Scheduling on Uniform Nonsimultaneous Parallel Machines

We consider the problem of scheduling on uniform processors which may not start processing at the same time with the purpose of minimizing the maximum completion time. We give a variant of the Multifit algorithm which generates schedules which end within 1.382 times the optimal maximum completion time for the general problem, and within √ 6/2 times the optimal maximum completion time for problem instances with at most two processors. This results from properties of a variant of the Multifit algorithm for scheduling on uniform processors with simultaneous start times. We also show that if a better approximation bound of the Multifit variant for scheduling on uniform processors will be found in the future, this bound will also apply to our Multifit variant for scheduling on nonsimultaneous uniform processors.