IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v20y2012i1p101-117.html
   My bibliography  Save this article

Stackelberg solutions for fuzzy random two-level linear programming through level sets and fractile criterion optimization

Author

Listed:
  • Masatoshi Sakawa

  • Hideki Katagiri

Abstract

This paper considers Stackelberg solutions for two-level linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random two-level linear programming problem, an α-stochastic two-level linear programming problem is defined through the introduction of α-level sets of fuzzy random variables. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the α-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through fractile criterion optimization in stochastic programming, the transformed stochastic two-level programming problem can be reduced to a deterministic two-level programming problem. An extended concept of Stackelberg solution is introduced and a numerical example is provided to illustrate the proposed method. Copyright Springer-Verlag 2012

Suggested Citation

  • Masatoshi Sakawa & Hideki Katagiri, 2012. "Stackelberg solutions for fuzzy random two-level linear programming through level sets and fractile criterion optimization," 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. 20(1), pages 101-117, March.
    • Handle: RePEc:spr:cejnor:v:20:y:2012:i:1:p:101-117
    DOI: 10.1007/s10100-010-0156-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10100-010-0156-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10100-010-0156-5?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Wayne F. Bialas & Mark H. Karwan, 1984. "Two-Level Linear Programming," Management Science, INFORMS, vol. 30(8), pages 1004-1020, August.
    2. Masatoshi Sakawa & Kosuke Kato, 2008. "Interactive Fuzzy Multi-Objective Stochastic Linear Programming," Springer Optimization and Its Applications, in: Cengiz Kahraman (ed.), Fuzzy Multi-Criteria Decision Making, pages 375-408, Springer.
    3. Katagiri, Hideki & Sakawa, Masatoshi & Ishii, Hiroaki, 2004. "Fuzzy random bottleneck spanning tree problems using possibility and necessity measures," European Journal of Operational Research, Elsevier, vol. 152(1), pages 88-95, January.
    4. Calvete, Herminia I. & Gale, Carmen, 2004. "A note on `bilevel linear fractional programming problem'," European Journal of Operational Research, Elsevier, vol. 152(1), pages 296-299, January.
    5. S. Dempe & J. F. Bard, 2001. "Bundle Trust-Region Algorithm for Bilinear Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 265-288, August.
    6. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    7. Amouzegar, Mahyar A. & Moshirvaziri, Khosrow, 1999. "Determining optimal pollution control policies: An application of bilevel programming," European Journal of Operational Research, Elsevier, vol. 119(1), pages 100-120, November.
    8. Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Nishizaki, Ichiro, 2008. "Interactive multiobjective fuzzy random linear programming: Maximization of possibility and probability," European Journal of Operational Research, Elsevier, vol. 188(2), pages 530-539, July.
    9. I. Nishizaki & M. Sakawa, 1999. "Stackelberg Solutions to Multiobjective Two-Level Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 161-182, October.
    10. Luhandjula, M.K., 2006. "Fuzzy stochastic linear programming: Survey and future research directions," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1353-1367, November.
    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. Rihab Said & Maha Elarbi & Slim Bechikh & Lamjed Ben Said, 2022. "Solving combinatorial bi-level optimization problems using multiple populations and migration schemes," Operational Research, Springer, vol. 22(3), pages 1697-1735, July.

    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. Luhandjula, M.K. & Joubert, J.W., 2010. "On some optimisation models in a fuzzy-stochastic environment," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1433-1441, December.
    2. Nishizaki, Ichiro & Hayashida, Tomohiro & Sekizaki, Shinya & Okabe, Junya, 2022. "Data envelopment analysis approaches for two-level production and distribution planning problems," European Journal of Operational Research, Elsevier, vol. 300(1), pages 255-268.
    3. G. Z. Ruan & S. Y. Wang & Y. Yamamoto & S. S. Zhu, 2004. "Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 409-429, November.
    4. Hang Li & Zhe Zhang & Xianggen Yin & Buhan Zhang, 2020. "Preventive Security-Constrained Optimal Power Flow with Probabilistic Guarantees," Energies, MDPI, vol. 13(9), pages 1-13, May.
    5. C. Audet & G. Savard & W. Zghal, 2007. "New Branch-and-Cut Algorithm for Bilevel Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 353-370, August.
    6. Yulei Xie & Linrui Wang & Guohe Huang & Dehong Xia & Ling Ji, 2018. "A Stochastic Inexact Robust Model for Regional Energy System Management and Emission Reduction Potential Analysis—A Case Study of Zibo City, China," Energies, MDPI, vol. 11(8), pages 1-24, August.
    7. Cao, Dong & Chen, Mingyuan, 2006. "Capacitated plant selection in a decentralized manufacturing environment: A bilevel optimization approach," European Journal of Operational Research, Elsevier, vol. 169(1), pages 97-110, February.
    8. Bilsel, R. Ufuk & Ravindran, A., 2011. "A multiobjective chance constrained programming model for supplier selection under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1284-1300, September.
    9. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    10. Sinha, Surabhi & Sinha, S. B., 2002. "KKT transformation approach for multi-objective multi-level linear programming problems," European Journal of Operational Research, Elsevier, vol. 143(1), pages 19-31, November.
    11. Zervopoulos, Panagiotis & Emrouznejad, Ali & Sklavos, Sokratis, 2019. "A Bayesian approach for correcting bias of data envelopment analysis estimators," MPRA Paper 91886, University Library of Munich, Germany.
    12. R. Caballero & E. Cerda & M. Muñoz & L. Rey, 2002. "Analysis and comparisons of some solution concepts for stochastic programming problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 101-123, June.
    13. Hongmin Li & Stephen C. Graves & Woonghee Tim Huh, 2014. "Optimal Capacity Conversion for Product Transitions Under High Service Requirements," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 46-60, February.
    14. Kuo, R.J. & Lee, Y.H. & Zulvia, Ferani E. & Tien, F.C., 2015. "Solving bi-level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1013-1026.
    15. Dariush Akbarian, 2020. "Overall profit Malmquist productivity index under data uncertainty," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-20, December.
    16. G. Hibino & M. Kainuma & Y. Matsuoka & T. Morita, 1996. "Two-level Mathematical Programming for Analyzing Subsidy Options to Reduce Greenhouse-Gas Emissions," Working Papers wp96129, International Institute for Applied Systems Analysis.
    17. Wenqing Chen & Melvyn Sim, 2009. "Goal-Driven Optimization," Operations Research, INFORMS, vol. 57(2), pages 342-357, April.
    18. Zio, E. & Bazzo, R., 2011. "Level Diagrams analysis of Pareto Front for multiobjective system redundancy allocation," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 569-580.
    19. Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
    20. Li, Ruijie & Liu, Yang & Liu, Xiaobo & Nie, Yu (Marco), 2024. "Allocation problem in cross-platform ride-hail integration," Transportation Research Part B: Methodological, Elsevier, vol. 188(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:20:y:2012:i:1:p:101-117. 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.