We investigate the problem of on-line scheduling open shops of two and three machines with an objective of minimizing the schedule makespan. We first propose a 1.848-competitive permutation algorithm for the non-preemptive scheduling problem of two machines and show that no permutation algorithm can be better than 1.754-competitive. Secondly, we develop a (27/19)-competitive algorithm for the preemptive scheduling problem of three machines, which is most competitive.
