Deadlock avoidance for production systems with flexible routing

The objective of this work is to characterize the deadlock avoidance problem for systems with flexible routing capabilities. Specifically, the paper addresses deadlock avoidance for single capacity systems (each machine has a single unit of buffer capacity), and mixed capacity systems (some machines have multiple units of buffer capacity). For each of these, we characterize deadlock and prove the correctness of several methods of suboptimal deadlock avoidance. We also address two interesting special cases. The first assumes that every stage of every part type can be performed on at least one multiple capacity machine, whereas the second provides a finite central buffer that can be revisited after every processing stage. For the first case, we present two suboptimal deadlock avoidance approaches, while for the second case, we show optimal deadlock avoidance to be computationally tractable.