Abstract
We investigate a single-machine common due date assignment scheduling problem with the objective of minimizing the generalized weighted earliness/tardiness penalties. The earliness/tardiness penalty includes not only a variable cost which depends upon the job earliness/tardiness but also a fixed cost for each early/tardy job. We provide an \(O(n^3)\) time algorithm for the case where all jobs have equal processing times. Under the agreeable ratio condition, we solve the problem by formulating a series of half-product problems, which permits us to devise a fully polynomial-time approximation scheme with \(O(n^3/\epsilon )\) time. \(\mathcal {NP}\)-hardness proof is proved for a very special case and fast FPTASes with \(O(n^2/\epsilon )\) running time are identified for two special cases.
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Acknowledgements
The authors are very grateful to the two referees for their helpful comments, which improved the paper substantially. This research was supported in part by the National Natural Science Foundation of China under Grant Number 11701595, the Key Research Projects of Henan Higher Education Institutions (20A110037) and the Young Backbone Teachers training program of Zhongyuan University of Technology.
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Li, SS., Chen, RX. Scheduling with common due date assignment to minimize generalized weighted earliness–tardiness penalties. Optim Lett 14, 1681–1699 (2020). https://doi.org/10.1007/s11590-019-01462-5
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DOI: https://doi.org/10.1007/s11590-019-01462-5