Manufacturing costs in serial production systems with rework

In this paper, we present a Markovian modelling framework that can describe any serial production system with rework. Each production stage is represented by a state in the Markov chain. Absorbing states indicate the events of scrapping a product at a production stage or the completion of the finished product. Generalizable formulae for the final absorption probabilities are derived that represent: (1) the probability that an unfinished product is scrapped at a certain production stage and (2) the yield of the system. We also derive various expected costs and quantities associated with all products ending in any absorbing state, as well as the equivalent costs and quantities for finished products. The applicability of our modelling framework is demonstrated in a real-life manufacturing environment in the food-packing industry.