Abstract
We consider a single-machine scheduling problem such that the processing time of each job is inversely proportional to the power of the amount of resource consumption. The objective is to minimize the sum of the total resource consumption cost and the total late work, or minimize the total late work with a constraint on the total resource consumption cost. Under any objective, we prove the NP-hardness of the case with more than or equal to two different due dates, and the polynomiality of the case with a common due date.
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