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Research on single-machine scheduling with position-dependent weights and past-sequence-dependent delivery times

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Abstract

This article studies scheduling problems with past-sequence-dependent delivery times (denoted by psddt) on a single-machine, i.e., the delivery time of a job depends on its waiting time of processing. We prove that the total (discounted) weighted completion time minimization can be solved in \(O(n\log n)\) time, where n is the number of jobs, and the weight is a position-dependent weight. For common (denoted by con) and slack (denoted by slk) due-date assignment and position-dependent weights (denoted by pdw), we prove that an objective cost minimization is solvable in \(O(n\log n)\) time. The model (i.e., psddt and pdw) can also be extended to position-dependent (time-dependent) processing times.

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Acknowledgements

This work was supported by the Natural Science Foundation of Liaoning Province, China (2020-MS-233).

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Correspondence to Wei-Wei Liu.

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Wang, JB., Cui, B., Ji, P. et al. Research on single-machine scheduling with position-dependent weights and past-sequence-dependent delivery times. J Comb Optim 41, 290–303 (2021). https://doi.org/10.1007/s10878-020-00676-z

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