Joint approach to design and control of process flows to avoid deadlocks in flexible production systems

In the paper we develop a discrete dynamic model of concurrent cyclic processes and state two formal decision problems concerning testing the realizability of such system at its design phase and testing the safety (with respect to deadlocks) of control decisions undertaken on-line. We prove the NP- completeness of the problems and point out that such complexity clearly hinders a practical application of the optimal (i.e. the least-restrictive) approach proposed. Thus, we discuss a pragmatic solution for deadlock handling being a compromise between the restriction level of the algorithms required and their computational time-complexity. We introduce a satisfactory condition for realizability of the system and prove that in the cyclic systems which satisfy the condition we can employ deadlock avoidance algorithms developed for pipeline processes.