Scheduling distributed flowshops with flexible assembly and set-up time to minimise makespan

The scheduling problems under distributed production or flexible assembly settings have achieved increasing attention in recent years. This paper considers scheduling the integration of these two environments and proposes an original distributed flowshop scheduling problem with flexible assembly and set-up time. Distributed production stage is deployed several homogeneous flowshop factories that process the jobs to be assembled into final products in the flexible assembly stage. The objective is to find a schedule, including a production subschedule for jobs and an assembly subschedule for products, to minimise the makespan. Such a scheduling problem involves four successive decisions: assigning jobs to production factories, sequencing jobs at every factory, designating an assembly machine for each product and sequencing products on each assembly machine. The computational model is first established, and then a constructive heuristic (TPHS) and two hybrid metaheuristics (HVNS and HPSO) are proposed. Numerical experiments have been carried out and results validate the algorithmic feasibility and effectiveness. TPHS can obtain reasonable solutions in a shorter time, while metaheuristics can report better solutions using more yet acceptable time. HPSO is statistically comparable yet less robust compared with HVNS for small-scale instances. For the large-scale case, HPSO outperforms HVNS on both effectiveness and robustness.