Optimising distributed heterogeneous flowshop group scheduling arising from PCB mounting: integrating construction and improvement heuristics

In real-world manufacturing systems for processing printed circuit boards (PCBs), the workshops integrating various flowline-based cells are common in large-scale enterprises. The scheduling problem within the systems is modelled as the distributed heterogeneous flowshop group scheduling problem (DHFGSP) in this study. Departing from practical requirements and considering the grouping characteristics among PCB components, we account for carryover sequence-dependent setup time (CSDST). Moreover, recognising the critical importance of just-in-time production in semiconductor manufacturing, the total tardiness, a previously unexplored objective within the DHFGSP context, is addressed. To tackle this problem, a mixed-integer linear programming (MILP) model, capable of obtaining optimal solutions for small-scale instances, is proposed. Due to the NP-hard nature of the problem, obtaining high-quality solutions in a reasonable time using the MILP model becomes challenging for large-scale instances. Therefore, a solution algorithm, comprising construction and improvement heuristics, is developed. Capitalising on the problem's characteristics, the construction heuristic efficiently generates high-quality feasible solutions in a very short time. Built primarily around artificial bee colony (ABC) optimisation, the improvement heuristic can significantly further enhance solutions by integrating the collaborative and restart operators. Comprehensive experiments on instances of varying scales demonstrate the effectiveness of the proposed algorithm for the problem under investigation.