IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v22y2014i1p37-52.html
   My bibliography  Save this article

Allocating slacks in stochastic PERT network

Author

Listed:
  • Javier Castro
  • Daniel Gómez
  • Juan Tejada

Abstract

The SPERT problem was defined, in a game theory framework, as the fair allocation of the slack or float among the activities in a PERT network previous to the execution of the project. Previous approaches tackle with this problem imposing that the durations of the activities are deterministic. In this paper, we extend the SPERT problem into a stochastic framework defining a new solution that tries also to maintain the good performance of some other approaches that have been defined for the deterministic case. Afterward, we present a polynomial algorithm for this new solution that also could be used for the calculation of other approaches founded in the deterministic SPERT literature. Copyright Springer-Verlag 2014

Suggested Citation

  • Javier Castro & Daniel Gómez & Juan Tejada, 2014. "Allocating slacks in stochastic PERT network," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 37-52, March.
    • Handle: RePEc:spr:cejnor:v:22:y:2014:i:1:p:37-52
    DOI: 10.1007/s10100-012-0264-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10100-012-0264-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10100-012-0264-5?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. Rodica Branzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2011. "A bonus-malus approach to project management," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 495-512, December.
    2. Rodica Brânzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2002. "Two Approaches to the Problem of Sharing Delay Costs in Joint Projects," Annals of Operations Research, Springer, vol. 109(1), pages 359-374, January.
    3. Bajis Dodin, 1985. "Bounding the Project Completion Time Distribution in PERT Networks," Operations Research, INFORMS, vol. 33(4), pages 862-881, August.
    4. Bergantinos, Gustavo & Lorenzo, Leticia, 2008. "The equal award principle in problems with constraints and claims," European Journal of Operational Research, Elsevier, vol. 188(1), pages 224-239, July.
    5. F. Brian Talbot & James H. Patterson, 1978. "An Efficient Integer Programming Algorithm with Network Cuts for Solving Resource-Constrained Scheduling Problems," Management Science, INFORMS, vol. 24(11), pages 1163-1174, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Krzysztof S. Targiel & Maciej Nowak & Tadeusz Trzaskalik, 2018. "Scheduling non-critical activities using multicriteria approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 585-598, September.
    2. J. C. Gonçalves-Dosantos & I. García-Jurado & J. Costa, 2020. "Sharing delay costs in stochastic scheduling problems with delays," 4OR, Springer, vol. 18(4), pages 457-476, December.
    3. Xiaowei Lin & Jing Zhou & Lianmin Zhang & Yinlian Zeng, 2021. "Revenue sharing for resource reallocation among project activity contractors," Annals of Operations Research, Springer, vol. 301(1), pages 121-141, June.
    4. Josefa Mula & Marija Bogataj, 2021. "OR in the industrial engineering of Industry 4.0: experiences from the Iberian Peninsula mirrored in CJOR," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(4), pages 1163-1184, December.

    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. Brucker, Peter & Drexl, Andreas & Mohring, Rolf & Neumann, Klaus & Pesch, Erwin, 1999. "Resource-constrained project scheduling: Notation, classification, models, and methods," European Journal of Operational Research, Elsevier, vol. 112(1), pages 3-41, January.
    2. Estévez-Fernández, Arantza, 2012. "A game theoretical approach to sharing penalties and rewards in projects," European Journal of Operational Research, Elsevier, vol. 216(3), pages 647-657.
    3. Jan Böttcher & Andreas Drexl & Rainer Kolisch & Frank Salewski, 1999. "Project Scheduling Under Partially Renewable Resource Constraints," Management Science, INFORMS, vol. 45(4), pages 543-559, April.
    4. Nima Zoraghi & Aria Shahsavar & Babak Abbasi & Vincent Peteghem, 2017. "Multi-mode resource-constrained project scheduling problem with material ordering under bonus–penalty policies," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 49-79, April.
    5. Schirmer, Andreas & Riesenberg, Sven, 1997. "Parameterized heuristics for project scheduling: Biased random sampling methods," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 456, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    6. Colin E. Bell & Jaemin Han, 1991. "A new heuristic solution method in resource‐constrained project scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 315-331, June.
    7. repec:ebl:ecbull:v:3:y:2008:i:56:p:1-10 is not listed on IDEAS
    8. Aristide Mingozzi & Vittorio Maniezzo & Salvatore Ricciardelli & Lucio Bianco, 1998. "An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation," Management Science, INFORMS, vol. 44(5), pages 714-729, May.
    9. Rodica Branzei & Sirma Zeynep Alparslan Gok, 2008. "Bankruptcy problems with interval uncertainty," Economics Bulletin, AccessEcon, vol. 3(56), pages 1-10.
    10. 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.
    11. Badinelli, Ralph D., 1996. "Approximating probability density functions and their convolutions using orthogonal polynomials," European Journal of Operational Research, Elsevier, vol. 95(1), pages 211-230, November.
    12. Arno Sprecher, 2000. "Scheduling Resource-Constrained Projects Competitively at Modest Memory Requirements," Management Science, INFORMS, vol. 46(5), pages 710-723, May.
    13. Kai Watermeyer & Jürgen Zimmermann, 2022. "A partition-based branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 575-602, June.
    14. Estevez Fernandez, M.A., 2008. "A Game Theoretical Approach to Sharing Penalties and Rewards in Projects," Other publications TiSEM e7bb0378-03bf-43ce-9cab-c, Tilburg University, School of Economics and Management.
    15. Kolisch, Rainer, 1994. "Serial and parallel resource-constrained projekt scheduling methodes revisited: Theory and computation," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 344, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    16. Kai Watermeyer & Jürgen Zimmermann, 2020. "A branch-and-bound procedure for the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 427-460, June.
    17. Simpson, Wendell P. & Patterson, James H., 1996. "A multiple-tree search procedure for the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 89(3), pages 525-542, March.
    18. Frank Schultmann & Otto Rentz, 2002. "Scheduling of deconstruction projects under resource constraints," Construction Management and Economics, Taylor & Francis Journals, vol. 20(5), pages 391-401.
    19. René Brink & Juan D. Moreno-Ternero, 2017. "The reverse TAL-family of rules for bankruptcy problems," Annals of Operations Research, Springer, vol. 254(1), pages 449-465, July.
    20. Lei Liu & Marcello Urgo, 2024. "Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type dis," Annals of Operations Research, Springer, vol. 338(1), pages 741-764, July.
    21. Sprecher, Arno, 1996. "Solving the RCPSP efficiently at modest memory requirements," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 425, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

    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:cejnor:v:22:y:2014:i:1:p:37-52. 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.