A Study of On-Line Scheduling Two-Stage Shops

Abstract

We investigate the problem of on-line scheduling two-stage shops with the objective of minimizing the maximum completion time. We show that for two-stage open shops, no on-line algorithm can have a worst-case performance ratio less than \(\tfrac{1}{2}(1 + \sqrt {5} ) \approx 1.618\) if preemption is not allowed. We provide an on-line heuristic algorithm with worst-case performance ratio 1.875. If preemption is allowed, however, we give an on-line algorithm with worst-case performance ratio 4/3, and show that it is a best possible on-line algorithm. On the other hand, for a two-stage flow shop or job shop, we prove that no on-line algorithm can outperform a simple one, which has a worst-case performance ratio of 2.