An efficient algorithm for maximizing the expected profit from a serial production line with inspection stations and rework

In this paper, an unreliable serial production line in which nonconforming items are sent back for rework is studied. The line consists of existing machines and optional quality control stations (QCSs). The designer of such a production line needs to decide where to install the QCSs along the line and to determine the production rate, so as to maximize the expected operational profit rate obtained at a steady state. An efficient algorithm for solving this problem is presented; several extensions of the problem are discussed. An extensive simulation study proves the applicability of the model in realistic settings and is used to derive some insights about the nature of optimal solutions.