Scheduling with Safety Distances

The authors investigate the problem of Scheduling with Safety Distances (SSD) that consists in scheduling jobs on two parallel machines without machine idle time. Every job is already assigned to its machine, and they just have to specify an ordering of the jobs for each machine. The goal is to find orderings of the jobs such that the minimum time elapsed between any two job completion times is maximized. The authors prove that this problem is NP-hard in general and give polynomial time algorithms for special cases. These results combined establish a sharp borderline between NP-complete and polynomial solvable versions of the problem SSD.