A characterization of the maximum throughput of unreliable transfer lines

Given an unreliable transfer line with fixed size finite buffer zones for work in process, the objective is to determine the maximum, if it exists, of the production rate sustainable by the line when the first machine is never starved and the last machine is either never blocked, or if it is, an infinite backlog is allowed. A recent single machine based, transfer line under fixed demand rate decomposition method, is used to rigorously establish the existence of a maximum sustainable demand, and to characterize such a demand level via a set of necessary and sufficient conditions. The foundation of the analysis is a recursive procedure called the iterated demand algorithm (IDA). It is shown to generate a sequence that geometrically converges to a limit point, later precisely identified as the required transfer line maximum throughput. IDA becomes our computational tool. For a collection of transfer lines, numerical performance of the proposed algorithm is compared with that obtained based on other alternatives, as well as Monte Carlo based line throughput maximization results.