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

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  • 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
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    References listed on IDEAS

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    1. Mario Vanhoucke, 2013. "Project Management with Dynamic Scheduling," Springer Books, Springer, edition 2, number 978-3-642-40438-2, March.
    2. 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.
    3. Nikolai Krivulin, 2020. "Using tropical optimization techniques in bi-criteria decision problems," Computational Management Science, Springer, vol. 17(1), pages 79-104, January.
    4. A. J. Hoffman, 1963. "On abstract dual linear programs," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 369-373, March.
    5. 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.
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    Cited by:

    1. Nikolai Krivulin & Sergey Gubanov, 2024. "Algebraic solution of project scheduling problems with temporal constraints," Operational Research, Springer, vol. 24(4), pages 1-27, December.

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