Maximum principle-based methods for production scheduling with partially sequence-dependent setups

This paper introduces a continuous-time optimal control approach to cope with scheduling problems in complex manufacturing systems. These systems are controlled under arbitrary changing demand profiles with respect to multi-level bills of materials, flexible flow shops with setup effects and finite production capacities. The suggested methods extend a general optimal control approach to handle with partially sequence-dependent setups on one hierarchical level along with production scheduling. The optimal scheduling method and its enhanced modifications are derived based on the maximum principle analysis and compared to the traditional two-level hierarchical approach.