This paper deals with the single machine scheduling problems, where the job processing times are given as linear functions dependent on the processing start time and the amount of resources allocated to the jobs. We consider two problems: the first one deals with the makespan minimization where the total amount of resources is limited; in the second one the value of makespan is limited and the considered criterion is the minimization of the total resource consumption. We present optimal algorithms for some special cases of the first problem. For the second problem we present a solving method which can be applied if only the symmetrical version of the problem is solvable in polynomial time and some additional conditions are satisfied.
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