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A linear time–cost tradeoff problem with multiple milestones under a comb graph

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  • Byung-Cheon Choi

    (Chungnam National University)

  • Changmuk Kang

    (Soongsil University)

Abstract

We consider a linear time–cost tradeoff problem (LTCTP) with multiple milestones under a comb graph. A time–cost tradeoff problem decides whether and how much to spend a cost to compress processing time of a job in order to meet promised due dates. This is common in managing a project because additional labors or resources are expensive. It is called linear where the compression cost linearly increases with reduced time. An objective of the LTCTP that this study addresses is to minimize the weighted number of tardy milestones plus the total compression cost. This study considers a special precedence structure, which is called a comb graph. A chain of jobs that sequentially precede each other forms a main process of a project, and other chains of jobs, corresponding to sub processes, precede each job in the main process. For this structure, we developed a strongly-polynomial-time algorithm. This is the first result of unveiling complexity of the multi-milestone LTCTP under a non-chain structure.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:2:d:10.1007_s10878-019-00385-2
    DOI: 10.1007/s10878-019-00385-2
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    References listed on IDEAS

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    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. 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.
    4. 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.
    5. James E. Kelley, 1961. "Critical-Path Planning and Scheduling: Mathematical Basis," Operations Research, INFORMS, vol. 9(3), pages 296-320, June.
    6. 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.
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    Cited by:

    1. 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.

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