On preemptive scheduling on unrelated machines using linear programming

<abstract><p>We consider a basic preemptive scheduling problem where $ n non-simultaneously released jobs are to be processed by m unrelated parallel machines so as minimize maximum job completion time. An optimal LP-solution has been used construct an schedule for simultaneously in time O(n^3) $. We propose fast O(m) algorithm that finds case the above possesses "small enough" number of non-zero elements. another linear program and show how can constructed also from solution program. Based on stronger formulation, we extend earlier known construction procedure jobs. The is important, particular, because there may exist no agrees with LP-solution. imposes preemptions, additional preemptions occur during process, might forced split same machine. if allowed, even restricted version three NP-hard. As result, obtain that, given LP-solution, it NP-hard find side at most m-1 preemptions.</p></abstract>