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An exact algorithm for the bi-objective timing problem

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Abstract

The timing problem in the bi-objective just-in-time single-machine job-shop scheduling problem (JiT-JSP) is the task to schedule N jobs whose order is fixed, with each job incurring a linear earliness penalty for finishing ahead of its due date and a linear tardiness penalty for finishing after its due date. The goal is to minimize the earliness and tardiness simultaneously. We propose an exact greedy algorithm that finds the entire Pareto front in \(O(N^2)\) time. This algorithm is asymptotically optimal.

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Acknowledgements

We acknowledge Dr. Martin Drozdik for proof reading the article and corrected mathematical proofs in the article during the revision phase.

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Authors and Affiliations

  1. Inria Lille - Nord Europe, ORKAD, CRIStAL, University of Lille 1, 59655, Villeneuve d’Ascq, France

    Sophie Jacquin, Fanny Dufossé & Laetitia Jourdan

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  1. Sophie Jacquin
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  2. Fanny Dufossé
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  3. Laetitia Jourdan
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Correspondence to Laetitia Jourdan.

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Jacquin, S., Dufossé, F. & Jourdan, L. An exact algorithm for the bi-objective timing problem. Optim Lett 12, 903–914 (2018). https://doi.org/10.1007/s11590-018-1237-y

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  • DOI: https://doi.org/10.1007/s11590-018-1237-y

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