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Critical Path Problems with Concave Cost-Time Curves

Author

Listed:
  • James E. Falk

    (The George Washington University)

  • Joel L. Horowitz

    (The Environmental Protection Agency, Washington, D.C.)

Abstract

This paper presents an algorithm for determining the minimum cost schedule of tasks in a critical path network in which task cost-time curves may be concave. A computer program for the case of cost-time curves that are piecewise linear in two segments is described, and a numerical example is presented.

Suggested Citation

  • James E. Falk & Joel L. Horowitz, 1972. "Critical Path Problems with Concave Cost-Time Curves," Management Science, INFORMS, vol. 19(4-Part-1), pages 446-455, December.
    • Handle: RePEc:inm:ormnsc:v:19:y:1972:i:4-part-1:p:446-455
    DOI: 10.1287/mnsc.19.4.446
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    Cited by:

    1. Byung-Cheon Choi & Myoung-Ju Park, 2020. "Scheduling two projects with controllable processing times in a single-machine environment," Journal of Scheduling, Springer, vol. 23(5), pages 619-628, October.
    2. Marcin Anholcer & Helena Gaspars-Wieloch, 2011. "Efficiency analysis of the Kaufmann and Dezbazeille algorithm for the deadline problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 5-18.
    3. Vanhoucke, Mario, 2005. "New computational results for the discrete time/cost trade-off problem with time-switch constraints," European Journal of Operational Research, Elsevier, vol. 165(2), pages 359-374, September.
    4. Jungen, F. J. & Kowalczyk, W., 1995. "An intelligent interactive project management support system," European Journal of Operational Research, Elsevier, vol. 84(1), pages 60-81, July.
    5. M. Vanhoucke, 2007. "An electromagnetic time/cost trade-off optimization in project scheduling," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 07/457, Ghent University, Faculty of Economics and Business Administration.
    6. S. Selcuk Erenguc & Taeho Ahn & Daniel G. Conway, 2001. "The resource constrained project scheduling problem with multiple crashable modes: An exact solution method," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(2), pages 107-127, March.
    7. Helena Gaspars, 2006. "A conception of a new algorithm for the project time-cost analysis," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 16(3-4), pages 5-27.
    8. Azaron, Amir & Tavakkoli-Moghaddam, Reza, 2007. "Multi-objective time-cost trade-off in dynamic PERT networks using an interactive approach," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1186-1200, August.
    9. 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.
    10. 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.
    11. Ahn, Taeho & Erenguc, S. Selcuk, 1998. "The resource constrained project scheduling problem with multiple crashable modes: A heuristic procedure," European Journal of Operational Research, Elsevier, vol. 107(2), pages 250-259, June.
    12. Jin, Maozhu & Song, Lijun & Wang, Yanan & Zeng, Yucheng, 2018. "Longitudinal cooperative robust optimization model for sustainable supply chain management," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 95-105.
    13. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    14. Jorgensen, Trond & Wallace, Stein W., 2000. "Improving project cost estimation by taking into account managerial flexibility," European Journal of Operational Research, Elsevier, vol. 127(2), pages 239-251, December.
    15. Xue Li & Zhengwen He & Nengmin Wang & Mario Vanhoucke, 2022. "Multimode time-cost-robustness trade-off project scheduling problem under uncertainty," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1173-1202, July.
    16. Thomas A. Roemer & Reza Ahmadi, 2004. "Concurrent Crashing and Overlapping in Product Development," Operations Research, INFORMS, vol. 52(4), pages 606-622, August.
    17. Choi, Byung-Cheon & Park, Myoung-Ju, 2015. "A continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs," European Journal of Operational Research, Elsevier, vol. 244(3), pages 748-752.
    18. 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.
    19. Azaron, Amir & Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Memariani, Azizollah, 2006. "A multi-objective resource allocation problem in PERT networks," European Journal of Operational Research, Elsevier, vol. 172(3), pages 838-854, August.

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