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.

翻译：已知具有截止日期的非同时到达工件在单机上调度以最小化最大延迟的问题属于强NP难问题。本文考虑允许压缩加工时间的扩展模型。压缩加工时间需要耗费额外的新兴资源，然而使用这些资源会产生一定成本。给定总允许成本上限U，目标是最小化最大延迟。显然，通过利用可用资源，部分工件可能提前完成，目标函数值相应减小。本文证明，通过缩短特定工件的加工时间，可降低目标函数值以最小化最大延迟。尽管该广义问题比原始不可压缩版本更难求解，但在额外资源“足够充足”的条件下，我们能够获得最优解。我们确定特定工件的压缩率，并设计出获取最优解的算法。该方法在实践中具有优势，因为制造商可获知解决问题所需额外资源的准确数量。若可用额外资源少于上述最优解所需量（即不可行），则问题转化为紧致极小可行解。