IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v275y2019i1p35-44.html
   My bibliography  Save this article

An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem

Author

Listed:
  • Arkhipov, Dmitry
  • Battaïa, Olga
  • Lazarev, Alexander

Abstract

Several algorithms for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem (RCPSP) were proposed in the literature. However, fast computable lower bounds usually do not provide the best estimations and the methods that obtain better bounds are mainly based on the cooperation between linear and constraint programming and therefore are time-consuming. In this paper, a new pseudo-polynomial algorithm is proposed to find a makespan lower bound for RCPSP with time-dependent resource capacities. Its idea is based on a consecutive evaluation of pairs of resources and their cumulated workload. Using the proposed algorithm, several bounds for the PSPLIB benchmark were improved. The results for industrial applications are also presented where the algorithm could provide good bounds even for very large problem instances.

Suggested Citation

  • Arkhipov, Dmitry & Battaïa, Olga & Lazarev, Alexander, 2019. "An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 275(1), pages 35-44.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:1:p:35-44
    DOI: 10.1016/j.ejor.2018.11.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718309305
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.11.005?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. David Applegate & William Cook, 1991. "A Computational Study of the Job-Shop Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 3(2), pages 149-156, May.
    2. Emmanuel Néron & Christian Artigues & Philippe Baptiste & Jacques Carlier & Jean Damay & Sophie Demassey & Philippe Laborie, 2006. "Lower Bounds for Resource Constrained Project Scheduling Problem," International Series in Operations Research & Management Science, in: Joanna Józefowska & Jan Weglarz (ed.), Perspectives in Modern Project Scheduling, chapter 0, pages 167-204, Springer.
    3. A. Alan B. Pritsker & Lawrence J. Waiters & Philip M. Wolfe, 1969. "Multiproject Scheduling with Limited Resources: A Zero-One Programming Approach," Management Science, INFORMS, vol. 16(1), pages 93-108, September.
    4. Ph. Baptiste & C. Le Pape & W. Nuijten, 1999. "Satisfiability tests and time‐bound adjustmentsfor cumulative scheduling problems," Annals of Operations Research, Springer, vol. 92(0), pages 305-333, January.
    5. Christofides, Nicos & Alvarez-Valdes, R. & Tamarit, J. M., 1987. "Project scheduling with resource constraints: A branch and bound approach," European Journal of Operational Research, Elsevier, vol. 29(3), pages 262-273, June.
    6. J. Carlier & E. Pinson, 1989. "An Algorithm for Solving the Job-Shop Problem," Management Science, INFORMS, vol. 35(2), pages 164-176, February.
    7. Brucker, Peter & Knust, Sigrid, 2000. "A linear programming and constraint propagation-based lower bound for the RCPSP," European Journal of Operational Research, Elsevier, vol. 127(2), pages 355-362, December.
    8. Carlier, J. & Pinson, E., 1994. "Adjustment of heads and tails for the job-shop problem," European Journal of Operational Research, Elsevier, vol. 78(2), pages 146-161, October.
    9. Kolisch, Rainer & Sprecher, Arno, 1997. "PSPLIB - A project scheduling problem library : OR Software - ORSEP Operations Research Software Exchange Program," European Journal of Operational Research, Elsevier, vol. 96(1), pages 205-216, January.
    10. Sigrid Knust, 2015. "Lower Bounds on the Minimum Project Duration," International Handbooks on Information Systems, in: Christoph Schwindt & Jürgen Zimmermann (ed.), Handbook on Project Management and Scheduling Vol.1, edition 127, chapter 0, pages 43-55, Springer.
    11. 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.
    12. Carlier, Jacques & Neron, Emmanuel, 2000. "A new LP-based lower bound for the cumulative scheduling problem," European Journal of Operational Research, Elsevier, vol. 127(2), pages 363-382, December.
    13. J. Carlier & E. Pinson, 1998. "Jackson's Pseudo Preemptive Schedule for the Pm/r i , q i /C max scheduling problem," Annals of Operations Research, Springer, vol. 83(0), pages 41-58, October.
    14. 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.
    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. Shibasaki, Rui S. & Rossi, André & Gurevsky, Evgeny, 2024. "A new upper bound based on Dantzig-Wolfe decomposition to maximize the stability radius of a simple assembly line under uncertainty," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1015-1030.

    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. Sophie Demassey & Christian Artigues & Philippe Michelon, 2005. "Constraint-Propagation-Based Cutting Planes: An Application to the Resource-Constrained Project Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 52-65, February.
    2. Alexander Tesch, 2020. "A polyhedral study of event-based models for the resource-constrained project scheduling problem," Journal of Scheduling, Springer, vol. 23(2), pages 233-251, April.
    3. 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.
    4. Carlier, Jacques & Neron, Emmanuel, 2007. "Computing redundant resources for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1452-1463, February.
    5. Francis Sourd & Wim Nuijten, 2000. "Multiple-Machine Lower Bounds for Shop-Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 341-352, November.
    6. Moukrim, Aziz & Quilliot, Alain & Toussaint, Hélène, 2015. "An effective branch-and-price algorithm for the Preemptive Resource Constrained Project Scheduling Problem based on minimal Interval Order Enumeration," European Journal of Operational Research, Elsevier, vol. 244(2), pages 360-368.
    7. Diarmuid Grimes & Emmanuel Hebrard, 2015. "Solving Variants of the Job Shop Scheduling Problem Through Conflict-Directed Search," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 268-284, May.
    8. Tom Rihm & Norbert Trautmann & Adrian Zimmermann, 2018. "MIP formulations for an application of project scheduling in human resource management," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 609-639, December.
    9. Da Col, Giacomo & Teppan, Erich C., 2022. "Industrial-size job shop scheduling with constraint programming," Operations Research Perspectives, Elsevier, vol. 9(C).
    10. Néron, Emmanuel & Baptiste, Philippe & Gupta, Jatinder N. D., 2001. "Solving hybrid flow shop problem using energetic reasoning and global operations," Omega, Elsevier, vol. 29(6), pages 501-511, December.
    11. Rolf H. Möhring & Andreas S. Schulz & Frederik Stork & Marc Uetz, 2003. "Solving Project Scheduling Problems by Minimum Cut Computations," Management Science, INFORMS, vol. 49(3), pages 330-350, March.
    12. Luis F. Machado-Domínguez & Carlos D. Paternina-Arboleda & Jorge I. Vélez & Agustin Barrios-Sarmiento, 2021. "A memetic algorithm to address the multi-node resource-constrained project scheduling problem," Journal of Scheduling, Springer, vol. 24(4), pages 413-429, August.
    13. Vipul Jain & Ignacio E. Grossmann, 2001. "Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 258-276, November.
    14. Moehring, Rolf & Uetz, Marc & Stork, Frederik & Schulz, Andreas S., 2002. "Solving Project Scheduling Problems by Minimum Cut," Working papers 4231-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    15. Francis Sourd, 2009. "New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 167-175, February.
    16. F. Guerriero, 2008. "Hybrid Rollout Approaches for the Job Shop Scheduling Problem," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 419-438, November.
    17. Coughlan, Eamonn T. & Lübbecke, Marco E. & Schulz, Jens, 2015. "A branch-price-and-cut algorithm for multi-mode resource leveling," European Journal of Operational Research, Elsevier, vol. 245(1), pages 70-80.
    18. Müller, David & Müller, Marcus G. & Kress, Dominik & Pesch, Erwin, 2022. "An algorithm selection approach for the flexible job shop scheduling problem: Choosing constraint programming solvers through machine learning," European Journal of Operational Research, Elsevier, vol. 302(3), pages 874-891.
    19. Blazewicz, Jacek & Domschke, Wolfgang & Pesch, Erwin, 1996. "The job shop scheduling problem: Conventional and new solution techniques," European Journal of Operational Research, Elsevier, vol. 93(1), pages 1-33, August.
    20. Carlos Mencía & María Sierra & Ramiro Varela, 2013. "Depth-first heuristic search for the job shop scheduling problem," Annals of Operations Research, Springer, vol. 206(1), pages 265-296, July.

    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:eee:ejores:v:275:y:2019:i:1:p:35-44. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.