Abstract
We consider the problem of constructing a feasible (in which all tasks complete before their due dates) schedule for a single machine with arbitrary due dates and maximum start time of the machine or minimum total earliness of the tasks completion times in relation to their due dates. It is shown that for the criterion of maximum start time of the machine the problem is polynomially solvable, we give a polynomial algorithm for its solving. With a fixed start time of the machine the problem is polynomially solvable for the criterion of minimizing the total earliness of the completion times of the tasks if qualitatively proven and statistically significant properties of an optimal solution (Heuristics 1 and 2) are met. The problem with an arbitrary start time of the machine to construct an optimal schedule minimizing the total earliness of the tasks completion times is intractable: an exact polynomial algorithm for its solving is not known. For the case if the Heuristics 1 and 2 are true for an arbitrary start time of the machine, we develop an efficient PSC-algorithm. For the opposite case, this PSC-algorithm is an efficient approximation algorithm for the problem solving.
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Zgurovsky, M.Z., Pavlov, A.A. (2019). Optimal Scheduling for Two Criteria for a Single Machine with Arbitrary Due Dates of Tasks. In: Combinatorial Optimization Problems in Planning and Decision Making. Studies in Systems, Decision and Control, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-98977-8_2
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DOI: https://doi.org/10.1007/978-3-319-98977-8_2
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