Joint assignment of buffer sizes and inspection points in unreliable transfer lines with scrapping of defective parts

An unreliable single part type transfer line with fixed inter machine buffer sizes is considered. In general, imperfect machines operating on imperfect raw material, or partially processed raw material, will result in the production of a mix of conforming and non conforming parts. The problem of optimal joint assignment of buffer sizes and inspection station positions is considered. The performance measure to be optimized is a combination of work in process storage, finished parts shortage, and parts inspection costs. A simplified quality aware machine Markovian model is proposed, and an approximate decomposition scheme for the analysis of the resulting transfer line model is developed, and then validated against detailed Monte Carlo simulations. The decomposition scheme lends to a dynamic programming based buffer size optimization scheme. The latter is implemented; joint buffer and inspections station positioning optimization results are reported.