Scheduling parallel serial-batch processing machines with incompatible job families, sequence-dependent setup times and arbitrary sizes

The scheduling of (parallel) serial-batch processing machines is a task arising in many industrial sectors. In the metal-processing industry for instance, cutting operations are necessary to fabricate varying metal pieces out of large base slides. Here, the (cutting) jobs have individual, arbitrary base slide capacity requirements (sizes), individual processing times and due dates, and specific material requirements (i.e. each job belongs to one specific job family, whereby jobs of different families cannot be processed within the same batch and thus are incompatible). In addition, switching of base metal slides and material dependent adjustments of machine parameters cause sequence-dependent setup times. All these conditions need to be considered while minimising total weighted tardiness. For solving the scheduling problem, a mixed-integer program and several tailor-made construction heuristics (enhanced by local search mechanisms) are presented. The experimental results show that problem instances with up to five machines and 60 jobs can be tackled using the optimisation model. The experiments on small and large problem instances (with up to 400 jobs) show that a purposefully used batch capacity limitation improves the solution quality remarkably. Applying the best heuristic to the data of two real-world application cases shows its huge potential to increase delivery reliability.