Optimal flow control for scheduling in manufacturing systems with continuous setups

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 multilevel 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