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Branch Less, Cut More and Schedule Jobs with Release and Delivery Times on Uniform Machines

Author

Listed:
  • Nodari Vakhania

    (Centro de Investigacion en Ciences, Universidad Autónoma del Estado de Morelos, Cuernavaca 62209, Mexico)

  • Frank Werner

    (Faculty of Mathemaics, Otto-von-Guericke University Magdeburg, PSF 4120, 39016 Magdeburg, Germany)

Abstract

We consider the problem of scheduling n jobs with identical processing times and given release as well as delivery times on m uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (“branch less and cut more”). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is O ( γ m 2 n log n ) , where γ can be either n or the maximum job delivery time q max . This complexity can even be reduced further by using a smaller number κ < n in the estimation describing the number of jobs of particular types. However, this number κ becomes only known when the algorithm has terminated.

Suggested Citation

  • Nodari Vakhania & Frank Werner, 2021. "Branch Less, Cut More and Schedule Jobs with Release and Delivery Times on Uniform Machines," Mathematics, MDPI, vol. 9(6), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:633-:d:518026
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    References listed on IDEAS

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    1. M.I. Dessouky & B.J. Lageweg & J.K. Lenstra & S.L. van de Velde, 1990. "Scheduling identical jobs on uniform parallel machines," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 44(3), pages 115-123, September.
    2. Carlier, Jacques, 1982. "The one-machine sequencing problem," European Journal of Operational Research, Elsevier, vol. 11(1), pages 42-47, September.
    3. Graham McMahon & Michael Florian, 1975. "On Scheduling with Ready Times and Due Dates to Minimize Maximum Lateness," Operations Research, INFORMS, vol. 23(3), pages 475-482, June.
    4. Nodari Vakhania, 2004. "Single-Machine Scheduling with Release Times and Tails," Annals of Operations Research, Springer, vol. 129(1), pages 253-271, July.
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