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Rescheduling with New Orders Under Bounded Disruption

Author

Listed:
  • Stefan Lendl

    (Department of Operations and Information Systems, University of Graz, 8010 Graz, Austria)

  • Ulrich Pferschy

    (Department of Operations and Information Systems, University of Graz, 8010 Graz, Austria)

  • Elena Rener

    (Department of Management and Production Engineering, Politecnico di Torino, 10129 Torino, Italy)

Abstract

Rescheduling problems arise when unpredicted events occur, such as the arrival of new orders. These new jobs should be integrated in a proper way in the existing schedule of the so-called old jobs, with the aim of minimizing an objective function for the joint set of jobs. To avoid a major disruption of the original schedule, each old job is not allowed to deviate from its original completion time by more than a certain threshold. Filling a gap in the existing literature, we consider the minimization of the total weighted completion time. The resulting rescheduling problem is shown to be weakly NP-hard and several properties of the structure of an optimal schedule are derived. These can be used for the construction of an exact dynamic programming algorithm with pseudo-polynomial running time. A fully polynomial time approximation scheme is obtained from the dynamic program by three different scaling and reduction steps. Finally, for the minimization of the number of late jobs a strong NP-hardness result is derived.

Suggested Citation

  • Stefan Lendl & Ulrich Pferschy & Elena Rener, 2024. "Rescheduling with New Orders Under Bounded Disruption," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1654-1675, December.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:6:p:1654-1675
    DOI: 10.1287/ijoc.2023.0038
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