An Intuitive and Efficient Approach to Process Scheduling with Sequence-Dependent Changeovers Using Timed Automata Models

In the process industries where multiple products have to be produced in the batch mode, the optimal assignment of the operations to the available resources and their sequencing can contribute considerably to economic success. Among the several methods proposed to model and solve batch scheduling problems, techniques based on a reachability analysis of timed automata (TA) models have gained attention recently. The appeal of the approach is the modular, intuitive, and straightforward graphical modeling of complex scheduling problems, and an efficient solution technique based upon reachability algorithms. In this contribution, we present an introduction to the TA-based approach to scheduling and specifically address the problem of batch scheduling with sequence-dependent setup and changeover times. In the TA-based approach, the resources, recipes, and additional timing constraints are modeled independently as sets of (priced) timed automata. The sets of individual automata are synchronized by means of synchronization labels and are composed by parallel composition to form a global automaton. A cost-optimal symbolic reachability analysis is performed on the composed automaton to derive schedules with the objective of minimizing makespan. The TA models of the recipes are extended here to include setup times as well as sequence-dependent changeovers. The performance of the approach to model and to solve real-world scheduling problems with sequence-dependent changeovers is demonstrated for two different case studies. A comparative study on the TA-based approach with various MILP formulations is performed on a famous case study from the literature, and the results are discussed.