A processing network problem is a network flow problem with the following characteristics:
1. conservation of flow in nodes and on arcs.
2. capacity bounds on arcs.
3. there is a non empty subset PN of the node set, such that for each node in PN the flows on the outgoing arcs (or on the incoming arcs) are proportional to each other.
A mathematical formulation of the min cost flow problem in a processing network will be given. The structure of a basis will be discussed. This structure can be used in specifications of the primal simplex algorithm for the min cost flow problem, in analogy with other type of network flow problems (pure, generalized and multicommodity networks).