An improved primal simplex variant for pure processing networks

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Abstract
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.