operations Research, 36, pp. 247-262.
18. Sancho, N. (1995) A suboptimal solution to a hierarchical network design problem using dynamic programming. European Journal of Operational Research, 83, pp. 237-244.
19. Sancho, N. (1996) The hierarchical network design problem with multiple primary paths. European Journal of Operational Research, 96, pp. 323-328.