We formulate a single machine online scheduling problem where jobs with distinct processing times, weights, and due dates arrive over time and must be processed one at a time without preemption in order to minimize the total weighted earliness and tardiness cost. We introduce a new scheduling policy, the list-based delayed shortest processing time (LDWSPT) policy, which is amenable to theoretical analysis. We develop lower and upper bounds on the performance of the LDWSPT policy for the minimization of total weighted (modified) earliness and tardiness cost for the case of equal earliness and tardiness costs, and then extend our results for the case when these costs are not equal. Finally, we close the optimality gap that currently exists in the literature for several variants of single machine online scheduling problems in the presence of earliness and tardiness by proving that our proposed policy is an optimal online algorithm for these variants.

我们制定了一个单机在线调度问题，其中具有不同处理时间、权重和截止日期的作业随着时间的推移到达并且必须一次处理一个而不能抢占，以最小化总加权提前和延迟成本。我们引入了一种新的调度策略，即基于列表的延迟最短处理时间（LDWSPT）策略，它适合于理论分析。我们为 LDWSPT 策略的性能制定了下限和上限，以便在提前和延迟成本相等的情况下最小化总加权（修改）提前和延迟成本，然后在这些成本不相等的情况下扩展我们的结果. 最后，