Necessary and sufficient optimality conditions for scheduling unit time jobs on identical parallel machines

Peter Brucker and Natalia V. Shakhlevich ()
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Peter Brucker: Universität Osnabrück
Natalia V. Shakhlevich: University of Leeds

Journal of Scheduling, 2016, vol. 19, issue 6, No 5, 659-685

Abstract: Abstract In this paper we characterize optimal schedules for scheduling problems with parallel machines and unit processing times by providing necessary and sufficient conditions of optimality. We show that the optimality conditions for parallel machine scheduling are equivalent to detecting negative cycles in a specially defined graph. For a range of the objective functions, we give an insight into the underlying structure of the graph and specify the simplest types of cycles involved in the optimality conditions. Using our results we demonstrate that the optimality check can be performed by faster algorithms in comparison with existing approaches based on sufficient conditions.

Keywords: Parallel machine scheduling; Unit processing times; Optimality conditions (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10951-016-0471-3

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