Scheduling of Parallel Print Machines with Sequence-Dependent Setup Costs: A Real-World Case Study

In the present work, we consider a real-world scheduling problem arising in the color printing industry. The problem consists in assigning print jobs to a heterogeneous set of flexographic printer machines, as well as in finding a processing sequence for the sets of jobs assigned to each printer. The aim is to minimize a weighted sum of total weighted tardiness and total setup times. The machines are characterized by a limited sequence of color groups and can equip additional components (e.g., embossing rollers and perforating rolls) to process jobs that require specific treatments. The process to equip a machine with an additional component or to clean a color group takes a long time, with the effect of significantly raising the setup costs. Furthermore, the time required to clean a color group between two different jobs depends directly on the involved colors. To tackle the problem, we propose a constructive heuristic followed by some local search procedures that are used one after the other in an iterative way. Extensive tests on real-world instances prove that the proposed algorithm can obtain very good-quality solutions within a limited computing time.