IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v123y2004i2d10.1007_s10957-004-5156-y.html
   My bibliography  Save this article

Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

Author

Listed:
  • G. Z. Ruan

    (Xiangtan University)

  • S. Y. Wang

    (Chinese Academy of Sciences
    Hunan University)

  • Y. Yamamoto

    (University of Tsukuba)

  • S. S. Zhu

    (Chinese Academy of Sciences
    Fudan University)

Abstract

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:2:d:10.1007_s10957-004-5156-y
    DOI: 10.1007/s10957-004-5156-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-004-5156-y
    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/s10957-004-5156-y?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. D. J. White, 1997. "Penalty Function Approach to Linear Trilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 183-197, April.
    2. 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.
    3. Bard, Jonathan F., 1985. "Geometric and algorithmic developments for a hierarchical planning problem," European Journal of Operational Research, Elsevier, vol. 19(3), pages 372-383, March.
    4. Jonathan F. Bard, 1983. "An Algorithm for Solving the General Bilevel Programming Problem," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 260-272, May.
    5. Wayne F. Bialas & Mark H. Karwan, 1984. "Two-Level Linear Programming," Management Science, INFORMS, vol. 30(8), pages 1004-1020, 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. Armita Khorsandi & Bing-Yuan Cao & Hadi Nasseri, 2019. "A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    2. Nuno Faísca & Pedro Saraiva & Berç Rustem & Efstratios Pistikopoulos, 2009. "A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems," Computational Management Science, Springer, vol. 6(4), pages 377-397, October.

    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. Wen, U. P. & Huang, A. D., 1996. "A simple Tabu Search method to solve the mixed-integer linear bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 563-571, February.
    2. H. I. Calvete & C. Galé, 1998. "On the Quasiconcave Bilevel Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 613-622, September.
    3. Liu, Yi-Hsin & Spencer, Thomas H., 1995. "Solving a bilevel linear program when the inner decision maker controls few variables," European Journal of Operational Research, Elsevier, vol. 81(3), pages 644-651, March.
    4. 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.
    5. Lorenzo Lampariello & Simone Sagratella, 2015. "It is a matter of hierarchy: a Nash equilibrium problem perspective on bilevel programming," DIAG Technical Reports 2015-07, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    6. 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.
    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. 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.
    9. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2024. "Bilevel Nash Equilibrium Problems: Numerical Approximation Via Direct-Search Methods," Dynamic Games and Applications, Springer, vol. 14(2), pages 305-332, May.
    10. 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.
    11. 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.
    12. 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.
    13. 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).
    14. 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.
    15. Frota Neto, J. Quariguasi & Bloemhof-Ruwaard, J.M. & van Nunen, J.A.E.E. & van Heck, E., 2008. "Designing and evaluating sustainable logistics networks," International Journal of Production Economics, Elsevier, vol. 111(2), pages 195-208, February.
    16. Liu, Shaonan & Kong, Nan & Parikh, Pratik & Wang, Mingzheng, 2023. "Optimal trauma care network redesign with government subsidy: A bilevel integer programming approach," Omega, Elsevier, vol. 119(C).
    17. Budnitzki, Alina, 2014. "Computation of the optimal tolls on the traffic network," European Journal of Operational Research, Elsevier, vol. 235(1), pages 247-251.
    18. Bo Zeng, 2020. "A Practical Scheme to Compute the Pessimistic Bilevel Optimization Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1128-1142, October.
    19. Syed Mohd Muneeb & Ahmad Yusuf Adhami & Zainab Asim & Syed Aqib Jalil, 2019. "Bi-level decision making models for advertising allocation problem under fuzzy environment," 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. 10(2), pages 160-172, April.
    20. Blom, Danny & Smeulders, Bart & Spieksma, Frits, 2024. "Rejection-proof mechanisms for multi-agent kidney exchange," Games and Economic Behavior, Elsevier, vol. 143(C), pages 25-50.

    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:joptap:v:123:y:2004:i:2:d:10.1007_s10957-004-5156-y. 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.