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An original problem statement and solution algorithms are presented for an applied problem in the scheduling theory. The idea of the optimal fleet assignment and Flight Scheduling problem considered in this paper is to find a scheduling control method that minimizes the losses of the airline company from aircraft schedule disruptions. The problem is NP-complete and cannot be solved accurately for any real-life number of dimensions. An efficient parametric algorithm is proposed for finding an approximate solution of the problem. The proposed algorithm is an extension of the schedule optimization algorithm for a system of unrelated parallel machines with job release dates, which is based on the makespan criterion (Cmax). A substantial example is presented of applying the algorithm, as well as statistics of testing it on the data of a generating problem by the Cmax criterion.

An optimal fleet assignment and flight scheduling problem for an airline company