A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation

References

  • Ahuja R. K., Dell'Amico M., Maffioli F., Martello S. Flows and paths. Annotated Bibliographies in Combinatorial Optimization (1997) (John Wiley & Sons Ltd., Chichester, NY) 283–309Google Scholar
  • Ahuja R. K., Magnanti T. L., Orlin J. B.Network Flows: Theory, Algorithms, and Applications (1993) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
  • Alevras D., Grötschel M., Wessäly R. A network dimensioningtool. (1996) . Technical Paper Preprint SC 96-49, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, GermanyGoogle Scholar
  • Ali I., Barnett D., Farhangian K., Kennington J., Patty B., Shetty B., McCarl B., Wong P. Multicommodity network problems: applications and computations. IIE Transactions (1984) 16:127–134CrossrefGoogle Scholar
  • Aneja Y. P., Aggarwal V., Nair K. K. Shortest chain subject to side constraints. Networks (1983) 13:295–302CrossrefGoogle Scholar
  • Aneja Y. P., Nair K. K. The constrained shortest path problem. Naval Research Logistics Quarterly (1978) 25:549–555CrossrefGoogle Scholar
  • Assad A. A. Multicommodity network flows—a survey. Networks (1978) 8:37–91CrossrefGoogle Scholar
  • Balakrishnan A., Altinkemer K. Using a hop-constrained model to generate alternative communication network design. ORSA Journal on Computing (1992) 4:192–205LinkGoogle Scholar
  • Balakrishnan A., Magnanti T. L., Mirchandani P., Dell'Amico M., Maffioli F., Martello S. Network design. Annotated Bibliographies in Combinatorial Optimization (1997) (John Wiley & Sons, Ltd., Chichester, NY) 311–334Google Scholar
  • Barnhart C. Dual-ascent methods for large-scale multicommodity flow problems. Naval Research Logistics (1993) 40:305–324CrossrefGoogle Scholar
  • Barnhart C., Hane C. A., Johnson E. L., Sigismondi G. A column generation and partitioning approach for multi-commodity flow problems. Telecommunication Systems (1995) 3:239–258CrossrefGoogle Scholar
  • Barnhart C., Hane C. A., Vance P. H., Pardalos P. M., Hearn D. W., Hager W. W. Integer multicommodity flow problems. Network Optimization, Lecture Notes in Economics and Mathematical Systems (1996) (Springer-Verlag, Berlin, Germany) 17–31CrossrefGoogle Scholar
  • Barnhart C., Sheffi Y. A network-based primal-dual heuristic for the solution of multicommodity network flow problems. Transportation Science (1993) 27:102–117LinkGoogle Scholar
  • Castro J. PPRN 1.0 user's guide. (1994) . Technical paper, Statistics and Operations Research Department, Universitat Politècnica de Catalunya, Barcelona, SpainGoogle Scholar
  • Castro J., Nabona N. An implementation of linear and nonlinear multicommodity network flows. European Journal of Operational Research (1996) 92:37–53CrossrefGoogle Scholar
  • Chen H., DeWald C. G. A generalized chain labelling algorithm for solving multicommodity flow problems. Computers and Operations Research (1974) 1:437–465CrossrefGoogle Scholar
  • Chen Y. L., Chin Y. H. Multicommodity network flows with safety considerations. Operations Research (1992) 40:48–55LinkGoogle Scholar
  • Climaco J. C. N., Martins E. Q. V. A bicriterion shortest path algorithm. European Journal of Operational Research (1982) 11:399–404CrossrefGoogle Scholar
  • Crowder H. Computational improvements for subgradient optimization. Symposia Mathematica, Vol XIX (1976) (Academic Press, London, U.K.) 357–372Google Scholar
  • Desrochers M., Soumis F. A generalized permanent labeling algorithm for the shortest path problem with time windows. INFOR (1988) 26:191–212Google Scholar
  • Desrosiers J., Dumas Y., Solomon M. M., Soumis F.Time Constrained Routing and Scheduling (1993) (North-Holland, Amsterdam, The Netherlands) Google Scholar
  • Desrosiers J., Pelletier P., Soumis F. Plus court chemin avec contraintes d'Horaires. RAIRO (1983) 17:357–377CrossrefGoogle Scholar
  • Farvolden J. M., Powell W. B., Lustig I. J. A primal partitioning solution for the arc-chain formulation of a multicommodity network flow problem. Operations Research (1993) 41:669–693LinkGoogle Scholar
  • Ford L. R., Fulkerson D. R. A suggested computation for maximal multi-commodity network flows. Management Science (1958) 5:97–101LinkGoogle Scholar
  • Frangioni A., Gallo G. A bundle type dual-ascent approach to linear multicommodity min-cost flow problems. INFORMS Journal on Computing (1999) 11:370–393LinkGoogle Scholar
  • Garey M. R., Johnson D. S.Computers and Intractability: A Guide to the Theory of NP-Completeness (1979) (W. H. Freeman and Company, New York) Google Scholar
  • Gendron B., Crainic T. G. Bounding procedures for multicommodity capacitated network design problems. (1995) . Technical Paper, Centre de recherche sur les transports, Université de Montréal, Montréal, CanadaGoogle Scholar
  • Gendron B., Crainic T. G., Frangioni A., Sansó B., Soriano P. Multicommodity capacitated network design. Telecommunications Network Planning (1999) (Kluwer Academic Publishers, Boston, MA) 1–19CrossrefGoogle Scholar
  • Geoffrion A. M., Graves G. W. Multicommodity distribution system design by Benders decomposition. Management Science (1974) 20:822–844LinkGoogle Scholar
  • Gersht A., Shulman A. A new algorithm for the solution of the minimum cost multicommodity flow problem. Proceedings of the 26th Conference on Decision and Control (1987) 748–758CrossrefGoogle Scholar
  • Gratzer F. J., Steiglitz K., Fox J. A heuristic approach to large multicommodity flow problems. Proceedings of the Symposium on Computer-Communications Networks and Teletraffic (1972) New York:311–324Google Scholar
  • Grigoriadis M. D., White W. W., Cottle R., Krarup J. Computational experience with a multicommodity network flow algorithm. Optimization Methods for Resource Allocation (1974) (The English Universities Press Ltd, London, U.K.) 205–227Google Scholar
  • Handler G. Y., Zang I. A dual algorithm for the constrained shortest path problem. Networks (1980) 10:293–310CrossrefGoogle Scholar
  • Hartman J. K., Lasdon L. S. A generalized upper bounding algorithm for multicommodity network flow problems. Networks (1972) 1:333–354CrossrefGoogle Scholar
  • Held M., Wolfe P., Crowder H. P. Validation of subgradient optimization. Mathematical Programming (1974) 6:62–88CrossrefGoogle Scholar
  • Henningson M., Holmberg K., Näsberg M. A capacitated bus grid network design problem. Proceedings 8th International Conference on Telecommunication Systems: Modeling and Analysis (2000) Nashville, TN:98–113Google Scholar
  • Holmberg K., Hellstrand J. Solving the uncapacitated network design problem by a Lagrangean heuristic and branch-and-bound. Operations Research (1998) 46:247–259LinkGoogle Scholar
  • Holmberg K., Joborn M., Lundgren J. T. Improved empty freight car distribution. Transportation Science (1998) 32:163–178LinkGoogle Scholar
  • Holmberg K., Yuan D. A Lagrangean heuristic based branch-and-bound approach for the capacitated network design problem. Operations Research (2000) 48:461–481LinkGoogle Scholar
  • Itai A., Perl Y., Shiloach Y. The complexity of finding maximum disjoint paths with length constraints. Networks (1982) 12:277–286CrossrefGoogle Scholar
  • Jaffe J. M. Algorithms for finding paths with multiple constraints. Networks (1984) 14:95–116CrossrefGoogle Scholar
  • Jones K. L., Lustig I. J., Farvolden J. M., Powell W. B. Multicommodity network flows: the impact of formulation on decomposition. Mathematical Programming (1993) 62:95–117CrossrefGoogle Scholar
  • Kennington J. L. Solving multicommodity transportation problems using a primal partitioning simplex technique. Naval Research Logistics Quarterly (1977) 24:309–325CrossrefGoogle Scholar
  • Kennington J. L. A survey of linear cost multicommodity network flows. Operations Research (1978) 26:209–236LinkGoogle Scholar
  • Kennington J. L., Shalaby M. An effective subgradient procedure for minimal cost multicommodity flow problems. Management Science (1977) 23:994–1004LinkGoogle Scholar
  • Maier S. F., Cottle R., Krarup J. A compact inverse scheme applied to a multicommodity network with resource constraints. Optimization Methods for Resource Allocation (1974) (The English Universities Press Ltd, London, U.K.) 179–203Google Scholar
  • McCallum C. J. A generalized upper bounding approach to a communications network planning problem. Networks (1977) 7:1–23CrossrefGoogle Scholar
  • Shetty B., Muthukrishnan R. A parallel projection for the multicommodity network model. Journal of the Operational Research Society (1990) 41:837–842CrossrefGoogle Scholar
  • Tomlin J. A. Minimum-cost multicommodity network flows. Operations Research (1966) 14:45–51LinkGoogle Scholar
  • White W. W., Fox J. Mathematical programming, multicommodity flows, and communication nets. Proceedings of the Symposium on Computer Communications Networks and Teletraffic (1972) New York:325–334Google Scholar
  • Wollmer R. D. Multicommodity networks with resource constraints: The generalized multicommodity flow problem. Networks (1972) 1:245–263CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.