A Primal Simplex algorithm for the minimal cost flow problem in a processing network

A specification of the Primal Simplex algorithm for the minimal cost flow problem in a processing network is presented in which the basis structure is exploited. In a processing network three types of processes are distinguished: transportation-, refining- and blending processes. Each process can be represented bya single column of the coefficient matrix. The steps of the Simplex algorithm can partly be done by graph theoretic means as for pure networks and partly by using the inverse of a working basis which is of the size equal to the number of basic refining and blending processes.