IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v300y2022i1p46-57.html
   My bibliography  Save this article

Exact solutions for the two-machine robust flow shop with budgeted uncertainty

Author

Listed:
  • Levorato, Mario
  • Figueiredo, Rosa
  • Frota, Yuri

Abstract

This work proposes an exact solution approach for the two-machine robust flow shop problem, where operation processing times are uncertain and vary in a given interval. Based on the concept of budgeted uncertainty, the objective is to obtain a robust scheduling that minimizes the makespan of the restricted worst-case scenario, where only a subset of job processing times will oscillate to their worst-case values. To our knowledge, this is the first work to obtain optimal solutions to this problem, by extending two classical MILP formulations for the deterministic case and combining them with a Column-and-Constraint Generation framework. For this purpose, a dynamic programming algorithm was also developed, allowing the identification of worst-case scenarios in polynomial time. Experiments on a set of literature instances confirm the efficacy of our approach, including a case study that shows little overhead in the expected solution value of obtained robust solutions.

Suggested Citation

  • Levorato, Mario & Figueiredo, Rosa & Frota, Yuri, 2022. "Exact solutions for the two-machine robust flow shop with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 300(1), pages 46-57.
    • Handle: RePEc:eee:ejores:v:300:y:2022:i:1:p:46-57
    DOI: 10.1016/j.ejor.2021.10.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721008705
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2021.10.021?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. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Silva, Marco & Poss, Michael & Maculan, Nelson, 2020. "Solution algorithms for minimizing the total tardiness with budgeted processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 283(1), pages 70-82.
    3. Ruiz Duarte, José Luis & Fan, Neng & Jin, Tongdan, 2020. "Multi-process production scheduling with variable renewable integration and demand response," European Journal of Operational Research, Elsevier, vol. 281(1), pages 186-200.
    4. Kasperski, Adam & Kurpisz, Adam & Zieliński, Paweł, 2012. "Approximating a two-machine flow shop scheduling under discrete scenario uncertainty," European Journal of Operational Research, Elsevier, vol. 217(1), pages 36-43.
    5. Harvey M. Wagner, 1959. "An integer linear‐programming model for machine scheduling," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 6(2), pages 131-140, June.
    6. Framinan, Jose M. & Perez-Gonzalez, Paz, 2015. "On heuristic solutions for the stochastic flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 246(2), pages 413-420.
    7. Nicholas G. Hall & Chelliah Sriskandarajah, 1996. "A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process," Operations Research, INFORMS, vol. 44(3), pages 510-525, June.
    8. Feizollahi, Mohammad Javad & Feyzollahi, Hadi, 2015. "Robust quadratic assignment problem with budgeted uncertain flows," Operations Research Perspectives, Elsevier, vol. 2(C), pages 114-123.
    9. Averbakh, Igor, 2006. "The minmax regret permutation flow-shop problem with two jobs," European Journal of Operational Research, Elsevier, vol. 169(3), pages 761-766, March.
    10. Kuo-Ching Ying, 2015. "Scheduling the two-machine flowshop to hedge against processing time uncertainty," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(9), pages 1413-1425, September.
    11. Yakov Shafransky & Viktor Shinkarevich, 2020. "On the complexity of constructing a minmax regret solution for the two-machine flow shop problem under the interval uncertainty," Journal of Scheduling, Springer, vol. 23(6), pages 745-749, December.
    12. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    13. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    14. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    15. Michał Ćwik & Jerzy Józefczyk, 2018. "Heuristic algorithms for the minmax regret flow-shop problem with interval processing times," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 215-238, March.
    16. T-C Lai & Y N Sotskov, 1999. "Sequencing with uncertain numerical data for makespan minimisation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(3), pages 230-243, March.
    17. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    18. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
    19. Nawaz, Muhammad & Enscore Jr, E Emory & Ham, Inyong, 1983. "A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem," Omega, Elsevier, vol. 11(1), pages 91-95.
    20. Tseng, Fan T. & Stafford, Edward F. & Gupta, Jatinder N. D., 2004. "An empirical analysis of integer programming formulations for the permutation flowshop," Omega, Elsevier, vol. 32(4), pages 285-293, August.
    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. Shen, Jiayu & Shi, Yuanji & Shi, Jianxin & Dai, Yunzhong & Li, Wei, 2023. "An uncertain permutation flow shop predictive scheduling problem with processing interruption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).

    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. Brammer, Janis & Lutz, Bernhard & Neumann, Dirk, 2022. "Permutation flow shop scheduling with multiple lines and demand plans using reinforcement learning," European Journal of Operational Research, Elsevier, vol. 299(1), pages 75-86.
    2. Michał Ćwik & Jerzy Józefczyk, 2018. "Heuristic algorithms for the minmax regret flow-shop problem with interval processing times," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 215-238, March.
    3. Pätzold, Julius & Schöbel, Anita, 2020. "Approximate cutting plane approaches for exact solutions to robust optimization problems," European Journal of Operational Research, Elsevier, vol. 284(1), pages 20-30.
    4. Jian Zhang & Guofu Ding & Yisheng Zou & Shengfeng Qin & Jianlin Fu, 2019. "Review of job shop scheduling research and its new perspectives under Industry 4.0," Journal of Intelligent Manufacturing, Springer, vol. 30(4), pages 1809-1830, April.
    5. Carrizosa, Emilio & Goerigk, Marc & Schöbel, Anita, 2017. "A biobjective approach to recoverable robustness based on location planning," European Journal of Operational Research, Elsevier, vol. 261(2), pages 421-435.
    6. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    7. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    8. M. J. Naderi & M. S. Pishvaee, 2017. "Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2689-2711, July.
    9. Zhang, Wei & (Ato) Xu, Wangtu, 2017. "Simulation-based robust optimization for the schedule of single-direction bus transit route: The design of experiment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 203-230.
    10. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    11. Vineet Jain & Tilak Raj, 2018. "An adaptive neuro-fuzzy inference system for makespan estimation of flexible manufacturing system assembly shop: a case study," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(6), pages 1302-1314, December.
    12. Hanks, Robert W. & Weir, Jeffery D. & Lunday, Brian J., 2017. "Robust goal programming using different robustness echelons via norm-based and ellipsoidal uncertainty sets," European Journal of Operational Research, Elsevier, vol. 262(2), pages 636-646.
    13. Roberto Gomes de Mattos & Fabricio Oliveira & Adriana Leiras & Abdon Baptista de Paula Filho & Paulo Gonçalves, 2019. "Robust optimization of the insecticide-treated bed nets procurement and distribution planning under uncertainty for malaria prevention and control," Annals of Operations Research, Springer, vol. 283(1), pages 1045-1078, December.
    14. Wang, Tian & Deng, Shiming, 2019. "Multi-Period energy procurement policies for smart-grid communities with deferrable demand and supplementary uncertain power supplies," Omega, Elsevier, vol. 89(C), pages 212-226.
    15. Oğuz Solyalı & Jean-François Cordeau & Gilbert Laporte, 2016. "The Impact of Modeling on Robust Inventory Management Under Demand Uncertainty," Management Science, INFORMS, vol. 62(4), pages 1188-1201, April.
    16. Detienne, Boris & Lefebvre, Henri & Malaguti, Enrico & Monaci, Michele, 2024. "Adjustable robust optimization with objective uncertainty," European Journal of Operational Research, Elsevier, vol. 312(1), pages 373-384.
    17. Donya Rahmani & Arash Zandi & Sara Behdad & Arezou Entezaminia, 2021. "A light robust model for aggregate production planning with consideration of environmental impacts of machines," Operational Research, Springer, vol. 21(1), pages 273-297, March.
    18. Roos, Ernst & den Hertog, Dick, 2019. "Reducing conservatism in robust optimization," Other publications TiSEM ad0238cd-de7a-4366-b487-b, Tilburg University, School of Economics and Management.
    19. Matthias Bultmann & Sigrid Knust & Stefan Waldherr, 2018. "Flow shop scheduling with flexible processing times," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 809-829, July.
    20. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.

    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:300:y:2022:i:1:p:46-57. 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.