Integration of a primal simplex network algorithm with a large-scale mathematical programming system
ACM Transactions on Mathematical Software (TOMS)
A primal simplex approach to pure processing networks
Management Science
Pivot Strategies for Primal-Simplex Network Codes
Journal of the ACM (JACM)
The Design of the XMP Linear Programming Library
ACM Transactions on Mathematical Software (TOMS)
The simplex method of linear programming using LU decomposition
Communications of the ACM
Algorithms for Network Programming
Algorithms for Network Programming
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In processing networks, ordinary network constraints are supplemented by proportional flow restrictions on arcs entering or leaving some nodes. This paper describes a new primal partitioning algorithm for solving pure processing networks using a working basis of variable dimension. In testing against MPSX/370 on a class of randomly generated problems, a FORTRAN implementation of this algorithm was found to be an order-of-magnitude faster. Besides indicating the use of our methods in stand-alone fashion, the computational results also demonstrate the desirability of using these methods as a high-level module in a mathematical programming system.