Abstract
A distribution network design problem arises in a lower level of an hierarchical modeling approach for telecommunication network planning. Improvements of technologies used to deploy distribution networks have contributed to make distribution network planning more similar to other levels of access network. The major points that differentiate distribution network design problems are its huge dimensions and the several technological options that could be used to connect customers. Major technological trends to deploy distribution networks are discussed here. As an extension of the capacitated network design problem, it is a NP-hard combinatorial optimization problem. The need to install facilities and capacities in discrete levels and the incorporation of addition technology-related cost terms and constraints makes the exact solution of the mixed integer programming model even harder. There are several models and strategies that might be devised for solving those models, we present some of them.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Bibliography
K. Aardal. Capacitated facility location: Separation algorithms and computational experience. Mathematical Programming, 81:149–175, 1998.
K. Aardal, Y. Pochet, and L. A. Wolsey. Capacitated facility location: Valid inequalities and facets. Mathematics of Operations Research, 20:562–582, 1995.
A. Agrawal, P.N. Klein, and R. Ravi. When trees collide: An approximation algorithm for the generalized steiner problem on networks. Technical Report CS-90-32, Department of Computer Science, Brown University, Providence, Rhode Island 02912, 1994.
Y.P. Aneja. An integer linear programming approach to Steiner problem in graphs. Networks, 10:167–178, 1980.
A. Balakrishnan, T.L. Magnanti, and P. Mirchandani. Modeling and heuristic worst-case performance analysis of two-level network design problem. Management Science, 40:846–867, 1994.
A. Balakrishnan, T.L. Magnanti, A. Shulman, and R.T. Wong. Models for planning capacity expansion in local access telecommunication networks. Annals of Operations Research, 33:239–284, 1991.
A. Balakrishnan, T.L. Magnanti, and R.T. Wong. A dual-ascent procedure for large-scale uncapacitated network design. Operations Research, 37:716–740, 1989.
J.E. Beasley. An algorithm for solving large capacitated warehouse location problems. Journal of the Operational Research Society, 33:314–325, 1988.
J.E. Beasley. An sst-based algorithm for the Steiner problem in graphs. Networks, 19: 1–16, 1989.
D. Bienstock. Computational experience with an effective heuristic for some capacity expansion problems in local access networks. Telecommunication Systems, 1:379–400, 1993a.
D. Bienstock. A lot-sizing problem on trees, related to network design. Mathematics of Operations Research, 18:402–422, 1993b.
D. Bienstock and O. Günlük. Computational experience with a difficult mixed-integer multicommodity flow problem. Mathematical Programming, 68:213–237, 1995.
D. Bienstock and O. Günlük. Capacitated network design-polyhedral structure and computation. INFORMS Journal on Computing, 8:243–259, 1996.
R.R. Boorstyn and H. Frank. Large-scale network topological optimization. IEEE Transactions Communications, 25(1):29–47, 1977.
B. Brockmüller, O. Günlük, and L. A. Wolsey. Designing private line networks-polyhedral analysis and computation. Technical report, CORE Discussion Paper, 1996.
C.M.F. Carlson and Gerard Authie. Optimized design of LMDS cells: site location, equipment sizing and users homing. In Proceeding 3rd IEEE International Conference on Mobile and Wireless Communications Networks (MWCN’2001), pages 111–118, Recife, Brazil, 2001.
T.M. Cavalier and H.D. Sherali. Network location problems with continuous link demands: p-medians on a chain and 2-medians on a tree. European Journal of Operational Research, 23:246–255, 1986.
W. Chou, F. Ferrante, and L. Gerke. An algorithm for optimally locating network access facilities. In Proceedings of ICC’ 78, pages 24.5.1–24.5.8, 1978.
W. Cook. Integer programming solution for capacity expansion of the local access network. Technical Report TM-ARH-017914, Bell Communications Research, 1990.
G. Dahl, A. Martin, and M. Stoer. Routing through virtual paths in layered telecommunication networks. Technical report, Telenor Research and Development, 1995.
P.S. Davis and T.L. Ray. A branch and bound algorithm for the capacitated facilities location problem. Naval Research Logistic Quarterly, 16(3):331–334, 1969.
C.W. Duin and A. Volgenant. Reduction tests for the Steiner problem in graphs. Networks, 19:549–567, 1989.
D. Erlenkotter. A dual-based procedure for uncapacitated facility location. Operations Research, 26(6):992–1009, 1978.
B. Gavish. Topological design of centralized computer networks-formulations and algorithms. Networks, 12:355–377, 1982.
B. Gavish. Formulations and algorithms for the capacitated minimal directed tree. Journal of the ACM, 30:118–132, 1983.
B. Gavish. Topological design of telecommunication networks-Local access design methods. Annals of Operations Research, 33:17–71, 1991.
M. Gerla and L. Kleinrock. On the topological design of distributed computer networks. IEEE Transactions on Communications, 25(1):48–60, 1977.
M. Grötschel and C. Monma. Integer polyhedra arising from certain network design problems with connectivity constraints. SIAM Journal on Discrete Mathematics, 3(4):502–523, 1990.
M. Grötschel, C. Monma, and M. Stoer. Polyhedral approaches to network survivability. In DIMACS Series in Discete Mathematics and Theoretical Computer Science, volume 5. American Mathematical Society, Providence, Rhode Island, 1991.
M. Grötschel, C. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309–330, 1992a.
M. Grötschel, C. Monma, and M. Stoer. Facets for polyhedra arising in the design of communication networks with low-connectivity constraints. SIAM Journal on Optimization, 2(3):474–504, 1992b.
M. Grötschel, C. Monma, and M. Stoer. Design of survivable networks. In M. O. Ball, T. L. Magnanti, C. L. Monma, and G. L. Nemhauser, editors, Handbooks in Operations Research and Management Science 7:Network Models. North-Holland, 1994.
O. Günlük. A branch-and-cut algorithm for capacitated network design problem. Technical report, School of Operations Research and Industrial Engineering, Cornell University, 1996.
S.L. Hakimi. Optimal locations of switching centers and the absolute centers and median of a graph. Operations Research, 12:450–459, 1964.
S.L. Hakimi. Steiner’s problem in graphs and its implications. Networks, 1:113–133, 1971.
G.Y. Handler and P.B. Mirchandani. Location on Networks-Theory and Algorithms. The MIT Press, Cambridge, Massachusetts, 1979.
J.W. Herrmann, G. Ioannou, I. Minis, and J. M. Proth. Fixed-charge capacitated network design problem. European Journal of Operational Research, 95:476–490, 1996.
D.S. Hochbaum and A. Segev. Analysis of a flow problem with fixed charges. Networks, 19:291–312, 1989.
S.K. Jacobsen. Heuristics for the capacitated plant location model. European Journal of Operational Research, 12:253–261, 1983.
J.B. Kruskal Jr. On the shortest spanning tree of a graph and the travelling salesman problem. Proc. Amer. Math. Society, 7:48–50, 1956.
A.A. Kuehn and M.J. Hamburger. A heuristic program for locating warehouses. Management Science, 9(4):643–666, 1963.
M. Laguna. Optimal design of sonet rings for interoffice telecommunication. Technical report, Graduate School of Business and Administration, University of Colorado, 1992.
J.M.Y. Leung and T.L. Magnanti. Valid inequalities and facets of the capacitated plant location problem. Mathematical Programming, 44:271–291, 1989.
L. Lovász and H. Scarf. The generalized basis reduction algorithm. Technical Report No. 946, Cowles Foundation Discussion Paper, Yale University, 1990.
H.P.L. Luna, N. Ziviani, and R.M.B. Cabral. The telephonic switching centre network problem: Formalization and computational experience. Discrete Applied Mathematics, 18:199–210, 1987.
N. Maculan. The Steiner problem in graphs. Annals of Discrete Mathematics, 31: 185–212, 1987.
T.L. Magnanti, P. Mirchandani, and R. Vachani. The convex hull of two core capacitated network design problems. Mathematical Programming, 60:233–250, 1993.
T.L. Magnanti and R.T. Wong. Network design and transportation planning: Models and algorithms. Transactions Science, 18(1): 1–55, 1984.
V. Marathe. A discrete equal-capacity p-median problem. Master’s thesis, Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 1992.
G.R. Mateus, F.R.B. Cruz, and H.P.L. Luna. Algorithm for hierarchical network design. Location Science, 2:149–164, 1994.
G.R. Mateus and R.V.L. Franqueira. Model and heuristic for a generalized access network design problem. Telecommunication Systems, 15:257–271, 2000.
G.R. Mateus and H.P.L. Luna. Decentralized decision-making and capacitated facility location. The Annals of Regional Science, 26:361–377, 1992.
G.R. Mateus, H.P.L. Luna, and A.B. Sirihal. Heuristics for distribution network design in telecommunication. Journal of Heuristics, 6:131–148, 2000.
F.F. Mazzini, G.R. Mateus, and J.M. Smith. Lagrangean based methods for solving large-scale cellular network design problems. Wireless Networks, 9:659–672, 2003.
P.V. McGregor and D. Shen. Network design: an algorithm for the access facility location problem. IEEE Transactions on Communications, 25(1):61–73, 1977.
M. Minoux. Network synthesis and optimum network design problems: Models, solution methods and applications. Networks, 19:313–360, 1989.
A. Mirzaian. Lagrangian relaxation for the star-star concentrator location problem: Approximation algorithm and bounds. Networks, 15:1–20, 1985.
Y. Myung, H. Kim,, and D. Tcha. Optimal load balancing on sonet bidirectional rings. Operations Research, 45(1): 148–152, 1997.
M.W. Padberg, T.J. Van Roy, and L.A. Wolsey. Valid linear inequalities for fixed charge problems. Operations Research, 33:842–861, 1985.
L. Pupillo and A. Conte. The economics of local loop architecture for multimedia services. Information Economics and Policy, 10:107–126, 1998.
R.L. Rardin. Tight relaxations of fixed charge network flow problems. Technical report, School of Industrial Engineering, Purdue University, West Lafayette, Indiana, 1982.
R.L. Rardin and U. Choe. Tighter relaxations of fixed charge network flow problems. Technical Report J-79-18, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, 1979.
R.L. Rardin and L.A. Wolsey. Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems. European Journal of Operational Research, 71:95–109, 1993.
G. Sa. Branch-and-bound and approximate solutions to the capacitated plant location problem. Operations Research, 17:1005–1016, 1969.
D.X. Shaw. Limited column generation technique for several telecommunication network design problems. Technical report, School of Industrial Engineering, Purdue University, West Lafayette, Indiana, 1993.
D.X. Shaw. Local access network design and its extensions. Technical report, School of Industrial Engineering, Purdue University, West Lafayette, Indiana, 1995.
H.D. Sherali. Capacitated, balanced, sequential location-allocation problems on chains and trees. Mathematical Programming, pages 381–396, 1991.
H.D. Sherali and F.L. Nordai. A capacitated balanced 2-median problem on a tree network with a continuum of link demands. Transportation Science, 22(1):70–73, 1988.
H.D. Sherali and T.P. Rizzo. Unbalanced, capacitated p-median problems on a chain graph with a continuum of link demands. Networks, 21:133–163, 1991.
A. Shulman, R. Vachani, J. Ward, and P. Kubat. Multicommodity flows in ring networks. Technical report, GTE Laboratories Inc., 1991.
M. Stoer and G. Dahl. A polyhedral approach to multicommodity survivable network design. Numerische Mathematik, 68:149–167, 1994.
O.J. Wasem. An algorithm for designing rings for survivable fiber network. IEEE Transactions on Reliability, 40:428–432, 1991.
R.T. Wong. A dual ascent algorithm for the steiner problem in directed graphs. Mathematical Programming, 28:271–287, 1984.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Mateus, G.R., Patrocínio, Z.K.G. (2006). Optimization Issues in Distribution Network Design. In: Resende, M.G.C., Pardalos, P.M. (eds) Handbook of Optimization in Telecommunications. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30165-5_14
Download citation
DOI: https://doi.org/10.1007/978-0-387-30165-5_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30662-9
Online ISBN: 978-0-387-30165-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)