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An interactive paired comparison method for bicriterion integer programming

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  • Wan S. Shin
  • Diane Breivik Allen

Abstract

This article proposes an interactive paired comparison region elimination method for bicriterion integer mathematical programming problems. The new method isolates the best compromise solution by successively evaluating a pair of associated supported non‐dominated solutions. The efficiency of the method is tested by solving randomly generated problems based on varying shapes of efficient frontiers. When compared with the existing branch‐and‐bound method, the method was effective in reducing the burden on the decision maker. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Wan S. Shin & Diane Breivik Allen, 1994. "An interactive paired comparison method for bicriterion integer programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 423-434, April.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:3:p:423-434
    DOI: 10.1002/1520-6750(199404)41:33.0.CO;2-E
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    References listed on IDEAS

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    1. Pekka Korhonen & Jyrki Wallenius & Stanley Zionts, 1984. "Solving the Discrete Multiple Criteria Problem using Convex Cones," Management Science, INFORMS, vol. 30(11), pages 1336-1345, November.
    2. Gerald W. Evans, 1984. "An Overview of Techniques for Solving Multiobjective Mathematical Programs," Management Science, INFORMS, vol. 30(11), pages 1268-1282, November.
    3. Yasemin Aksoy, 1990. "An interactive branch‐and‐bound algorithm for bicriterion nonconvex/mixed integer programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 403-417, June.
    4. Czuchra, Waldemar, 1988. "A graphical bicriteria approach to the resource allocation problem," European Journal of Operational Research, Elsevier, vol. 34(1), pages 86-91, February.
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    Cited by:

    1. Sun, Minghe, 2005. "Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures," European Journal of Operational Research, Elsevier, vol. 162(2), pages 468-483, April.
    2. Aksoy, Yasemin & Butler, Timothy W. & Minor, Elliott D., 1996. "Comparative studies in interactive multiple objective mathematical programming," European Journal of Operational Research, Elsevier, vol. 89(2), pages 408-422, March.
    3. Ted Ralphs & Matthew Saltzman & Margaret Wiecek, 2006. "An improved algorithm for solving biobjective integer programs," Annals of Operations Research, Springer, vol. 147(1), pages 43-70, October.
    4. Alves, Maria Joao & Climaco, Joao, 2007. "A review of interactive methods for multiobjective integer and mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 99-115, July.
    5. J. Fülöp & L. D. Muu, 2000. "Branch-and-Bound Variant of an Outcome-Based Algorithm for Optimizing over the Efficient Set of a Bicriteria Linear Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 37-54, April.

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