IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v213y2014i1p115-13010.1007-s10479-012-1106-5.html
   My bibliography  Save this article

Approximability results for the resource-constrained project scheduling problem with a single type of resources

Author

Listed:
  • Evgeny Gafarov
  • Alexander Lazarev
  • Frank Werner

Abstract

In this paper, we consider the well-known resource-constrained project scheduling problem. We give some arguments that already a special case of this problem with a single type of resources is not approximable in polynomial time with an approximation ratio bounded by a constant. We prove that there exist instances for which the optimal makespan values for the non-preemptive and the preemptive problems have a ratio of O(logn), where n is the number of jobs. This means that there exist instances for which the lower bound of Mingozzi et al. has a bad relative error of O(logn), and the calculation of this bound is an NP-hard problem. In addition, we give a proof that there exists a type of instances for which known approximation algorithms with polynomial time complexity have an approximation ratio of at least equal to $O(\sqrt{n})$ , and known lower bounds have a relative error of at least equal to O(logn). This type of instances corresponds to the single machine parallel-batch scheduling problem 1|p−batch,b=∞|C max . Copyright Springer Science+Business Media, LLC 2014

Suggested Citation

  • Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2014. "Approximability results for the resource-constrained project scheduling problem with a single type of resources," Annals of Operations Research, Springer, vol. 213(1), pages 115-130, February.
    • Handle: RePEc:spr:annopr:v:213:y:2014:i:1:p:115-130:10.1007/s10479-012-1106-5
    DOI: 10.1007/s10479-012-1106-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1106-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1106-5?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. Demeulemeester, Erik L. & Herroelen, Willy S., 1996. "An efficient optimal solution procedure for the preemptive resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 90(2), pages 334-348, April.
    2. Kolisch, R. & Padman, R., 2001. "An integrated survey of deterministic project scheduling," Omega, Elsevier, vol. 29(3), pages 249-272, June.
    3. Hartmann, Sonke & Kolisch, Rainer, 2000. "Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 127(2), pages 394-407, December.
    4. Brucker, Peter & Knust, Sigrid & Schoo, Arno & Thiele, Olaf, 1998. "A branch and bound algorithm for the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 107(2), pages 272-288, June.
    5. Kolisch, Rainer & Hartmann, Sönke, 1998. "Heuristic algorithms for solving the resource-constrained project scheduling problem: Classification and computational analysis," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 469, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    6. Carlier, J. & Neron, E., 2003. "On linear lower bounds for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 149(2), pages 314-324, September.
    7. Hartmann, Sönke & Kolisch, R., 2000. "Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 11180, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    8. T.C.E. Cheng & C.T. Ng & J.J. Yuan & Z.H. Liu, 2004. "Single machine parallel batch scheduling subject to precedence constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(7), pages 949-958, October.
    9. Kolisch, Rainer & Hartmann, Sonke, 2006. "Experimental investigation of heuristics for resource-constrained project scheduling: An update," European Journal of Operational Research, Elsevier, vol. 174(1), pages 23-37, October.
    10. Silvano Martello & Michele Monaci & Daniele Vigo, 2003. "An Exact Approach to the Strip-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 310-319, August.
    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. Péter Györgyi & Tamás Kis, 2015. "Approximability of scheduling problems with resource consuming jobs," Annals of Operations Research, Springer, vol. 235(1), pages 319-336, December.
    2. Zdeněk Hanzálek & Přemysl Šůcha, 2017. "Time symmetry of resource constrained project scheduling with general temporal constraints and take-give resources," Annals of Operations Research, Springer, vol. 248(1), pages 209-237, January.

    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. Guo, Weikang & Vanhoucke, Mario & Coelho, José, 2023. "A prediction model for ranking branch-and-bound procedures for the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 306(2), pages 579-595.
    2. Weglarz, Jan & Józefowska, Joanna & Mika, Marek & Waligóra, Grzegorz, 2011. "Project scheduling with finite or infinite number of activity processing modes - A survey," European Journal of Operational Research, Elsevier, vol. 208(3), pages 177-205, February.
    3. R. Christopher L. Riley & Cesar Rego, 2019. "Intensification, diversification, and learning via relaxation adaptive memory programming: a case study on resource constrained project scheduling," Journal of Heuristics, Springer, vol. 25(4), pages 793-807, October.
    4. 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.
    5. Hartmann, Sönke & Briskorn, Dirk, 2008. "A survey of variants and extensions of the resource-constrained project scheduling problem," Working Paper Series 02/2008, Hamburg School of Business Administration (HSBA).
    6. D. Debels & M. Vanhoucke, 2006. "The impact of various activity assumptions on the lead-time and resource utilization of resource-constrained projects," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/385, Ghent University, Faculty of Economics and Business Administration.
    7. Debels, Dieter & De Reyck, Bert & Leus, Roel & Vanhoucke, Mario, 2006. "A hybrid scatter search/electromagnetism meta-heuristic for project scheduling," European Journal of Operational Research, Elsevier, vol. 169(2), pages 638-653, March.
    8. Rodrigues, Sávio B. & Yamashita, Denise S., 2010. "An exact algorithm for minimizing resource availability costs in project scheduling," European Journal of Operational Research, Elsevier, vol. 206(3), pages 562-568, November.
    9. Peteghem, Vincent Van & Vanhoucke, Mario, 2010. "A genetic algorithm for the preemptive and non-preemptive multi-mode resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 201(2), pages 409-418, March.
    10. Servranckx, Tom & Vanhoucke, Mario, 2019. "A tabu search procedure for the resource-constrained project scheduling problem with alternative subgraphs," European Journal of Operational Research, Elsevier, vol. 273(3), pages 841-860.
    11. D. Debels & M. Vanhoucke, 2005. "A Decomposition-Based Heuristic For The Resource-Constrained Project Scheduling Problem," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 05/293, Ghent University, Faculty of Economics and Business Administration.
    12. Valls, Vicente & Ballestin, Francisco & Quintanilla, Sacramento, 2008. "A hybrid genetic algorithm for the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 185(2), pages 495-508, March.
    13. Song, Jie & Martens, Annelies & Vanhoucke, Mario, 2021. "Using Schedule Risk Analysis with resource constraints for project control," European Journal of Operational Research, Elsevier, vol. 288(3), pages 736-752.
    14. Dieter Debels & Mario Vanhoucke, 2007. "A Decomposition-Based Genetic Algorithm for the Resource-Constrained Project-Scheduling Problem," Operations Research, INFORMS, vol. 55(3), pages 457-469, June.
    15. F. Perez & T. Gomez, 2016. "Multiobjective project portfolio selection with fuzzy constraints," Annals of Operations Research, Springer, vol. 245(1), pages 7-29, October.
    16. Bouleimen, K. & Lecocq, H., 2003. "A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode version," European Journal of Operational Research, Elsevier, vol. 149(2), pages 268-281, September.
    17. Hartmann, Sönke & Briskorn, Dirk, 2022. "An updated survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 1-14.
    18. Moumene, Khaled & Ferland, Jacques A., 2009. "Activity list representation for a generalization of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 199(1), pages 46-54, November.
    19. Tseng, Lin-Yu & Chen, Shih-Chieh, 2006. "A hybrid metaheuristic for the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 175(2), pages 707-721, December.
    20. Abdollah Arasteh, 2020. "Considering Project Management Activities for Engineering Design Groups," SN Operations Research Forum, Springer, vol. 1(4), pages 1-29, December.

    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:annopr:v:213:y:2014:i:1:p:115-130:10.1007/s10479-012-1106-5. 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.