Stability and performance of distributed production control methods based on continuous-flow models

Investigates the stability and performance of a two-level production control method for part release, routing, and machine scheduling in manufacturing systems. At the first level (off line), a continuous-flow (fluid) approximation of the production control problem is formulated and solved as a linear program. At the second level (on line), simple distributed control policies are used to track the solution of the continuous-flow model of level one. A major research issue concerns the potential instability of decentralized tracking policies due to the discreteness of the decision space (caused by the sequential nature of operations and their discrete processing times). The author considers a broad class of distributed tracking policies, which is called nonidling-nonexceeding (NINE) and finds a sufficient condition for their stability. The results show the NINE policies potential instability for nonacyclic systems due to machine starvation, which is caused by tracking delays induced by the discrete nature of operations. The sufficient stability condition takes a familiar form, namely that, the largest eigenvalue of a matrix-which captures the dynamics of tracking delays in the system-must be less than one. It ensures the contraction of tracking delays in the feedback loops of material flow in the system. When this condition is met, an upper bound on the performance of the policy is readily obtained. It is further shown that any nonidling dispatching policy can be considered as a special NINE policy, and thus the same stability and performance results apply to the class of all nonidling policies. The author also investigates NINE policies with buffer priorities and shows that a NINE policy with certain buffer priority ordering is always stable. Simulation experiments show that near-zero work-in-process and finished-parts´ inventory can be achieved with the method even for demands that are very close to the production capacity of the system