Stability and performance of continuous-flow based distributed real-time production control policies under bounded variability

In a recent work Sharifnia considered distributed tracking policies, for real-time production control of manufacturing systems, that are guided by the solution of a continuous-flow relaxation model of the system. This model can be solved efficiently, and its solution provides production target (reference) trajectories, for individual operations, to be tracked in a distributed way over time. A sufficient stability condition and tracking error bounds were found for a large class of distributed tracking policies called “nonidling-nonexceeding (NINE)”. In that work it was assumed that operations processing times and machines availabilities are deterministic and constant. In this paper we investigate the stability and performance of NINE policies in cases where these quantities may have a bounded cumulative variability. Our main result is that the condition for stability remains the same as in the case with no variability, but the tracking error bounds degrade in the presence of variability