Optimization Letters

, Volume 12, Issue 4, pp 903–914 | Cite as

An exact algorithm for the bi-objective timing problem

  • Sophie Jacquin
  • Fanny Dufossé
  • Laetitia Jourdan
Original Paper


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.


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



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Inria Lille - Nord Europe, ORKAD, CRIStALUniversity of Lille 1Villeneuve d’AscqFrance

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