We study minmax due-date based on common flow-allowance assignment and scheduling problems on a single machine, and extend known results in scheduling theory by considering convex resource allocation. The total cost function of a given job consists of its earliness, tardiness and flow-allowance cost components. Thus, the common flow-allowance and the actual jobs’ processing times are decision variables, implying that the due-dates and actual processing times can be controlled by allocating additional resource to the job operations. Consequently, our goal is to optimize a cost function by seeking the optimal job sequence, the optimal job-dependent due-dates along with the actual processing times. In all addressed problems we aim to minimize the maximal cost among all the jobs subject to a constraint on the resource consumption. We start by analyzing and solving the problem with position-independent workloads and then proceed to position-dependent workloads. Finally, the results are generalized to the method of common due-window. For all studied problems closed form solutions are provided, leading to polynomial time solutions.

我们基于单台机器上常见的流量分配和调度问题研究minmax到期日，并通过考虑凸资源分配来扩展调度理论中的已知结果。给定工作的总成本函数由其早期，拖延和允许流动的成本组成。因此，公共流程许可和实际作业的处理时间是决策变量，这意味着可以通过为作业操作分配额外的资源来控制截止日期和实际处理时间。因此，我们的目标是通过寻找最佳作业顺序，最佳作业相关的到期日期以及实际处理时间来优化成本函数。在所有已解决的问题中，我们的目标是使所有作业中受资源消耗限制的最大成本降至最低。我们首先分析和解决与位置无关的工作负载的问题，然后再进行与位置相关的工作工作量。最后，将结果推广到通用到期窗口方法。对于所有研究的问题，提供封闭形式的解决方案，从而产生多项式时间解。