Abstract
This paper introduces a new environment of online scheduling in which jobs are scheduled under the non-delayed processing (NDP) constraint, where NDP means that the available jobs cannot be delayed for processing when some machine is idle. We study in this paper the single-machine online scheduling to minimize the maximum weighted completion time ( $${\textit{WC}}_{\mathrm{max}}$$ ) or the maximum delivery completion time ( $$L_{\mathrm{max}}$$ ) under the NDP constraint. For the first problem, we establish a lower bound 2 and provide an online algorithm which has a competitive ratio of $$(3+\sqrt{5})/2\approx 2.618$$ . We present a 3/2-competitive best possible online algorithm for the second problem.
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