Optimal flow control of flexible manufacturing systems: Setup localization by an iterative procedure

This paper develops a method for continuous-time optimal control scheduling problems in flexible manufacturing systems. These systems operate under arbitrarily changing demand profiles with respect to multi-level bills of materials. Differential equations are used to model production and setup processes. Direct application of the maximum principle to the problem leads to shooting procedures effective only for small-scale manufacturing systems. The proposed method improves the direct approach by replacing the original problem with two simplified problems constructed so that solving them cyclically tends to the solution of the original one. The approach is compared with the shooting method and a two-level hierarchical scheduling approach implicating a widely used clear-a-fraction policy.