Abstract
This paper studies single machine scheduling with batch deliveries, where a common due window for all jobs has to be determined, not given in advance. The objective is to minimize the overall cost for the process and delivery. Concretely, it includes the penalty of a job being early or tardy, the cost for holding and delivering a job, and the cost incurred by a late starting or a long duration of the common due window. Observing the NP-hardness, we provide an optimal algorithm of the problem and convert it to a fully polynomial time approximation scheme for a special case.
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Acknowledgements
Dedicated to Professor Minyi Yue on the Occasion of His \(100^{th}\) Birthday. This work was supported by the National Science Foundation of China under Grants 11771251 and 71771138, Special Foundation for Taishan Scholars of Shandong Province, China under Grant tsqn201812061, and Science and Technology Research Program for Higher Education of Shandong Province, China under Grant 2019KJI006.
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Zhang, L., Zhang, Y. & Bai, Q. An approximation algorithm for a supply-chain scheduling problem with an assignable common due window and holding time. J Comb Optim 44, 2167–2179 (2022). https://doi.org/10.1007/s10878-020-00594-0
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DOI: https://doi.org/10.1007/s10878-020-00594-0