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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.

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The problem of optimal regulation of fleet assignments for airline flights is considered. The optimal scheduling consists in such scheduling or change of schedules that minimize the increase in the total length of the schedule or the losses of the system from violations of the set departure schedules. This is an NP-hard problem and has no effective algorithms for exact solution. A detailed review of approaches to solving its modifications and related fleet management tasks is given. Original formal setting and solutions are presented. The statistics of the testing of its software solution means modifications are presented, which proves the actual effectiveness of the developed tools.