Computational complexity of determining resource loops in re-entrant flow lines

This paper presents a comparison study of the computational complexity of the general job shop protocol and the more structured flow line protocol in a flexible manufacturing system. It is shown that the representative problem of finding resource invariants is NP-complete in the case of the job shop, while in the flow line case it admits a closed form solution. The importance of correctly selecting part flow and job routing protocols in flexible manufacturing systems to reduce complexity is thereby conclusively demonstrated.