This paper will study an online non-uniform length order scheduling problem. For the case where online strategies have the knowledge of Δ beforehand, which is the ratio between the longest and shortest length of order, Ting [3] proved an upper bound of ((6Δ)/(logΔ) + O(Δ~(5/6))) and Zheng et al. [2] proved a matching lower bound. This work will consider the scenario where online strategies do not have the knowledge of A at the beginning. Our main work is a ((6Δ)/(logΔ) + O(Δ~(5/6)))-competitive optimal strategy, extending the result of Ting [3] to a more general scenery.
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