A two-stage ant colony algorithm for hybrid flow shop scheduling with lot sizing and calendar constraints in printed circuit board assembly

This paper investigates a multi-stage hybrid flow shop scheduling problem with challenging characteristics including lot sizing, calendar constraints and sequence-dependent setup times in a real-world printed circuit board (PCB) assembly shop. Besides, other characteristics such as unrelated parallel machines and stage skipping also complicate the problem. Such features make the scheduling problem very difficult to find an optimal or near optimal solution. To reduce the complexity of such a PCB scheduling problem, this study develops a hierarchical approach which decomposes the original problem into two highly coupled sub-problems including job sequencing and lot scheduling with lot sizing, and further proposes a two-stage ant colony algorithm with lot sizing to evolve best results in the makespan performance. Extensive computational experiments have been conducted to illustrate the superiority of the algorithm in terms of computational time and stability.