Abstract
Given a communication demand between each pair of nodes of a network, we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy a given demand between each pair of nodes. The feasible capacities that can be leased from a network provider are of a particular kind in our case. There are a few so-called basic capacities having the property that every basic capacity is an integral multiple of every smaller basic capacity. An edge can be equipped with a capacity only if it is an integer combination of the basic capacities. In addition, we treat several restrictions on the routings of the demands (length restriction, diversification) and failures of single nodes or single edges. We formulate the problem as a mixed integer linear programming problem and develop a cutting plane algorithm as well as several heuristics to solve it. We report on computational results for real-world data.
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References
D. Alevras, M. Grötschel and R. Wessäly, A network dimensioning tool, Preprint SC 96-49, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, 1996.
F. Barahona, Network design using cut inequalities, SIAM Journal on Optimization 6(1996)823 -837.
D. Bienstock, S. Chopra, O. Günlük and C.-Y. Tsai, Minimum cost capacity installation for multicommodity network flows, Mathematical Programming, Special Issue on Computational Integer Programming (1995).
D. Bienstock and O. Günlük, Computational experience with a difficult mixed-integer multicommodity flow problem, Mathematical Programming 68(1995)213 - 237.
A. Bley, Node-disjoint length-restricted paths, Diplomarbeit, TU Berlin, Germany, 1997.
CPLEX Optimization, Inc., Suite 279, 930 Tahoe Blvd., Bldg 802, Incline Village, NV 89451, USA, Using the CPLEX Callable Library, 1995. Information available via WWW at URL http:// www.cplex.com.
G. Dahl and M. Stoer, A cutting plane algorithm for multicommodity survivable network design problems, INFORMS Journal on Computing (to appear).
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NPCompleteness, Freeman, San Francisco, 1979.
M. Grötschel and C.L. Monma, Integer polyhedra associated with certain network design problems with connectivity constraints, SIAM Journal on Discrete Mathematics 3(1990)502 - 523.
M. Grötschel, C.L. Monma and M. Stoer, Design of survivable networks, in: Handbooks in Operations Research and Management Science, volume on Network Models, North-Holland, 1995, chap. 10, pp. 617 - 672.
M. Iri, On an extension of the maximum-flow minimum-cut theorem to multicommodity flows, Journal of the Operations Research Society of Japan 13(1971)129 - 135.
O. Kakusho and K. Onaga, On feasibility conditions of multicommodity flows in networks, Transactions on Circuit Theory 18(1971)425 - 429.
A. Lisser, R. Sarkissian and J.P. Vial, Optimal joint syntheses of base and spare telecommunication networks, Technical Report, University of Geneva, November 1995.
T.L. Magnanti, P. Mirchandani and R. Vachani, Modeling and solving the two-facility capacitated network loading problem, Operations Research 43(1995)142 - 156.
M. Minoux, Optimum synthesis of a network with non-simultaneous multicommodity flow requirements, in: Studies on Graphs and Discrete Programming, P. Hansen, ed., North-Holland, 1981, pp. 269 - 277.
Y. Pochet and L.A. Wolsey, Integer knapsack and flow covers with divisible coefficients: Polyhedra, optimization and separation, Discrete Applied Mathematics 59(1995)57 - 74.
M. Stoer, Design of Survivable Networks, Lecture Notes in Mathematics, vol. 1531, Springer, 1992.
M. Stoer and G. Dahl, A polyhedral approach to multicommodity survivable network design, Numerische Mathematik 68(1994)149 - 167.
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Alevras, D., Grötschel, M. & Wessäly, R. Cost-efficient network synthesis from leased lines. Annals of Operations Research 76, 1–20 (1998). https://doi.org/10.1023/A:1018984102311
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DOI: https://doi.org/10.1023/A:1018984102311