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Scheduling activities in project network with feeding precedence relations: an earliest start forward recursion algorithm

Author

Listed:
  • Lucio Bianco

    (University of Rome “Tor Vergata”)

  • Massimiliano Caramia

    (University of Rome “Tor Vergata”)

  • Stefano Giordani

    (University of Rome “Tor Vergata”)

  • Alessio Salvatore

    (CNR)

Abstract

In some production processes, the effort associated with a certain activity for its execution can vary over time. In this case, the amount of work per time unit devoted to each activity, so as its duration, is not univocally determined. This kind of problem can be represented by an activity project network with the so-called feeding precedence relations, and activity variable execution intensity. In this paper, we propose a forward recursion algorithm able to find the earliest start and finish times of each activity, in $$O(m \log n)$$ O ( m log n ) time, with n and m being the number of activities and the number of precedence relations, respectively. In particular, this requires the calculation of the (optimal) execution intensity profile, for each activity, that warrants the earliest start schedule and the minimum completion time of the project.

Suggested Citation

  • Lucio Bianco & Massimiliano Caramia & Stefano Giordani & Alessio Salvatore, 2024. "Scheduling activities in project network with feeding precedence relations: an earliest start forward recursion algorithm," Annals of Operations Research, Springer, vol. 338(1), pages 193-224, July.
    • Handle: RePEc:spr:annopr:v:338:y:2024:i:1:d:10.1007_s10479-023-05521-0
    DOI: 10.1007/s10479-023-05521-0
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    References listed on IDEAS

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    1. Salah E. Elmaghraby & Jerzy Kamburowski, 1992. "The Analysis of Activity Networks Under Generalized Precedence Relations (GPRs)," Management Science, INFORMS, vol. 38(9), pages 1245-1263, September.
    2. Quintanilla, Sacramento & Pérez, Ángeles & Lino, Pilar & Valls, Vicente, 2012. "Time and work generalised precedence relationships in project scheduling with pre-emption: An application to the management of Service Centres," European Journal of Operational Research, Elsevier, vol. 219(1), pages 59-72.
    3. Bianco, Lucio & Caramia, Massimiliano & Giordani, Stefano, 2022. "Project scheduling with generalized precedence relations: A new method to analyze criticalities and flexibilities," European Journal of Operational Research, Elsevier, vol. 298(2), pages 451-462.
    4. Valls, Vicente & Pérez, Ángeles & Quintanilla, Sacramento, 2009. "Skilled workforce scheduling in Service Centres," European Journal of Operational Research, Elsevier, vol. 193(3), pages 791-804, March.
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