调度带有可压缩作业的单机以最小化最大延迟
Scheduling a single machine with compressible jobs to minimize maximum lateness
AI总结：
针对带交货期的非同时到达作业的单机调度强NP难问题，提出允许作业加工时间压缩的扩展模型，确定特定作业压缩率并开发最优算法，可在资源充足时得最优解，资源不足时转换为最小可行解，为制造商提供资源需求参考。
摘要：
在单机上调度带有交货期的非同时到达作业、以最小化最大作业延迟的问题已被证明是强NP难的。本文研究了一个扩展模型，该模型允许压缩作业的加工时间。压缩作业加工时间需要投入额外的新兴资源，但资源的使用会产生一定成本。在给定总允许成本上限$U$的条件下，研究目标是最小化最大作业延迟。显然，通过利用可用资源，部分作业可以更早完成，目标函数值也会相应降低。本文研究表明，为最小化最大作业延迟，通过缩短某些特定作业的加工时间，可以降低目标值。尽管该广义问题比常规的不可压缩版本更难，但在提供“充足数量”的额外资源时，我们可以最优地求解该问题。本文确定了特定作业的压缩率，并开发了一种可得到最优解的算法。该方法在实际中具有应用价值，因为它可以为制造商提供最优求解问题所需的额外资源量信息。若可用额外资源量少于上述解中使用的资源量（即该解不可行），则将其转换为严格的最小可行解。
英文摘要：
The problem of scheduling non-simultaneously released jobs with due dates on a single machine with the objective to minimize the maximum job lateness is known to be strongly NP-hard. Here we consider an extended model in which the compression of the job processing times is allowed. The compression is accomplished at the cost of involving additional emerging resources, whose use, however, yields some cost. With a given upper limit $U$ on the total allowable cost, one wishes to minimize the maximum job lateness. It is clear that, by using the available resources, some jobs may complete earlier and the objective function value may respectively be decreased. As we show here, for minimizing the maximum job lateness, by shortening the processing time of some specially determined jobs, the objective value can be decreased. Although the generalized problem is harder than the generic non-compressible version, given a ``sufficient amount'' of additional resources, we can solve the problem optimally. We determine the compression rate for some specific jobs and develop an algorithm that obtains an optimal solution. Such an approach can be beneficial in practice since the manufacturer can be provided with an information about the required amount of additional resources in order to solve the problem optimally. In case the amount of the available additional resources is less than used in the above solution, i.e., it is not feasible, it is transformed to a tight minimal feasible solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
