Multicommodity Network Problems: Applications and Computations

Abstract It is well documented that pure network problems can be solved from 10 to 100 times faster using specialized primal simplex software as compared to general linear programming systems. For multi-commodity network flow problems, the computational savings are a function of the number of tight-side constraints. In this study, we present three real-world multicommodity models and data concerning the number of tight-side constraints. We also present the results of a computational study on a set of 25 randomly generated test problems which have a wide range of number of tight-side constraints. We conclude that a specialized multicommodity network code is three times as fast as a general code, while a specialized network with general side constraints code has twice the speed of a general LP code.

[1]  James E. Kalan.  Aspects of large-scale in-core linear programming , 1971, ACM '71.

[2]  Leon S. Lasdon,et al.  A generalized upper bounding algorithm for multicommodity network flow problems , 1971, Networks.

[3]  Darwin Klingman,et al.  Augmented Threaded Index Method for Network Optimization. , 1974 .

[4]  R. V. Helgason,et al.  Algorithms for network programming , 1980 .

[5]  Roy E. Marsten,et al.  The Design of the XMP Linear Programming Library , 1981, TOMS.

[6]  Eli Hellerman,et al.  Reinversion with the preassigned pivot procedure , 1971, Math. Program..

[7]  Darwin Klingman,et al.  IMPROVED COMPUTER-BASED PLANNING TECHNIQUES , 1977 .

[8]  Bruce A. Murtagh,et al.  Advanced linear programming: Computation and practice , 1981 .

[9]  Michael A. Saunders,et al.  A FAST, STABLE IMPLEMENTATION OF THE SIMPLEX METHOD USING BARTELS-GOLUB UPDATING , 1976 .

[10]  Wm. Orchard-Hays.  An exercise in basis inversion , 1973, SMAP.

[11]  Gerald G. Brown,et al.  Design and Implementation of Large-Scale Primal Transshipment Algorithms , 1976 .

[12]  A. Ali,et al.  Technical Note - Computational Comparison among Three Multicommodity Network Flow Algorithms , 1980, Oper. Res..

[13]  Richard V. Helgason,et al.  Spike Swapping In Basis Reinversion. , 1979 .

[14]  Gene H. Golub,et al.  The simplex method of linear programming using LU decomposition , 1969, Commun. ACM.

[15]  Jeffery L. Kennington,et al.  A product form representation of the inverse of a multicommodity cycle matrix , 1977, Networks.

[16]  Michael A. Saunders,et al.  Large-scale linearly constrained optimization , 1978, Math. Program..

[17]  Michael Engquist,et al.  Efficient Tree Handling Procedures for Allocation/Processing Networks. , 1982 .