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Minimizing the number of tardy jobs in two-machine settings with common due date

Author

Listed:
  • Federico Della Croce

    (D.A.I., Politecnico di Torino
    CNR, IEIIT)

  • Christos Koulamas

    (Florida International University)

  • Vincent T’kindt

    (Université Francois-Rabelais, CNRS, LI EA 6300, OC ERL CNRS 6305)

Abstract

We consider two-machine scheduling problems with job selection. We analyze first the two-machine open shop problem and provide a best possible linear time algorithm. Then, a best possible linear time algorithm is derived for the job selection problem on two unrelated parallel machines. We also show that an exact approach can be derived for both problems with complexity $$O(p(n) \times \sqrt{2}^n)$$ O ( p ( n ) × 2 n ) , p being a polynomial function of n.

Suggested Citation

  • Federico Della Croce & Christos Koulamas & Vincent T’kindt, 2017. "Minimizing the number of tardy jobs in two-machine settings with common due date," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 133-140, July.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:1:d:10.1007_s10878-016-0054-4
    DOI: 10.1007/s10878-016-0054-4
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    References listed on IDEAS

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    1. Lin, B.M.T. & Kononov, A.V., 2007. "Customer order scheduling to minimize the number of late jobs," European Journal of Operational Research, Elsevier, vol. 183(2), pages 944-948, December.
    2. Silvano Martello & Paolo Toth, 2003. "An Exact Algorithm for the Two-Constraint 0--1 Knapsack Problem," Operations Research, INFORMS, vol. 51(5), pages 826-835, October.
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