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.

本文介绍了一种在线调度的新环境，在该环境中，作业是在非延迟处理（NDP）约束下进行调度的，其中NDP意味着当某些计算机处于空闲状态时，可用作业不会被延迟进行处理。我们在本文中研究了单机在线调度，以最小化最大加权完成时间（\（{\ textit {WC}} _​​ {\ mathrm {max}} \））或最大交付完成时间（\（L_ { \ mathrm {max}} \））在NDP约束下。对于第一个问题，我们建立一个下界2并提供一种在线算法，该算法的竞争比为\（（3+ \ sqrt {5}）/ 2 \约2.618 \）。针对第二个问题，我们提出了一个3/2竞争的最佳可能在线算法。