Lead time distribution in unreliable production lines processing perishable products

The integrated analysis of quality and production logistics in manufacturing systems has recently attracted increasing interest among researchers and industrialists. It has been shown that several links exist among the manufacturing system design and the product quality, which are dominated by complex dynamic interactions. However, these interactions have never been addressed in manufacturing systems producing perishable products. The quality characteristics of perishable products deteriorate over time. Several examples of this phenomenon are found in the food industry, in semiconductor manufacturing, and in polymers forming processes. If the time parts spend in the system exceeds a certain threshold the inventory becomes obsolete and defective parts need to be scrapped. A similar problem is also found in highly dynamic supply chains. In this paper, we provide an analytical method to model the dynamics of this phenomenon in a buffered two-machines line with general Markovian machines. The main contribution is a method for the calculation of the lead time distribution, that allows us to derive predictions of the effective throughout and scrap rate. In case of two-state machines the approach leads to symbolic expressions while in case of general Markovian machines numerical solutions can be obtained. Numerical results provide relevant insights on the problem and show counterintuitive behaviors paving the way to the design of buffers for product quality.