Abstract
In scheduling with early work, jobs are assigned to a machine by maximizing the parts of non-preemptive jobs executed before their due dates. This paper considers a weighted early work maximization problem on parallel, identical machines with an antithetical property, which holds that \(w_i \le w_j\) implies \(d_i \ge d_j\) for any two jobs i and j where \(w_j\) and \(d_j\) are weight and due date of job j, respectively. We show that the problem is weakly NP-hard. Due to the high complexity of dynamic programming, we develop three solution approaches: mixed-integer programming, heuristics, and a branch-and-bound algorithm. Through numerical experiments, we verify their performance.
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The data used to support the findings of this study are available from the corresponding author upon request.
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Acknowledgements
The corresponding author’s work was supported by the Basic Science Research Program (2019R1G1A1085191) through the National Research Foundation of Korea (NRF).
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Min, Y., Choi, BC., Park, MJ. et al. A parallel-machine scheduling problem with an antithetical property to maximize total weighted early work. 4OR-Q J Oper Res 21, 421–437 (2023). https://doi.org/10.1007/s10288-022-00517-1
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DOI: https://doi.org/10.1007/s10288-022-00517-1