Minimal processes of limited capacity in production networks (Q1088591)

Multistage production systems such as workshops, factories, or associations are considered where the transportation and manufacturing capacity is limited and demand for the product is specified. A set of admissible processes is defined and this set is given a natural ranking. The problem is solved by designing an operator whose fixed points agree with the feasible processes relative to this ranking. A meaningful interpretation is given. The minimal processes specified are of interest for on-line production control. A case is discussed where the set of feasible processes includes a unique minimal process. This process is shown to be optimal for a class of linear cost functions.