Performance evaluation in finite production run-based serial lines with geometric machines

A production run is usually referred to as a group of identical or similar goods that is produced by a particular manufacturing process. In various manufacturing industries, the manufacturing activity is carried out by deploying a series of production runs of different products according to customer orders. 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. For one-machine case, exact Markovian analysis approach is used. Closed-form formulae are derived to calculate the transient performance of the production line during the processing of a finite-size production run as well as mean of its completion time. For two- and multi-machine lines, an aggregation-based computationally efficient approach is proposed to approximate the system performance measures. The accuracy of the algorithms developed are justified using numerical simulations.