On capacitated network design cut–set polyhedra

Abstract.This paper provides an analysis of capacitated network design cut–set polyhedra. We give a complete linear description of the cut–set polyhedron of the single commodity – single facility capacitated network design problem. Then we extend the analysis to single commodity – multifacility and multicommodity – multifacility capacitated network design problems. Valid inequalities described here are applicable to directed network design problems with any number of facility types and any level of capacities. We report results from a computational study done for testing the effectiveness of the new inequalities.

[1]  Oktay Günlük,et al.  A branch-and-cut algorithm for capacitated network design problems , 1999, Math. Program..

[2]  Richard M. Karp,et al.  On linear characterizations of combinatorial optimization problems , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[3]  Oktay Günlük,et al.  Capacitated Network Design - Polyhedral Structure and Computation , 1996, INFORMS J. Comput..

[4]  Itzhak Gilboa,et al.  Source Sink Flows with Capacity Installation in Batches , 1998, Discret. Appl. Math..

[5]  Cynthia Barnhart,et al.  Multimodal Express Package Delivery: A Service Network Design Application , 1999, Transp. Sci..

[6]  Alper Atamtürk,et al.  Sequence Independent Lifting for Mixed-Integer Programming , 2004, Oper. Res..

[7]  Oktay Günlük,et al.  Minimum cost capacity installation for multicommodity network flows , 1998, Math. Program..

[8]  Laurence A. Wolsey,et al.  Integer Knapsack and Flow Covers with Divisible Coefficients: Polyhedra, optimization and Separation , 1995, Discret. Appl. Math..

[9]  Laurence A. Wolsey,et al.  Valid Inequalities and Superadditivity for 0-1 Integer Programs , 1977, Math. Oper. Res..

[10]  Thomas L. Magnanti,et al.  Shortest paths, single origin-destination network design, and associated polyhedra , 1993, Networks.

[11]  Laurence A. Wolsey,et al.  Technical Note - Facets and Strong Valid Inequalities for Integer Programs , 1976, Oper. Res..

[12]  V. Rich.  Personal communication , 1989, Nature.

[13]  Thomas L. Magnanti,et al.  The convex hull of two core capacitated network design problems , 1993, Math. Program..

[14]  Michael Florian,et al.  The engine scheduling problem in a railway network , 1976 .

[15]  Diego Klabjan,et al.  A Polyhedral Study of Integer Variable Upper Bounds , 2002, Math. Oper. Res..

[16]  Alper Atamtürk,et al.  On splittable and unsplittable flow capacitated network design arc–set polyhedra , 2002, Math. Program..

[17]  Martin Grötschel,et al.  The ellipsoid method and its consequences in combinatorial optimization , 1981, Comb..

[18]  Richard M. Karp,et al.  On Linear Characterizations of Combinatorial Optimization Problems , 1982, SIAM J. Comput..

[19]  Thomas L. Magnanti,et al.  Modeling and Solving the Two-Facility Capacitated Network Loading Problem , 1995, Oper. Res..

[20]  Jennifer Ryan,et al.  A column generation algorithm for bandwidth packing , 1993, Telecommun. Syst..