IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v28y1980i3-part-iip785-793.html
   My bibliography  Save this article

Identifying Efficient Vectors: Some Theory and Computational Results

Author

Listed:
  • Stanley Zionts

    (State University of New York, Buffalo, New York)

  • Jyrki Wallenius

    (Purdue University, Lafayette, Indiana, and University of Jyvaskyla, Finland)

Abstract

Five problems of finding efficient vectors as a subset of a finite set of vectors are shown to be related and a common methodology based on the simplex method of linear programming is developed for solving all of them. Randomly generated problems for one of the five types are solved using the method, and the implications regarding computational requirements are discussed.

Suggested Citation

  • Stanley Zionts & Jyrki Wallenius, 1980. "Identifying Efficient Vectors: Some Theory and Computational Results," Operations Research, INFORMS, vol. 28(3-part-ii), pages 785-793, June.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:3-part-ii:p:785-793
    DOI: 10.1287/opre.28.3.785
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.28.3.785
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.28.3.785?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kim, B. & Gel, E.S. & Fowler, J.W. & Carlyle, W.M. & Wallenius, J., 2006. "Evaluation of nondominated solution sets for k-objective optimization problems: An exact method and approximations," European Journal of Operational Research, Elsevier, vol. 173(2), pages 565-582, September.
    2. Karakaya, G. & Köksalan, M. & Ahipaşaoğlu, S.D., 2018. "Interactive algorithms for a broad underlying family of preference functions," European Journal of Operational Research, Elsevier, vol. 265(1), pages 248-262.
    3. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
    4. Gutierrez, J. & Puerto, J. & Sicilia, J., 2004. "The multiscenario lot size problem with concave costs," European Journal of Operational Research, Elsevier, vol. 156(1), pages 162-182, July.
    5. Alves, Maria João & Costa, João Paulo, 2009. "An exact method for computing the nadir values in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 198(2), pages 637-646, October.
    6. Alves, Maria João & Henggeler Antunes, Carlos, 2022. "A new exact method for linear bilevel problems with multiple objective functions at the lower level," European Journal of Operational Research, Elsevier, vol. 303(1), pages 312-327.
    7. Fernandez, Elena & Puerto, Justo, 2003. "Multiobjective solution of the uncapacitated plant location problem," European Journal of Operational Research, Elsevier, vol. 145(3), pages 509-529, March.
    8. Halme, Merja & Korhonen, Pekka & Eskelinen, Juha, 2014. "Non-convex value efficiency analysis and its application to bank branch sales evaluation," Omega, Elsevier, vol. 48(C), pages 10-18.
    9. Gallagher, Richard J. & Saleh, Ossama A., 1995. "A representation of an efficiency equivalent polyhedron for the objective set of a multiple objective linear program," European Journal of Operational Research, Elsevier, vol. 80(1), pages 204-212, January.
    10. Canan Ulu & Murat Köksalan, 2001. "An interactive procedure for selecting acceptable alternatives in the presence of multiple criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 592-606, October.
    11. R. Ramesh & Mark H. Karwan & Stanley Zionts, 1989. "Interactive multicriteria linear programming: An extension of the method of Zionts and Wallenius," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 321-335, June.
    12. Steuer, Ralph E. & Piercy, Craig A., 2005. "A regression study of the number of efficient extreme points in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 162(2), pages 484-496, April.
    13. Kasanen, Eero & Wallenius, Hannele & Wallenius, Jyrki & Zionts, Stanley, 2000. "A study of high-level managerial decision processes, with implications for MCDM research," European Journal of Operational Research, Elsevier, vol. 120(3), pages 496-510, February.
    14. Farahani, Reza Zanjirani & Asgari, Nasrin, 2007. "Combination of MCDM and covering techniques in a hierarchical model for facility location: A case study," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1839-1858, February.
    15. Park, K. Sam & Shin, Dong Eun, 2012. "Interactive multiobjective optimization approach to the input–output design of opening new branches," European Journal of Operational Research, Elsevier, vol. 220(2), pages 530-538.

    More about this item

    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:inm:oropre:v:28:y:1980:i:3-part-ii:p:785-793. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.