A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times

In this study, we consider the problem of scheduling a set of independent jobs with sequence-dependent setup times and job splitting, on a set of identical parallel machines such that maximum completion time (makespan) is minimized. For this NP-hard problem, we suggest a heuristic algorithm improving an existing one, using a linear programming modeling with setup times and job splitting considerations. The performance of our new method is tested on over 6000 instances with different size by comparing it with a lower bound.