An optimal control model for continuous time production and setup scheduling

This paper concerns a new approach to continuous time optimal scheduling problems for a large class of manufacturing systems. The proposed approach states the problem in terms of optimal control with setup and production rates controllable on one hierarchical level. This allows for the traditional disadvantages of the two-level problem consideration (one level for defining the target production rates, and the other for scheduling the setup changes) to be avoided and stable control strategies to be obtained. Analysis of the maximum principle results in setup conditions of the optimal schedule and special regimes to which the optimal tends between subsequent setups. Based on these results, a numerical method is developed to define the sequence of the special regimes and the timing for getting into and out of them. An example illustrates the effectiveness of the approach.