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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.

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In this work, the operation of modular flexible continuous polymerization plants is investigated. For a benchmark problem (six products with an overall yearly demand of 20,000 t, two continuous production lines with modules that can be moved between the lines) that is defined by industrial speciality polymer producers, the optimal campaign planning problem is solved, minimizing the cost of cleaning and waste production. The results are compared to the production of the same portfolio of products in a batch plant. The results show that the changeovers between different products and production parameters lead to a loss of production capacity and additional costs. For long production campaigns (demand satisfaction on a monthly basis), these costs and losses are comparatively small, whereas for short demand satisfaction periods (one week) they are significant. On the other hand, longer demand satisfaction periods require a significant amount of product inventory and hence storage facilities.

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