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We consider the resource allocation problem under a two-machine flow shop environment where the job sequence has been determined in advance. The resource is used to reduce the processing time that is inversely proportional to the resource consumption amount. Furthermore, there exist the lower and upper bounds on the amount of the resources consumed by each job. The objective is to minimize the makespan plus the total resource consumption cost. We show that the problem can be solved in strongly polynomial time.
Choi et al. (Sat,) studied this question.