# Scheduling jobs online on 3 identical machines – a lower bound of 5/3

Consider the Online Scheduling Problem with $$3$$ identical machines. Jobs, with arbitrary size, arrive online one after another and need to be scheduled on one of the $$3$$ machines without ever moving them again.

How can I show, that there can’t be any deterministic Online-Algorithm which achieves a competitive ratio of $$c<\frac{5}{3}$$.

This should be solved by just giving some instance $$\sigma$$ and arguing that no det. algorithm can do better. Same can easily be done for $$2$$ machines and $$c<\frac{3}{2}$$. Sadly I can’t find any solution to this (more or less) textbook answer.