Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation

Authors:
V. S. Gordon;C. N. Potts;V. A. Strusevich;J. D. Whitehead
Affiliations:
United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk, Belarus;University of Southampton, Southampton, UK;School of Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, London, UK SE10 9LS;University of Southampton, Southampton, UK
Venue:
Journal of Scheduling
Year:
2008

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Abstract

We consider various single machine scheduling problems in which the processing time of a job depends either on its position in a processing sequence or on its start time. We focus on problems of minimizing the makespan or the sum of (weighted) completion times of the jobs. In many situations we show that the objective function is priority-generating, and therefore the corresponding scheduling problem under series-parallel precedence constraints is polynomially solvable. In other situations we provide counter-examples that show that the objective function is not priority-generating.