LPT Scheduling for Multipurpose Machines

We consider scheduling jobs on multipurpose machines where jobs can be processed by a subset of the machines operated in parallel with the objective of minimizing makespan. We apply LPT(Longest Processing Time first) algorithm and prove that its posterior worst-case performance ratio is at most $log_24m/(1+{\lambda})$, where \lambda is the number of machines eligible for processing the job with the latest completion time. In general, LPT is shown to always find a schedule with makespan at most $log_24m/3$ times optimum.

여러 종류의 작업 처리가 가능한 기계 시스템에 대한 LPT 스케줄링