Scheduling jobs on unrelated parallel machines so as to minimize makespan is one of the basic problems in the area of machine scheduling. In the first part of the paper, we prove that the power of preemption, i.e., the worst-case ratio between the makespan of an optimal nonpreemptive and that of an optimal preemptive schedule, is at least 4. This matches the upper bound proposed in Lin and Vitt...

Abstract In many applications in the context of patient appointment scheduling there are recurring tasks with fixed delays between them. These commonly referred to as coupled-task jobs. settings, each job consists two whereby second task must start processing after an exact time lag following completion first task. this paper, we introduce problem a set jobs on parallel identical machines objec...