Discrete event control of production flows: Make-to-stock and make-to-order environments

This paper focuses on discrete event control of production flows. The modelled manufacturing system, based on multi-level bills of materials, is characterized by flexible machines with negligible setups and fixed production rates. Two formulations of the production flow control problem are stated as dynamic models for two contrasting make-to-stock and make-to-order environments. Study of these models with the aid of the maximum principle reveals that there are common properties for their optimal solution despite the inherent differences in the two production environments. As a result, a fast time-decomposition algorithm is suggested which takes advantage of those analytical properties to solve the problem.