Minimal processes of limited capacity in production networks

Multi-staged manufacturing systems such as workshops, factories or amalgamations are considered where the transportation and manufacturing potential is constrained and the demand for the product specified. The set of admissible processes is defined and a natural ranking of this set is introduced. An operator is designed whose fixed points are minimal, relative to this ranking, feasible processes. This problem is interpreted in meaningful terms. Minimal processes are specified which are enlightening for on-line process control. Cases are discussed where the set of feasible processes includes a minimal feasible process. This process is shown to be optimal for the class of linear cost Junctions.