Abstract
Network design models have wide applications in telecommunications and transportation planning; see, for example, the survey articles by Magnanti and Wong (1984), Minoux (1989), Chapter 16 of the book by Ahuja, Magnanti and Orlin (1993), Section 13 of Ahuja et al. (1995). In particular, Gavish (1991) and Balakrishnan et al. (1991) present reviews of important applications in telecommunications. In many of these applications, it is required to send flows (which may be fractional) to satisfy demands given arcs with existing capacities, or to install, in discrete amounts, additional facilities with fixed capacities. In doing so, one pays a price not only for routing flows, but also for using an arc or installing additional facilities. The objective is then to determine the optimal amounts of flows to be routed and the facilities to be installed.
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References
Ahuja, R.K., T.L. Magnanti and J.B. Orlin. (1993). Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Englewood Cliffs, NJ.
Ahuja, R.K., T.L. Magnanti, J.B. Orlin and M.R. Reddy. (1995). Applications of Network Optimization. In M.O. Ball, T.L. Magnanti and G.L. Nemhauser (eds), Network Models, Handbooks of Operations Research and Management Science, pages 1–83. Elsevier, North-Holland, Amsterdam.
Balakrishnan, A. (1984). Valid Inequalities and Algorithms for the Network Design Problem with an Application to LTL Consolidation Problem. Ph.D. thesis, Sloan School of Management, Massachusetts Institute of Technology.
Balakrishnan, A. (1987). LP Extreme Points and Cuts for the Fixed-Charge Network Design Problem. Mathematical Programming, 39:263–284.
Balakrishnan, A. and S.C. Graves. (1989). A Composite Algorithm for a Concave-Cost Network Flow Problem. Networks, 19:175–202.
Balakrishnan, A., T.L. Magnanti and P. Mirchandani. (1994). A Dual-Based Algorithm for Multi-Level Network Design Problem. Management Science, 40(5):567–581.
Balakrishnan, A., T.L. Magnanti and P. Mirchandani. (1994). Modeling and Worst-Case Performance Analysis of the Two-Level Network Design Problem. Management Science, 40(7):846–867.
Balakrishnan, A., T.L. Magnanti, A. Shulman and R.T. Wong. (1991). Models for Planning Capacity Expansion in Local Access Telecommunication Networks. Annals of Operartions Research, 33:239–284.
Balakrishnan, A., T.L. Magnanti and R.T. Wong. (1989). A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design. Operations Research, 37:716–740.
Balakrishnan, A., T.L. Magnanti and R.T. Wong. (1995). A Decomposition Algorithm for Local Access Telecommunications Network Expansion Planning. Operations Research, 43(1):58–76.
Balas, E., S. Ceria and G. Cornuéjols. (1993). A Lift-and-Project Cutting Plane Algorithm for Mixed 0-1 Programs. Mathematical Programming, 58:295–324.
Balas, E., S. Ceria and G. Cornuéjols. (1995). Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework. Working paper, Graduate School of Business, Columbia University.
Barahona, F. (1996). Network Design using Cut Inequalities. SIAM Journal on Optimization, 6(3):823–837.
Barnhart, C., C.A. Hane, E.L. Johnson and G. Sigismondi. (1995). A Column Generation and Partitioning Approach for Multicommodity Flow Problems. Telecommunications Systems, 3:239–258.
Barnhart, C., C.A. Hane and P.H. Vance. (1996). Integer Multicommodity Flow Problems. Working paper, Center for Transportation Studies, Massachusetts Institute of Technology.
Bienstock, D., S. Chopra, O. Günlük and C.-Y. Tsai. (1995). Minimum-Cost Capacity Installation for Multicommodity Network Flows. Working paper, Department of Industrial Engineering and Operations Research, Columbia University.
Bienstock, D. and O. Günlük. (1995). Computational Experience with a Difficult Mixed-Integer Multicommodity Flow Problem. Mathematical Programming, 68(2):213–237.
Bienstock, D. and O. Günlük. (1996). Capacitated Network Design-Polyhedral Structure and Computation. INFORMS Journal on Computing, 8(3):243–259.
Carraresi, P., A. Frangioni and M. Nonato. (1996). Applying Bundle Methods to the Optimization of Polyhedral Functions: An Applications-Oriented Development. Working paper, Dipartimento di informatica, Università di Pisa.
Chang, S.-G. and B. Gavish. (1995). Lower Bounding Procedures for Multiperiod Telecommunications Network Expansion Problems. Operations Research, 43(1):43–57.
Crainic, T.G., M. Gendreau and J. Farvolden. (1996). Simplex-Based Tabu Search for the Multicommodity Capacitated Fixed Charge Network Design Problem. Publication CRT-96-07, Centre de recherche sur les transports, Université de Montréal.
Crainic, T.G., M. Toulouse and M. Gendreau. (1993). Towards a Taxonomy of Parallel Tabu Search Algorithms. INFORMS Journal on Computing, 9(1):61–72.
Eckstein, J. (1995). Parallel Branch-and-Bound Algorithms for General Mixed-Integer Programming on the CM-5. SIAM Journal on Optimization, 4(4):794–814.
Farvolden, J.M., W.B. Powell and I.J. Lustig. (1993). A Primal Partitioning Solution for the Arc-Chain Formulation of a Multicommodity Network Flow Problem. Operations Research, 41(4):669–693.
Fetterolf, P.C. and G. Anandalingam. (1992). A Lagrangean Relaxation Technique for Optimizing Interconnection of Local Area Networks. Operations Research, 40(4):678–688.
Fisher, M.L. (1994). Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees. Operations Research, 42:393–410.
Frangioni, A. (1995). Solving Semidefinite Quadratic Problems within Nonsmooth Optimization Algorithms. Working paper, Dipartimento di informatica, Università di Pisa.
Frangioni, A. and G. Gallo. (1996). A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min Cost Flow Problems. Working paper, Dipartimento di informatica, Università di Pisa.
Gavish, B. (1985). Augmented Lagrangean Based Algorithms for Centralized Netowrk Design. IEEE Transactions on Communications, 33(12):1247–1257.
Gavish, B. (1991). Topological Design of Telecommunications Networks — Local Access Design Methods. Annals of Operations Research, 33:17–71.
Gavish, B. and K. Altinkemer. (1990). Backbone Network Design Tools with Economic Tradeoffs. ORSA Journal on Computing, 2(3):236–252.
Gendron, B. (1994). Nouvelles méthodes de résolution de problèmes de conception de réseaux et leur implantation en environnement parallèle. Ph.D. thesis, Département d’informatique et de recherche opérationnelle, Université de Montréal. Publication CRT-94-50, Centre de recherche sur les transports, Université de Montréal.
Gendron, B. and T.G. Crainic. (1994). Relaxations for Multicommodity Capacitated Network Design Problems. Publication CRT-965, Centre de recherche sur les transports, Université de Montréal.
Gendron, B. and T.G. Crainic. (1994). Parallel Branch-and-Bound Algorithms: Survey And Synthesis. Operations Research, 42(6):1042–1066.
Gendron, B. and T.G. Crainic. (1994). Parallel Implementations of Bounding Procedures for Multicommodity Capacitated Network Design Problems. Publication CRT-94-45, Centre de recherche sur les transports, Université de Montréal.
Gendron, B. and T.G. Crainic. (1996). Bounding Procedures for Multicommodity Capacitated Fixed Charge Network Design Problems. Publication CRT-96-06, Centre de recherche sur les transports, Université de Montréal.
Geoffrion, A.M. (1974). Lagrangean Relaxation for Integer Programming. Mathematical Programming Study, 2:82–114.
Gouveia, L. (1995). A 2n Constraint Formulation for the Capacitated Minimal Spanning Tree Problem. Operations Research, 43(1):130–141.
Grötschel, M., C.L. Monma and M. Stoer. (1995). Design of Survivable Networks. In M.O. Ball, T.L. Magnanti and G.L. Nemhauser (eds), Network Models, Handbooks in Operations Research and Management Science, pages 617–672. Elsevier, North-Holland, Amsterdam.
Hall, L. (1996). Experience with a Cutting Plane Algorithm for the Capacitated Spanning Tree Problem. INFORMS Journal on Computing, 8(3):219–234.
Held, M. and R.M. Karp. (1970). The Traveling Salesman Problem and Minimum Spanning Trees. Operations Research, 18:1138–1162.
Held, M. and R.M. Karp. (1971). The traveling Salesman Problem and Minimum Spanning Trees: Part II. Mathematical Programming, 1:6–25.
Helgason, R.V. (1980). A Lagrangean Relaxation Approach to the Generalized Fixed Charge Multicommodity Minimal Cost Network Flow Problem. Ph.D. thesis, School of engineering and Applied Science, Southern Methodist University.
Hellstrand, J., T. Larsson and A. Migdalas. (1992). A Characterization of the Unca-pacitated Network Design Polytope. Operations Research Letters, 12:159–163.
Holmberg, K. and D. Yuan. (1996). A Lagrangean Heuristic Based Branch-and-Bound Approach for the Capacitated Netowrk Design Problem. Research report LiTH-MAT-R-1996-23, Department of Mathematics, Linkoping Institute of Technology.
Kennington, J.L. and R.V. Helgason. (1980). Algorithms for Network Programming. John Wiley and Sons, New York, NY.
Kim, D. and C. Barnhart. (1996). Multimodal Express Shipment Service Design: Models and Algorithms. Working paper, Center for Transportation Studies, Massachusetts Institute of Technology.
Lemaréchal, C. (1989). Nondifferentiable Optimization. In G.L. Nemhauser, A.H.G. Rinnooy Kan and M.J, Todd (eds), Optimization, Handbooks in Operations Research and Management Science, pages 529–572. Elsevier, North-Holland, Amsterdam.
Lucena, A. (1993). Steiner Problem in Graphs: Lagrangean Relaxation and Cutting-Planes. Presented at NETFLOW′93, San Miniato, Italy, October 3–7 (technical report TR-21/93, Dipartimento di informatica, Università di Pisa, 147-154).
Magnanti, T.L. and P. Mirchandani. (1993). Shortest Paths, Single Origin-Destination Network Design, and Associated Polyhedra. Networks, 23(2):103–121.
Magnanti, T.L., P. Mirchandani and R. Vachani. (1993). The Convex Hull of Two Core Capacitated Network Design Problems. Mathematical Programming, 60:233–250.
Magnanti, T.L., P. Mirchandani and R. Vachani. (1995). Modeling and Solving the Two-Facility Capacitated Network Loading Problem. Operations Research, 43(1):142–157.
Magnanti, T.L. and S. Raghavan. (1994). A Flow-Based Approach to Low Connectivity Network Design. Working paper, Operations Research Center, Massachusetts Institute of Technology.
Magnanti, T.L. and L.A. Wolsey. (1995). Optimal Trees. In M.O. Ball, T.L. Magnanti and G.L. Nemhauser (eds), Network Models, Handbooks in Operations Research and Management Science, pages 503–615. Elsevier, North-Holland, Amsterdam.
Magnanti, T.L. and R.T. Wong. (1984). Network Design and Transportation Planning: Models and Algorithms. Transportation Science, 18(1):1–55.
Minoux, M. (1989). Network Synthesis and Optimum Network Design Problems: Models, Solution Methods and Applications. Networks, 19:313–360.
Mirchandani, P. (1992). Projections of the Capacitated Network Loading Problem. Working paper, Katz Graduate School of Business, University of Pittsburgh.
Rardin, R.L. (1982). Tight Relaxations of Fixed Charge Network Flow Problems. Working paper, School of Industrial and Systems Engineering, Georgia Institute of Technology.
Rardin, R.L. and U. Choe. (1979). Tighter Relaxations of Fixed Charge Network Flow Problems. Working paper, School of Industrial and Systems Engineering, Georgia Institute of Technology.
Rardin, R.L. and L.A. Wolsey. (1993). Valid Inequalities and Projecting the Multi-commodity Extended Formulation for Uncapacitated Fixed Charge Network Flow Problems. European Journal of Operational Research, 71:95–109.
Stoer, M. and G. Dahl. (1994). A Polyhedral Approach to Multicommodity Survivable Network Design. Numerische Mathematik, 68:149–167.
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Gendron, B., Crainic, T.G., Frangioni, A. (1999). Multicommodity Capacitated Network Design. In: Sansò, B., Soriano, P. (eds) Telecommunications Network Planning. Centre for Research on Transportation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5087-7_1
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