Serial production lines with geometric machines and finite production runs: performance analysis and system-theoretic properties

A production run is typically referred to as a group of identical goods that is produced by a particular manufacturing process. In many discrete manufacturing practices, the manufacturing activity is carried out by deploying a series of production runs of different products according to customer orders. If the volume of a production run is relatively small and process changeovers are necessary, the production system operates partially (or entirely) in the transient regime, especially at the beginning and near the end of a production run. In this case, the traditional steady-state analysis approach may become inapplicable. In this paper, we consider finite production run-based manufacturing in serial lines with machines obeying the geometric reliability model and buffers having finite capacity. Exact Markovian analysis is first used to derive the closed-form formulae to calculate the transient performance of the production line during a production run as well as the distribution, mean, and standard deviation of its completion time in one- and two-machine lines. For multi-machine lines, an aggregation-based approach is proposed to approximate the system performance measures with high accuracy and computational efficiency. In addition, system-theoretic properties of production run completion time with respect to machine and buffer parameters are discussed.