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A minmax regret approach to the critical path method with task interval times

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  • Conde, Eduardo

Abstract

The execution of a given project, with a number of interrelated tasks due to precedence constraints, represents a challenge when one must to control the available resources and the compromised due dates. In this paper, we analyse this problem under uncertain individual task completing times, specifically, we will assume that a given range, for the admissible values of each individual completing time, is available. Taking into account that the precedence relations between tasks must be preserved, each realization of the admissible execution times for the set of tasks will define a new scenario determining the ending time for the project and the subset of critical tasks. The minmax regret criterion will be used in order to obtain a robust approximation to the critical set of tasks determining the overall execution time for the project.

Suggested Citation

  • Conde, Eduardo, 2009. "A minmax regret approach to the critical path method with task interval times," European Journal of Operational Research, Elsevier, vol. 197(1), pages 235-242, August.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:1:p:235-242
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    References listed on IDEAS

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    1. Chen, Shih-Pin, 2007. "Analysis of critical paths in a project network with fuzzy activity times," European Journal of Operational Research, Elsevier, vol. 183(1), pages 442-459, November.
    2. Chanas, Stefan & Zielinski, Pawel, 2002. "The computational complexity of the criticality problems in a network with interval activity times," European Journal of Operational Research, Elsevier, vol. 136(3), pages 541-550, February.
    3. Zielinski, Pawel, 2004. "The computational complexity of the relative robust shortest path problem with interval data," European Journal of Operational Research, Elsevier, vol. 158(3), pages 570-576, November.
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    Cited by:

    1. Öncü Hazir & Gündüz Ulusoy, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," Post-Print hal-02898162, HAL.
    2. Hazır, Öncü & Ulusoy, Gündüz, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," International Journal of Production Economics, Elsevier, vol. 223(C).
    3. Conde, Eduardo, 2012. "On a constant factor approximation for minmax regret problems using a symmetry point scenario," European Journal of Operational Research, Elsevier, vol. 219(2), pages 452-457.
    4. Savic, Aleksandar & Kratica, Jozef & Milanovic, Marija & Dugosija, Djordje, 2010. "A mixed integer linear programming formulation of the maximum betweenness problem," European Journal of Operational Research, Elsevier, vol. 206(3), pages 522-527, November.

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