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Stackelberg Solutions to Multiobjective Two-Level Linear Programming Problems

Author

Listed:
  • I. Nishizaki

    (Hiroshima University)

  • M. Sakawa

    (Hiroshima University)

Abstract

In this paper, we consider a multiobjective two-level linear programming problem in which the decision maker at each level has multiple-objective functions conflicting with each other. The decision maker at the upper level must take account of multiple or infinite rational responses of the decision maker at the lower level in the problem. We examine three kinds of situations based on anticipation of the decision maker at the upper level: optimistic anticipation, pessimistic anticipation, and anticipation arising from the past behavior of the decision maker at the lower level. Mathematical programming problems for obtaining the Stackelberg solutions based on the three kinds of anticipation are formulated and algorithms for solving the problems are presented. Illustrative numerical examples are provided to understand the geometrical properties of the solutions and demonstrate the feasibility of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:103:y:1999:i:1:d:10.1023_a:1021729618112
    DOI: 10.1023/A:1021729618112
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    References listed on IDEAS

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    1. Jonathan F. Bard, 1983. "An Efficient Point Algorithm for a Linear Two-Stage Optimization Problem," Operations Research, INFORMS, vol. 31(4), pages 670-684, August.
    2. Wayne F. Bialas & Mark H. Karwan, 1984. "Two-Level Linear Programming," Management Science, INFORMS, vol. 30(8), pages 1004-1020, August.
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    Cited by:

    1. 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.
    2. Sauli Ruuska & Kaisa Miettinen & Margaret M. Wiecek, 2012. "Connections Between Single-Level and Bilevel Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 60-74, April.
    3. Lina Mallozzi & Roberta Messalli, 2017. "Multi-Leader Multi-Follower Model with Aggregative Uncertainty," Games, MDPI, vol. 8(3), pages 1-14, June.
    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. Lin, Gui-Hua & Zhang, Dali & Liang, Yan-Chao, 2013. "Stochastic multiobjective problems with complementarity constraints and applications in healthcare management," European Journal of Operational Research, Elsevier, vol. 226(3), pages 461-470.

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