This paper studies the complexity of single-machine scheduling with an external resource, which is rented for a non-interrupted period. Jobs that need this external resource are executed only when the external resource is available. There is a cost associated with the scheduling of jobs and a cost associated with the duration of the renting period of the external resource. We look at four classes of problems with an external resource: a class of problems where the renting period is budgeted and the scheduling cost needs to be minimized, a class of problems where the scheduling cost is budgeted and the renting period needs to be minimized, a class of two-objective problems where both, the renting period and the scheduling cost, are to be minimized, and a class of problems where a linear combination of the scheduling cost and the renting period is minimized. We provide a thorough complexity analysis (NP-hardness proofs and (pseudo-)polynomial algorithms) for different members of these four classes.

中文翻译：

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具有外部资源的单机调度

本文研究了具有外部资源的单机调度的复杂性，该资源是在非中断期间租用的。需要此外部资源的作业仅在外部资源可用时执行。有一个与作业调度相关的成本和一个与外部资源租用期的持续时间相关的成本。我们看四类关于外部资源的问题：一类是租用周期已预算且调度成本需要最小化的问题，一类是调度成本已预算且租用周期需要最小化的问题，一类双目标问题，其中租期和调度成本都需要最小化，以及一类问题，其中调度成本和租用周期的线性组合最小。我们为这四类的不同成员提供了彻底的复杂性分析（NP 硬度证明和（伪）多项式算法）。