IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v244y2015i3p748-752.html
   My bibliography  Save this article

A continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs

Author

Listed:
  • Choi, Byung-Cheon
  • Park, Myoung-Ju

Abstract

We consider a continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs. If a milestone is tardy, a penalty cost may be imposed. The processing times of jobs can be compressed by additional resources or activities that incur compression costs. The objective is to minimize the total penalty cost plus the total compression cost. We show that the problem is NP-hard, even if the compression cost is described as a concave function, and we present a pseudo-polynomial time algorithm for that case. Furthermore, we show that the problem is polynomially solvable if the compression cost function is convex.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:244:y:2015:i:3:p:748-752
    DOI: 10.1016/j.ejor.2015.02.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171500123X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2015.02.022?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. D. R. Fulkerson, 1961. "A Network Flow Computation for Project Cost Curves," Management Science, INFORMS, vol. 7(2), pages 167-178, January.
    2. Choi, Byung-Cheon & Chung, Jibok, 2014. "Complexity results for the linear time–cost tradeoff problem with multiple milestones and completely ordered jobs," European Journal of Operational Research, Elsevier, vol. 236(1), pages 61-68.
    3. E. B. Berman, 1964. "Resource Allocation in a PERT Network Under Continuous Activity Time-Cost Functions," Management Science, INFORMS, vol. 10(4), pages 734-745, July.
    4. 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.
    5. Anthony V. Fiacco & Garth P. McCormick, 1964. "Computational Algorithm for the Sequential Unconstrained Minimization Technique for Nonlinear Programming," Management Science, INFORMS, vol. 10(4), pages 601-617, July.
    6. L. R. Lamberson & R. R. Hocking, 1970. "Optimum Time Compression in Project Scheduling," Management Science, INFORMS, vol. 16(10), pages 597-606, June.
    7. 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.
    8. Thomas A. Roemer & Reza Ahmadi, 2004. "Concurrent Crashing and Overlapping in Product Development," Operations Research, INFORMS, vol. 52(4), pages 606-622, August.
    9. Anthony V. Fiacco & Garth P. McCormick, 1964. "The Sequential Unconstrained Minimization Technique for Nonlinear Programing, a Primal-Dual Method," Management Science, INFORMS, vol. 10(2), pages 360-366, January.
    10. 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.
    11. James E. Kelley, 1961. "Critical-Path Planning and Scheduling: Mathematical Basis," Operations Research, INFORMS, vol. 9(3), pages 296-320, June.
    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. Byung-Cheon Choi & Changmuk Kang, 2019. "A linear time–cost tradeoff problem with multiple milestones under a comb graph," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 341-361, August.
    2. 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.
    3. Seyed Hossein Razavi Hajiagha & Hannan Amoozad Mahdiraji & Maryam Behnam & Boshra Nekoughadirli & Rohit Joshi, 2022. "A scenario-based robust time–cost tradeoff model to handle the effect of COVID-19 on supply chains project management," Operations Management Research, Springer, vol. 15(1), pages 357-377, June.
    4. Abdollah Arasteh, 2020. "Considering Project Management Activities for Engineering Design Groups," SN Operations Research Forum, Springer, vol. 1(4), pages 1-29, December.
    5. 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.

    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. Byung-Cheon Choi & Changmuk Kang, 2019. "A linear time–cost tradeoff problem with multiple milestones under a comb graph," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 341-361, August.
    2. 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.
    3. Choi, Byung-Cheon & Chung, Jibok, 2014. "Complexity results for the linear time–cost tradeoff problem with multiple milestones and completely ordered jobs," European Journal of Operational Research, Elsevier, vol. 236(1), pages 61-68.
    4. 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.
    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. 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. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Kolisch, R. & Padman, R., 2001. "An integrated survey of deterministic project scheduling," Omega, Elsevier, vol. 29(3), pages 249-272, June.
    19. Thomas A. Roemer & Reza Ahmadi, 2004. "Concurrent Crashing and Overlapping in Product Development," Operations Research, INFORMS, vol. 52(4), pages 606-622, August.
    20. Thomas A. Roemer & Reza Ahmadi & Robert H. Wang, 2000. "Time-Cost Trade-Offs in Overlapped Product Development," Operations Research, INFORMS, vol. 48(6), pages 858-865, 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:eee:ejores:v:244:y:2015:i:3:p:748-752. 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.