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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
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.

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