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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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Correspondence to Laetitia Jourdan.

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Cite this article

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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Keywords

  • Just-in-time scheduling
  • Bi-objective
  • Timing problem
  • Exact algorithm