Multi-product batch scheduling with intermediate due dates using priced timed automata models

In this contribution, we discuss an extension of the earlier work on scheduling using reachability analysis of timed automata (TA) models, specifically addressing the problem of tardiness minimization. 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. The global automaton has an initial location where no operations have been started and at least one target location where all operations that are required to produce the demanded quantities of end-products within the specified due dates have been finished. A cost-optimal symbolic reachability analysis is performed on the composed automaton to derive schedules with the objective of minimizing tardiness. The model formulation is extended to include release dates of the raw materials and due dates of the production orders. The meeting of due dates is modeled by causing additional costs (e.g. penalties for late delivery and storage costs for early production). The modeling approach and the performance of the approach are tested for two different case studies and the results are compared with that of a MILP formulation solved using the standard solver CPLEX. The numerical experiments demonstrate, that the TA-based approach is competitive compared to standard commercial solvers and good feasible solutions are obtained with considerably reduced computational effort.