Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-18T16:36:06.850Z Has data issue: false hasContentIssue false
  • English
  • Français

Flots entiers et multiflots fractionnaires couplés par une contrainte de capacité

Published online by Cambridge University Press:  25 January 2006

Alain Quilliot ,
Fatiha Bendali  and
Jean Mailfert
Alain Quilliot
Affiliation:
Bât. ISIMA, BP 125, Campus des Cézeaux, Université Blaise Pascal, 63173 Aubiere, France ; alain.quilliot@isima.fr
Fatiha Bendali
Affiliation:
Bât. ISIMA, BP 125, Campus des Cézeaux, Université Blaise Pascal, 63173 Aubiere, France ; alain.quilliot@isima.fr
Jean Mailfert
Affiliation:
Bât. ISIMA, BP 125, Campus des Cézeaux, Université Blaise Pascal, 63173 Aubiere, France ; alain.quilliot@isima.fr
Get access

Abstract

Nous modélisons ici plusieurs problèmes de Transport et de Gestion de Flux à l'aide d'un flot entier et d'un multiflot fractionnaire couplés par une contrainte de capacité. Pour le problème ainsi obtenu, nous proposons différents schémas de résolution par relaxation et décomposition, qui induisent la recherche d'un flot auxiliaire dont la partie entière supérieure doit minimiser un certain coût, et qui requièrent la mise en œuvre d'un processus d'agrégation. Nous en déduisons diverses heuristiques que nous testons.

Keywords

FlotsMultiflotsCircuits NégatifsRoutageTransport.
Type
Research Article
Information
RAIRO - Operations Research , Volume 39 , Issue 3 , July 2005 , pp. 185 - 224
Copyright
© EDP Sciences, 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahuja, R.K., Orlin, J.B. and Sharma, D., Multiexchance neighbourhood structures for the capacitated minimum spanning tree problem. Math Programming 91 (2001) 71–97. CrossRef
R.K. Ahuja, T.L. Magnanti, J.B. Orlin and M.R. Reddy, Applications of network optimization. Chapter 1 of Network Models, Handbook of Operation Research and Management Science 7 (1995)1–83.
R.V. Ahuja, T.L. Magnanti and J.B. Orlin, Network Flows: Theory, Algorithms and Applications. Prentice hall, Englewood Cliffs, N.J. (1993).
Aronson, J.E., A survey on dynamic network flows. Ann. Oper. Res. 20 (1989) 1–66. CrossRef
Assad, A., Multicommodity networks flows: a survey. Networks 8 (1978) 37–91. CrossRef
Balakrishnan, A., Magnanti, T. and Mirchandani, P., Designing hierarchical survivable networks. Oper. Res. 46 (1998) 116–130. CrossRef
Balakrishnan, A., Magnanti, T. and Mirchandani, P., A dual based algorithm for multi level network design. Manage. Sci. 40 (1994) 567–580. CrossRef
Balinski, M., Fixed cost transportation problems. Nov. Res. Log. Quart 8 (1961) 41–54. CrossRef
Barahona, F., Network design using cut inequalities. SIAM J. Optim. 6 (1995) 822–837.
Ben Ameur, W., Constrained length connectivity and survivable networks. Networks 36 (2000) 1.
Benchakroun, A., Ferland, J. and Gascon, V., Benders decomposition for network design problems with underlying tree structure. Investigacion operativa 6 (1997) 165–180.
J.F. Benders, Partitionning procedures for solving mixed variable programming problems. Num. Math. 4 (1962) 238–252.
Bertsimas, D. and Stock Patterson, S., The air traffic flow problem with en route capacities. Oper. Res. 46-3 (1998) 406–422. CrossRef
Bienstock, D. and Unluk, O., Capacited network design: polyedral structure and computation. Inform. J. Comput. 8 (1996) 243–259. CrossRef
Boffey, T. and Hinxman, A., Solving for optimal network problem. EJOR 3 (1979) 386–393. CrossRef
A. Caminada, J.K. Hao, J.L. Lutton and V. Martin, L'optimisation des réseaux de télécommunications. Recherche Opérationnelle et Réseaux : Méthodes d'Analyse Spatiale. Collection IGAT, Hermes, Chap. 7 (2002) 191–236.
Chang, S.G. and Gavish, B., Telecommunication network topological design and capacity expansion: formulations and algorithms. Telecom. Syst. 1 (1993) 99–131. CrossRef
Chardaire, P., Costa, M.C. and Sutter, A., Solving the dynamic facility location problem. Networks 28 (1996) 117–124. 3.0.CO;2-H>CrossRef
Chifflet, J., Lisser, A. and Tolla, P., Interior point methods for multicommodity netflow problems. Perquisa Operacional 15 (1994) 1.
Chopra, S. and Rao, M., The Steiner tree problem I: formulations, composition and extension of facets. Math Programming 64 (1994) 209–229. CrossRef
N. Christophides, C.A. Whitlock, Network synthesis with connectivity constraint: a survey. Oper. Res. (1981) 705–723.
Cordeau, J.P., Toth, P. and Vigo, D., A survey of optimization models for train routing and scheduling. Transportation Science 32 (1998) 380–404. CrossRef
Crainic, T., Gendreau, M. and Farvolden, J.M., A simplex based tabu search method for capacitated network design. Inform. J. Comput. 12 (2000) 223–236. CrossRef
Crainic, T. and Rousseau, J.M., Multicommodity, multimode freight transportation: a general modeling and algorithmic framework for the service network design problem. Transport Research B 20 (1988) 290–297.
Crainic, T., Frangioni, A. and Gendron, B., Bundle based relaxation methods for multicommodity capacitated fixed charge network design. Discrete Appl. Math. 112 (2001) 73–99. CrossRef
Dahl, G. and Stoer, M., A polyedral approach to multicommodity survivable network design. Numer. Math. 68 (1994) 149–167.
Dejax, P. and Crainic, T., A review of empty flow and fleet management models in freight transportation. Transportation Science 21 (1987) 227–247. CrossRef
De Wolf, D. and Smeers, Y., Optimal dimensionning of pipe networks with application to gas transmission networks. Oper. Res. 44-4 (1996) 596–608. CrossRef
Dionne, A. and Florian, M., Exact and approximate algorithms for optimal network design. Networks 9 (1979) 37–59. CrossRef
Z. Drezner and T. Drezner, Applied location theory models, in Modern Methods for Business Research, edited by Lawrence Erlbaum Mahwa, N.J. (1998) 79–120.
Eiselt, H.A., Laporte, G. and Thisse, J.F., Competitive location models: a framework and bibliography. Transportation Sciences 27 (1993) 44–54. CrossRef
Ferreira Filho, V. and Galvao, J., A survey of computer network design problems. Investigacion Operativa 4 (1994) 183–211.
M. Florian, An introduction to network models used in transportation planning, in Transp. Plann. Models, edited by M. Florian, North Holland, Amsterdam (1984) 137–152.
J.M. Forvalden, W.B. Powell and I. Lustig, A primal partitionning solution for the arc chain formulation of a multicommodity network flow problem. Oper. Res. 41 (1993) 669–693.
Gallo, G., Lower planes for the network design problem. Networks 13 (1983) 411–426. CrossRef
Gavish, B., Topological design of telecommunication networks: local access design methods. Ann. Oper. Res. 33 (1991) 17–71. CrossRef
Geoffrion, A., Lagrangean relaxation and its uses in integer programming. Math. Prog. Study 2 (1974) 82–114. CrossRef
Geoffrion, A., Generalized Benders decomposition. J. Optim. Theory Appl. 10 (1972) 237–260. CrossRef
Girard, A. and Liau, B., Dimensioning of adaptatively routed networks. IEE/ACM Trans. Networking 1-4 (1993) 460–468. CrossRef
A. Golberg and R. Tarjan, Finding minimum cost circulation by cancelling negative cycles, JACM 36 (1989) 873–886.
H. Hoang, Topological optimization of networks: a non linear mixed model employing generalized Benders decomposition. IEEE Trans. Automat. Control. AC-27 (1982) 164–169.
Hossein, P.A., Bertsekas, D.P. and Tseng, P., Relaxation methods for network problems with convex arc costs. SIAM J. Control Optim. 5 (1987) 1219–1243.
F.K. Hwang, D.S. Richards and P. Winter, The Steiner Tree Problem. North Holland (1992).
Jaillet, P., Song, G. and Airline, G. Yu network design and hub location problems. Location Science 4 (1997) 195–212. CrossRef
Johnson, D., Lenstra, J., RInnoy-Khan, A., The complexity of the Network Design Problem. Networks 8 (1978) 279–285. CrossRefPubMed
Jones, K.L., Lustig, I.J., Farvolden, J.M. and Powel, W.B., Multicommodity network flows: the impact of formulation on decomposition. Math. Programming 62 (1993) 95–117. CrossRef
J.L. Kennington and R.V. Helgason, Algorithms for network programming. Wiley N.Y. (1980).
Khumalala, B.M., Warehouse location problem efficient branch and bound algorithm. Manage. Sciences B 18 (1972) 718–731. CrossRef
J.G. Klincewicz and M.B. Rosenwein, Planning and consolidating shipments from a warehouse. J. Operat. Res. Soc. 48 (1997) 241–246.
L.J. Leblanc, An algorithm for discrete network design. Trans. Sci. 9 (1975) 283–287.
Lederer, P.J. and Nambimadom, R.S., Airline network design. Oper. Res. 46-6 (1998) 785–804. CrossRef
J. Mac Gregor Smith and P. Winter, Topological Network Design. Ann. Oper. Res. 33 (1991).
Magnanti, T., Combinatorial optimization and vehicle fleet planning: perspectives and prospects. Networks 11 (1981) 179–214. CrossRef
Magnanti, T. and Wong, R.T., Network design and transportation planning models and algorithms. Trans. Sci. 18 (1984) 1–5. CrossRef
Mahey, P., Benchakroun, A. and Boyer, F., Capacity and flow assignment of data networks by generalized Benders decomposition. J. Global Optim. 20 (2001) 173–193. CrossRef
Marin, A. and Salmeron, J., Tactical design of rail freight networks: part 1- exact and heuristic methods. EJOR 90 (1996) 26–44. CrossRef
Minoux, M., Network synthesis and optimum network design problems: models, solution methods and application. Networks 19 (1989) 313–360. CrossRef
M. Minoux, Optimum synthesis of a network with non simultaneous multicommodity flow requirements, Studies on graphs and Discrete Programming, Annals of Disc. Math., edited by P. Hansen, North Holland 11 (1981) 269–277.
P.B. Mirchandani and L.R. Francis, Discrete Location Theory. John Wiley Eds, N.Y. (1990).
Norenkov, I., Yevstifeyev, Y. and Manichev, V., A method for an accelerated analysis of multiperiod electronic circuits. Telecom Radio Engin. 42 (1987) 123–126.
Ouorou, A., Mahey, P. and Vial, J.P., A survey of algorithms for convex multicommodity flow problems. Manage. Science 46 (2000) 126–147. CrossRef
P.M. Pardalos and D.Z. Du, Network design: connectivity and facility location. DIMACS Series 40, N.Y., American Math Society (1998).
R. Rebai, Optimisation de réseaux de télécommunications avec sécurisation. Thèse Paris-Dauphine (2000).
Scott, T. and Read, E., Modelling hydroreservoir operation in a deregulated electricity market. ITOR 3 (1996) 243–253.
P.A. Steenbrink, Optimization of transport networks. Wiley, N.Y. (1974).
Tseng, P., Dual Ascent methods for problems with strictly convex costs and linear constraints: a unified approach. SIAM J. Control Optim. 28 (1990) 214–242. CrossRef
Vijay, R., Kanda, A. and Vrat, P., Multiperiod capacity expansion of road networks: formulation and algorithms. Oper. Res. 30 (1993) 117–140.
R.T. Wong, Worst case analysis of network design problem heuristics. SIAM J. Alg. Disc. Meth. 1 (1980) 51–63.