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Abstract We consider a two-machine flow shop scheduling problem in which the processing time of each operation is inversely proportional to the power of the amount of resources consumed by it. The objective is to minimize the sum of the makespan and the total resource consumption cost. We show that the problem is NP-hard, and its constrained version remains so. Then, we develop 1.25- and 2-approximation algorithms for the problem and its constrained version, respectively.
Choi et al. (Fri,) studied this question.