Worst-Case Analysis of LPT Scheduling on a Small Number of Non-Identical Processors

The approximation ratio of the longest processing time (LPT) scheduling algorithm has been investigated in various studies. While tight is known for cases when all processors are identical, unknown have different speeds. In this study, we provide a three, four, and five processors. We show that ratios these no larger than lower bound provided by Gonzalez, Ibarra, Sahni (SIAM J. Computing 1977). approximately 1.38, 1.43, 1.46 processors, respectively.