A Markov Chain Model of Serial Production Systems with Rework

In this paper, we present a Markovian modeling framework that can describe any serial production system with rework. Under this framework, 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 scraped 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 modeling framework is demonstrated in a real-life manufacturing environment in the food-packing industry. We show how the model can be used to assess the impact of changes in the transition probabilities on the various expected costs and quantities. The model can be used as a decision-making tool to assist management identify the production stage(s) that if improved, will yield the maximum benefit in terms of the costs and yield of the serial production system.