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Solving the discrete-continuous project scheduling problem via its discretization

Author

Listed:
  • Joanna Józefowska
  • Marek Mika
  • Rafał Różycki
  • Grzegorz Waligóra
  • Jan Weglarz

Abstract

In this paper a discrete-continuous project scheduling problem is considered. In this problem activities simultaneously require discrete and continuous resources. The processing rate of each activity depends on the amount of the continuous resource allotted to this activity at a time. All the resources are renewable ones. The activities are nonpreemtable and the objective is to minimize the makespan. Discretization of this problem leading to a classical (i.e. discrete) project scheduling problem in the multi-mode version is presented. A simulated annealing (SA) approach to solving this problem is described and tested computationally in two versions: with and without finding an optimal continuous resource allocation for the final schedule. In the former case a nonlinear solver is used for solving a corresponding convex programming problem. The results are compared with the results obtained using SA for the discrete-continuous project scheduling problem where the nonlinear solver is used for exact solving the continuous part in each iteration. The results of a computational experiment are analyzed and some conclusions are included. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Joanna Józefowska & Marek Mika & Rafał Różycki & Grzegorz Waligóra & Jan Weglarz, 2000. "Solving the discrete-continuous project scheduling problem via its discretization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(3), pages 489-499, December.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:3:p:489-499
    DOI: 10.1007/s001860000094
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    Citations

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    Cited by:

    1. Joanna Józefowska & Mariusz Nowak & Rafał Różycki & Grzegorz Waligóra, 2022. "Survey on Optimization Models for Energy-Efficient Computing Systems," Energies, MDPI, vol. 15(22), pages 1-20, November.
    2. Ernst Althaus & André Brinkmann & Peter Kling & Friedhelm Meyer Heide & Lars Nagel & Sören Riechers & Jiří Sgall & Tim Süß, 2018. "Scheduling shared continuous resources on many-cores," Journal of Scheduling, Springer, vol. 21(1), pages 77-92, February.
    3. Hartmann, Sönke & Briskorn, Dirk, 2008. "A survey of variants and extensions of the resource-constrained project scheduling problem," Working Paper Series 02/2008, Hamburg School of Business Administration (HSBA).
    4. Naber, Anulark & Kolisch, Rainer, 2014. "MIP models for resource-constrained project scheduling with flexible resource profiles," European Journal of Operational Research, Elsevier, vol. 239(2), pages 335-348.
    5. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.

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