Optimal flow control for continuous-time scheduling in flexible manufacturing systems

This paper introduces a new approach to continuous-time optimal scheduling problems for a large class of manufacturing systems. This class belongs to a make-to-order production environment, based on multi-level bills of materials, flexible flow shops with setup effects and finite capacities on the shop floor. So far the setup and production planning had to be decomposed into two levels; the present model allows treating these two issues on one level, thus potentially achieving better production results. The proposed approach states the problem in terms of optimal control and investigates control strategies by means of the maximum principle for the problems with constraints on state variables. A numerical method concludes this investigation, sustaining the effectiveness of the approach on a robotic cell example.