A two-stage three-machine assembly scheduling problem with deterioration effect

The two-stage assembly scheduling problem has received growing attention in the research community. Furthermore, in many two-stage assembly scheduling problems, the job processing times are commonly assumed as a constant over time. However, it is at odds with real production situations some times. In fact, the dynamic nature of processing time may occur when machines lose their performance during their execution times. In this case, the job that is processed later consumes more time than another one processed earlier. In view of these observations, we address the two-stage assembly linear deterioration scheduling problem in which there are two machines at the first stage and an assembly machine at the second stage. The objective is to complete all jobs as soon as possible (or to minimise the makespan, implies that the system can yield a better and efficient task planning to limited resources). Given the fact that this problem is NP-hard, we then derive some dominance relations and a lower bound used in the branch-and-bound method for finding the optimal solution. We also propose three metaheuristics, including dynamic differential evolution (DDE), simulated annealing (SA) algorithm, and cloud theory-based simulated annealing (CSA) algorithm for find near-optimal solutions. The performances of the proposed algorithms are reported as well.