IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v17y2020i3d10.1007_s10287-020-00374-5.html
   My bibliography  Save this article

Tropical optimization technique in bi-objective project scheduling under temporal constraints

Author

Listed:
  • Nikolai Krivulin

    (St. Petersburg State University)

Abstract

We consider a project that consists of a set of activities performed in parallel under constraints on their start and finish times, including start-finish precedence relationships, release start times, release end times, and deadlines. The problems of interest are to decide on the optimal schedule of the activities to minimize both the maximum flow-time over all activities, and the project makespan. We formulate these problems as bi-objective optimization problems in the framework of tropical mathematics which investigates the theory and applications of algebraic systems with idempotent operations and has various applications in management science and operations research. Then, the use of methods and techniques of tropical optimization allows to derive complete Pareto-optimal solutions of the problems in a direct explicit form ready for further analysis and straightforward computation. We discuss the computational complexity of the solution and give illustrative examples.

Suggested Citation

  • Nikolai Krivulin, 2020. "Tropical optimization technique in bi-objective project scheduling under temporal constraints," Computational Management Science, Springer, vol. 17(3), pages 437-464, October.
    • Handle: RePEc:spr:comgts:v:17:y:2020:i:3:d:10.1007_s10287-020-00374-5
    DOI: 10.1007/s10287-020-00374-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-020-00374-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-020-00374-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. A. J. Hoffman, 1963. "On abstract dual linear programs," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 369-373, March.
    2. Francisco Ballestín & Rosa Blanco, 2015. "Theoretical and Practical Fundamentals," International Handbooks on Information Systems, in: Christoph Schwindt & Jürgen Zimmermann (ed.), Handbook on Project Management and Scheduling Vol.1, edition 127, chapter 0, pages 411-427, Springer.
    3. Mario Vanhoucke, 2013. "Project Management with Dynamic Scheduling," Springer Books, Springer, edition 2, number 978-3-642-40438-2, February.
    4. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
    5. Nikolai Krivulin, 2020. "Using tropical optimization techniques in bi-criteria decision problems," Computational Management Science, Springer, vol. 17(1), pages 79-104, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nikolai Krivulin, 2021. "Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons," Mathematics, MDPI, vol. 9(4), pages 1-22, February.
    2. Rastegar, Narges & Khorram, Esmaile, 2014. "A combined scalarizing method for multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 236(1), pages 229-237.
    3. Elzbieta Rynska & Joanna Klimowicz & Slawomir Kowal & Krzysztof Lyzwa & Michal Pierzchalski & Wojciech Rekosz, 2020. "Smart Energy Solutions as an Indispensable Multi-Criteria Input for a Coherent Urban Planning and Building Design Process—Two Case Studies for Smart Office Buildings in Warsaw Downtown Area," Energies, MDPI, vol. 13(15), pages 1-24, July.
    4. P. Velumani & N. V. N. Nampoothiri & M. Urbański, 2021. "A Comparative Study of Models for the Construction Duration Prediction in Highway Road Projects of India," Sustainability, MDPI, vol. 13(8), pages 1-13, April.
    5. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    6. Ana B. Ruiz & Francisco Ruiz & Kaisa Miettinen & Laura Delgado-Antequera & Vesa Ojalehto, 2019. "NAUTILUS Navigator: free search interactive multiobjective optimization without trading-off," Journal of Global Optimization, Springer, vol. 74(2), pages 213-231, June.
    7. Tobias Kuhn & Stefan Ruzika, 2017. "A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions," Journal of Global Optimization, Springer, vol. 67(3), pages 581-600, March.
    8. Gabriele Eichfelder, 2009. "Scalarizations for adaptively solving multi-objective optimization problems," Computational Optimization and Applications, Springer, vol. 44(2), pages 249-273, November.
    9. Shao, Lizhen & Ehrgott, Matthias, 2016. "Discrete representation of non-dominated sets in multi-objective linear programming," European Journal of Operational Research, Elsevier, vol. 255(3), pages 687-698.
    10. Rennen, G. & van Dam, E.R. & den Hertog, D., 2009. "Enhancement of Sandwich Algorithms for Approximating Higher Dimensional Convex Pareto Sets," Other publications TiSEM e2255959-6691-4ef1-88a4-5, Tilburg University, School of Economics and Management.
    11. Toly Chen, 2021. "A diversified AHP-tree approach for multiple-criteria supplier selection," Computational Management Science, Springer, vol. 18(4), pages 431-453, October.
    12. Kalyan Shankar Bhattacharjee & Hemant Kumar Singh & Tapabrata Ray, 2017. "An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making," Journal of Global Optimization, Springer, vol. 68(1), pages 71-93, May.
    13. Bordley, Robert F. & Keisler, Jeffrey M. & Logan, Tom M., 2019. "Managing projects with uncertain deadlines," European Journal of Operational Research, Elsevier, vol. 274(1), pages 291-302.
    14. Nikolai Krivulin, 2017. "Direct solution to constrained tropical optimization problems with application to project scheduling," Computational Management Science, Springer, vol. 14(1), pages 91-113, January.
    15. Esra Karasakal & Murat Köksalan, 2009. "Generating a Representative Subset of the Nondominated Frontier in Multiple Criteria Decision Making," Operations Research, INFORMS, vol. 57(1), pages 187-199, February.
    16. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 195-227, May.
    17. Gabriele Eichfelder & Leo Warnow, 2022. "An approximation algorithm for multi-objective optimization problems using a box-coverage," Journal of Global Optimization, Springer, vol. 83(2), pages 329-357, June.
    18. Markus Hartikainen & Alberto Lovison, 2015. "PAINT–SiCon: constructing consistent parametric representations of Pareto sets in nonconvex multiobjective optimization," Journal of Global Optimization, Springer, vol. 62(2), pages 243-261, June.
    19. Notte, Gastón & Cancela, Héctor & Pedemonte, Martín & Chilibroste, Pablo & Rossing, Walter & Groot, Jeroen C.J., 2020. "A multi-objective optimization model for dairy feeding management," Agricultural Systems, Elsevier, vol. 183(C).
    20. Kathrin Klamroth & Kaisa Miettinen, 2008. "Integrating Approximation and Interactive Decision Making in Multicriteria Optimization," Operations Research, INFORMS, vol. 56(1), pages 222-234, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:comgts:v:17:y:2020:i:3:d:10.1007_s10287-020-00374-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.