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Complexity results for the linear time–cost tradeoff problem with multiple milestones and completely ordered jobs

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  • Choi, Byung-Cheon
  • Chung, Jibok

Abstract

We consider two linear project time–cost tradeoff problems with multiple milestones. Unless a milestone is completed on time, penalty costs for tardiness may be imposed. However, these penalty costs can be avoided by compressing the processing times of certain jobs that require additional resources or costs. Our model describes these penalty costs as the total weighted number of tardy milestone. The first problem tries to minimize the total weighted number of tardy milestones within the budget for total compression costs, while the second problem tries to minimize the total weighted number of tardy milestones plus total compression costs. We develop a linear programming formulation for the case with a fixed number of milestones. For the case with an arbitrary number of milestones, we show that under completely ordered jobs, the first problem is NP-hard in the ordinary sense while the second problem is polynomially solvable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:61-68
    DOI: 10.1016/j.ejor.2013.11.009
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    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. 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.
    3. 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.
    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. Zhao, Mingxuan & Zhou, Jian & Wang, Ke & Pantelous, Athanasios A., 2023. "Project scheduling problem with fuzzy activity durations: A novel operational law based solution framework," European Journal of Operational Research, Elsevier, vol. 306(2), pages 519-534.

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