IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v31y2023i3d10.1007_s10100-022-00804-6.html
   My bibliography  Save this article

Various approaches to multiobjective linear programming problems with interval costs and interval weights

Author

Listed:
  • Milan Hladík

    (Charles University)

Abstract

Optimization problems are often subject to various kinds of inexactness or inaccuracy of input data. Here, we consider multiobjective linear programming problems, in which two kinds of input entries have the form of interval data. First, we suppose that the objectives entries are interval values, and, second, we suppose that we have an interval estimation of weights of the particular criteria. These two types of interval data naturally lead to various definitions of efficient solutions. We discuss six meaningful concepts of efficient solutions and compare them to each other. For each of them, we attempt to characterize the corresponding kind efficiency and investigate computational complexity of deciding whether a given solution is efficient.

Suggested Citation

  • Milan Hladík, 2023. "Various approaches to multiobjective linear programming problems with interval costs and interval weights," 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. 31(3), pages 713-731, September.
    • Handle: RePEc:spr:cejnor:v:31:y:2023:i:3:d:10.1007_s10100-022-00804-6
    DOI: 10.1007/s10100-022-00804-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-022-00804-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10100-022-00804-6?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. Henriques, C.O. & Inuiguchi, M. & Luque, M. & Figueira, J.R., 2020. "New conditions for testing necessarily/possibly efficiency of non-degenerate basic solutions based on the tolerance approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 341-355.
    2. Gabriel R. Bitran, 1980. "Linear Multiple Objective Problems with Interval Coefficients," Management Science, INFORMS, vol. 26(7), pages 694-706, July.
    3. Sandra González-Gallardo & Ana B. Ruiz & Mariano Luque, 2021. "Analysis of the Well-Being Levels of Students in Spain and Finland through Interval Multiobjective Linear Programming," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    4. S. Rivaz & M. A. Yaghoobi & M. Hladík, 2016. "Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 237-253, September.
    5. S. Rivaz & M. Yaghoobi, 2013. "Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients," 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. 21(3), pages 625-649, September.
    6. Oliveira, Carla & Antunes, Carlos Henggeler, 2007. "Multiple objective linear programming models with interval coefficients - an illustrated overview," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1434-1463, September.
    7. Hladík, Milan & Sitarz, Sebastian, 2013. "Maximal and supremal tolerances in multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 228(1), pages 93-101.
    8. Elif Garajová & Milan Hladík & Miroslav Rada, 2019. "Interval linear programming under transformations: optimal solutions and optimal value range," 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. 27(3), pages 601-614, September.
    9. Amin Mostafaee & Milan Hladík, 2020. "Optimal value bounds in interval fractional linear programming and revenue efficiency measuring," 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(3), pages 963-981, September.
    10. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    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. Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2023. "60 years of OR in Slovenia: development from a first conference to a vibrant community," 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. 31(3), pages 681-690, September.

    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. P. Kumar & A. K. Bhurjee, 2022. "Multi-objective enhanced interval optimization problem," Annals of Operations Research, Springer, vol. 311(2), pages 1035-1050, April.
    2. Henriques, C.O. & Inuiguchi, M. & Luque, M. & Figueira, J.R., 2020. "New conditions for testing necessarily/possibly efficiency of non-degenerate basic solutions based on the tolerance approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 341-355.
    3. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    4. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    5. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    6. S. Rivaz & M. A. Yaghoobi & M. Hladík, 2016. "Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 237-253, September.
    7. Mehdi Allahdadi & Aida Batamiz, 2021. "Generation of some methods for solving interval multi-objective linear programming models," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1077-1115, December.
    8. Schöbel, Anita & Zhou-Kangas, Yue, 2021. "The price of multiobjective robustness: Analyzing solution sets to uncertain multiobjective problems," European Journal of Operational Research, Elsevier, vol. 291(2), pages 782-793.
    9. Sandra González-Gallardo & Ana B. Ruiz & Mariano Luque, 2021. "Analysis of the Well-Being Levels of Students in Spain and Finland through Interval Multiobjective Linear Programming," Mathematics, MDPI, vol. 9(14), pages 1-27, July.
    10. Henriques, C.O. & Luque, M. & Marcenaro-Gutierrez, O.D. & Lopez-Agudo, L.A., 2019. "A multiobjective interval programming model to explore the trade-offs among different aspects of job satisfaction under different scenarios," Socio-Economic Planning Sciences, Elsevier, vol. 66(C), pages 35-46.
    11. Masahiro Inuiguchi & Zhenzhong Gao & Carla Oliveira Henriques, 2023. "Robust optimality analysis of non-degenerate basic feasible solutions in linear programming problems with fuzzy objective coefficients," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 51-79, March.
    12. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2018. "Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs," European Journal of Operational Research, Elsevier, vol. 270(1), pages 40-50.
    13. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
    14. María Luisa Nolé & David Soler & Juan Luis Higuera-Trujillo & Carmen Llinares, 2022. "Optimization of the Cognitive Processes in a Virtual Classroom: A Multi-objective Integer Linear Programming Approach," Mathematics, MDPI, vol. 10(7), pages 1-20, April.
    15. Carla Oliveira Henriques & Maria Elisabete Neves & Licínio Castelão & Duc Khuong Nguyen, 2022. "Assessing the performance of exchange traded funds in the energy sector: a hybrid DEA multiobjective linear programming approach," Annals of Operations Research, Springer, vol. 313(1), pages 341-366, June.
    16. Carla Oliveira Henriques & Dulce Helena Coelho & Maria Elisabete Duarte Neves, 2022. "Investment planning in energy efficiency programs: a portfolio based approach," Operational Research, Springer, vol. 22(1), pages 615-649, March.
    17. Hladík, Milan, 2016. "Robust optimal solutions in interval linear programming with forall-exists quantifiers," European Journal of Operational Research, Elsevier, vol. 254(3), pages 705-714.
    18. Hladík, Milan & Sitarz, Sebastian, 2013. "Maximal and supremal tolerances in multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 228(1), pages 93-101.
    19. Yao, Zhaosheng & Wang, Zhiyuan & Ran, Lun, 2023. "Smart charging and discharging of electric vehicles based on multi-objective robust optimization in smart cities," Applied Energy, Elsevier, vol. 343(C).
    20. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," 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. 29(3), pages 773-790, September.

    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:spr:cejnor:v:31:y:2023:i:3:d:10.1007_s10100-022-00804-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.