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Complexity of the Discrete Time-Cost Tradeoff Problem for Project Networks

Author

Listed:
  • Prabuddha De

    (University of Dayton, Dayton, Ohio)

  • E. James Dunne

    (University of Dayton, Dayton, Ohio)

  • Jay B. Ghosh

    (University of Dayton, Dayton, Ohio)

  • Charles E. Wells

    (University of Dayton, Dayton, Ohio)

Abstract

This note addresses the discrete version of the well-known time-cost tradeoff problem for project networks, which has been studied previously in the standard project management literature as well as in the related literature on Decision-CPM. All the algorithms proposed thus far for the solution of the general problem exhibit exponential worst-case complexity, with the notable exception of the pseudo-polynomial dynamic program due to Hindelang and Muth. We first demonstrate that this algorithm is flawed, and that when we correct it, it no longer remains pseudo-polynomial. Continuing on in the main result of the note, we show that this is not at all surprising, since the problem is strongly NP-hard. Finally, we discuss the complexities of various network structures and validate an old conjecture that certain structures are necessarily more difficult to solve.

Suggested Citation

  • Prabuddha De & E. James Dunne & Jay B. Ghosh & Charles E. Wells, 1997. "Complexity of the Discrete Time-Cost Tradeoff Problem for Project Networks," Operations Research, INFORMS, vol. 45(2), pages 302-306, April.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:2:p:302-306
    DOI: 10.1287/opre.45.2.302
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    Citations

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    Cited by:

    1. A B Hafızoğlu & M Azizoğlu, 2010. "Linear programming based approaches for the discrete time/cost trade-off problem in project networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(4), pages 676-685, April.
    2. Kolisch, R. & Padman, R., 2001. "An integrated survey of deterministic project scheduling," Omega, Elsevier, vol. 29(3), pages 249-272, June.
    3. R L Bregman, 2009. "Preemptive expediting to improve project due date performance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 120-129, January.
    4. Eleni Hadjiconstantinou & Evelina Klerides, 2010. "A new path-based cutting plane approach for the discrete time-cost tradeoff problem," Computational Management Science, Springer, vol. 7(3), pages 313-336, July.
    5. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.
    6. Zhengwen He & Nengmin Wang & Pengxiang Li, 2014. "Simulated annealing for financing cost distribution based project payment scheduling from a joint perspective," Annals of Operations Research, Springer, vol. 213(1), pages 203-220, February.
    7. Bregman, Robert L., 2009. "A heuristic procedure for solving the dynamic probabilistic project expediting problem," European Journal of Operational Research, Elsevier, vol. 192(1), pages 125-137, January.
    8. Hongbo Li & Zhe Xu & Wenchao Wei, 2018. "Bi-Objective Scheduling Optimization for Discrete Time/Cost Trade-Off in Projects," Sustainability, MDPI, vol. 10(8), pages 1-15, August.
    9. Kosztyán, Zsolt T. & Pribojszki-Németh, Anikó & Szalkai, István, 2019. "Hybrid multimode resource-constrained maintenance project scheduling problem," Operations Research Perspectives, Elsevier, vol. 6(C).
    10. Chung-Lun Li & Nicholas G. Hall, 2019. "Work Package Sizing and Project Performance," Operations Research, INFORMS, vol. 67(1), pages 123-142, January.
    11. Xinhua Mao & Xin Lou & Changwei Yuan & Jibiao Zhou, 2020. "Resilience-Based Restoration Model for Supply Chain Networks," Mathematics, MDPI, vol. 8(2), pages 1-16, January.
    12. Nicole Megow & Rolf H. Möhring & Jens Schulz, 2011. "Decision Support and Optimization in Shutdown and Turnaround Scheduling," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 189-204, May.
    13. Zsolt T. Kosztyán & István Szalkai, 2020. "Multimode resource-constrained project scheduling in flexible projects," Journal of Global Optimization, Springer, vol. 76(1), pages 211-241, January.
    14. Wei He & Wenjing Li & Wei Wang, 2021. "Developing a Resource Allocation Approach for Resource-Constrained Construction Operation under Multi-Objective Operation," Sustainability, MDPI, vol. 13(13), pages 1-22, June.
    15. Akkan, Can & Drexl, Andreas & Kimms, Alf, 2000. "Network decomposition-based lower and upper bounds for the discrete time-cost tradeoff problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 527, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    16. Antonio J. Conejo & Nicholas G. Hall & Daniel Zhuoyu Long & Runhao Zhang, 2021. "Robust Capacity Planning for Project Management," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1533-1550, October.

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