IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v308y2023i3p1074-1090.html
   My bibliography  Save this article

Single-machine scheduling of multiple projects with controllable processing times

Author

Listed:
  • Geng, Zhichao
  • Yuan, Jinjiang

Abstract

This paper studies the single-machine multiple-project scheduling problem with controllable processing times, in which the cost of a project refers to the total compression cost of its jobs plus the weighted number of tardy jobs in a schedule satisfying some given precedence constraints. It involves four specific problems: (i) minimizing the total cost of an arbitrary number of projects, (ii) being the same as (i) except the jobs from the same project having a common due date, (iii) having a fixed number of projects and minimizing the cost of one project subject to the cost of each of other projects not exceeding a given threshold, and (iv) being the same as (iii) except all jobs having identical weights. We show that a special version of (i) in which each project has only two jobs and all jobs have unit weights and cannot be compressed is strongly NP-hard (it implies the strong NP-hardness of (i)), (ii) is weakly NP-hard and admits a pseudo-polynomial algorithm and a fully polynomial time approximation scheme, (iii) is pseudo-polynomially solvable by a two-phase transformation, and (iv) is weakly NP-hard even if there are only two projects and all jobs have identical maximum compression amounts and identical processing times.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:308:y:2023:i:3:p:1074-1090
    DOI: 10.1016/j.ejor.2023.01.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723000449
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.01.026?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. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "Complexity results for scheduling chains on a single machine," European Journal of Operational Research, Elsevier, vol. 4(4), pages 270-275, April.
    2. 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.
    3. Akiyoshi Shioura & Natalia V. Shakhlevich & Vitaly A. Strusevich, 2020. "Scheduling problems with controllable processing times and a common deadline to minimize maximum compression cost," Journal of Global Optimization, Springer, vol. 76(3), pages 471-490, March.
    4. T.C.E. Cheng & Zhi‐Long Chen & Chung‐Lun Li & B.M.‐T. Lin, 1998. "Scheduling to minimize the total compression and late costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 67-82, February.
    5. Šůcha, Přemysl & Agnetis, Alessandro & Šidlovský, Marko & Briand, Cyril, 2021. "Nash equilibrium solutions in multi-agent project scheduling with milestones," European Journal of Operational Research, Elsevier, vol. 294(1), pages 29-41.
    6. 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.
    7. Joseph Y.-T. Leung & Michael Pinedo & Guohua Wan, 2010. "Competitive Two-Agent Scheduling and Its Applications," Operations Research, INFORMS, vol. 58(2), pages 458-469, April.
    8. Byung-Cheon Choi & Myoung-Ju Park, 2015. "Min-Max Regret Version of the Linear Time–Cost Tradeoff Problem with Multiple Milestones and Completely Ordered Jobs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-16.
    9. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
    10. Rubing Chen & Jinjiang Yuan & Yuan Gao, 2019. "The complexity of CO-agent scheduling to minimize the total completion time and total number of tardy jobs," Journal of Scheduling, Springer, vol. 22(5), pages 581-593, October.
    11. 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.
    12. He, Naihui & Zhang, David Z. & Yuce, Baris, 2022. "Integrated multi-project planning and scheduling - a multiagent approach," European Journal of Operational Research, Elsevier, vol. 302(2), pages 688-699.
    13. 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.
    14. Jinjiang Yuan, 2017. "Unary NP-hardness of minimizing the number of tardy jobs with deadlines," Journal of Scheduling, Springer, vol. 20(2), pages 211-218, April.
    15. Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    16. 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.
    17. Perez-Gonzalez, Paz & Framinan, Jose M., 2014. "A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 1-16.
    18. James E. Kelley, 1961. "Critical-Path Planning and Scheduling: Mathematical Basis," Operations Research, INFORMS, vol. 9(3), pages 296-320, June.
    19. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
    20. 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.
    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. Zhang, Wenyu & Gan, Jie & He, Shuguang & Li, Ting & He, Zhen, 2024. "An integrated framework of preventive maintenance and task scheduling for repairable multi-unit systems," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    2. Tan, Zhen & Fu, Guanqi, 2024. "Just-in-time scheduling problem with affine idleness cost," European Journal of Operational Research, Elsevier, vol. 313(3), pages 954-976.

    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 & 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. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    3. 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.
    4. Wan, Long & Mei, Jiajie & Du, Jiangze, 2021. "Two-agent scheduling of unit processing time jobs to minimize total weighted completion time and total weighted number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 290(1), pages 26-35.
    5. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    6. Shi-Sheng Li & Ren-Xia Chen, 2023. "Competitive two-agent scheduling with release dates and preemption on a single machine," Journal of Scheduling, Springer, vol. 26(3), pages 227-249, June.
    7. 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.
    8. Choi, Byung-Cheon & Park, Myoung-Ju, 2017. "Two-agent parallel machine scheduling with a restricted number of overlapped reserved tasks," European Journal of Operational Research, Elsevier, vol. 260(2), pages 514-519.
    9. Ruyan He & Jinjiang Yuan, 2020. "Two-Agent Preemptive Pareto-Scheduling to Minimize Late Work and Other Criteria," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    10. Ren-Xia Chen & Shi-Sheng Li, 2019. "Two-agent single-machine scheduling with cumulative deterioration," 4OR, Springer, vol. 17(2), pages 201-219, June.
    11. Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.
    12. Tang, Lixin & Zhao, Xiaoli & Liu, Jiyin & Leung, Joseph Y.-T., 2017. "Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine," European Journal of Operational Research, Elsevier, vol. 263(2), pages 401-411.
    13. Gao, Yuan & Yuan, Jinjiang & Ng, C.T. & Cheng, T.C.E., 2019. "A further study on two-agent parallel-batch scheduling with release dates and deteriorating jobs to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 273(1), pages 74-81.
    14. 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.
    15. Dujuan Wang & Yugang Yu & Huaxin Qiu & Yunqiang Yin & T. C. E. Cheng, 2020. "Two‐agent scheduling with linear resource‐dependent processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 573-591, October.
    16. Zhang Xingong & Wang Yong, 2017. "Two-agent scheduling problems on a single-machine to minimize the total weighted late work," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 945-955, April.
    17. Shi-Sheng Li & Ren-Xia Chen & Qi Feng, 2016. "Scheduling two job families on a single machine with two competitive agents," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 784-799, October.
    18. Shisheng Li & T.C.E. Cheng & C.T. Ng & Jinjiang Yuan, 2017. "Two‐agent scheduling on a single sequential and compatible batching machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 628-641, December.
    19. Du-Juan Wang & Yunqiang Yin & Shuenn-Ren Cheng & T.C.E. Cheng & Chin-Chia Wu, 2016. "Due date assignment and scheduling on a single machine with two competing agents," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1152-1169, February.
    20. Yuan Gao & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2022. "Pareto-scheduling with family jobs or ND-agent on a parallel-batch machine to minimize the makespan and maximum cost," 4OR, Springer, vol. 20(2), pages 273-287, June.

    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:308:y:2023:i:3:p:1074-1090. 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.