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An original statement and solution algorithms are presented for one of the key problems in the scheduling theory. The problem of optimal scheduling for a parallel system consists in the generation or control of schedules to minimize the schedule length or the losses from schedule disruptions in the completion of jobs on machines. This problem is NP-hard and cannot be solved exactly for any real-life number of dimensions. A series of modifications of the efficient parametric algorithm is proposed to find an approximate solution, which are an extension of a similar algorithm for optimal scheduling on unrelated parallel machines with release dates using the performance criterion ( Stakh ). Software implementations of the algorithm modifications have been tested on the data of a generating problem by the  Stakh  criterion; the corresponding statistics is provided.

Implementation of an efficient parametric algorithm for optimal scheduling on parallel machines with release dates