We consider the problem of scheduling on uniform processors with nonsimultaneous machine available times with the purpose of mini\-mi\-zing 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 times. This results from properties of the Multifit algorithm when used for scheduling on uniform processors with simultaneous start times. We also show that if a better approximation bound of Multifit 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 if a property of the proof of the simultaneous uniform processor bound is met.
in Liliana Grigoriu Scheduling on parallel machines with variable availability patterns, doctoral thesis, University Politehnica Bucharest, October 2012