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Two-Level Linear Programming

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Author Info

  • Wayne F. Bialas

    (Department of Civil Engineering, MIT, Cambridge, Massachusetts 02139)

  • Mark H. Karwan

    (Department of Industrial Engineering, State University of New York, Buffalo, New York 14260)

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    Abstract

    Decentralized planning has long been recognized as an important decision making problem. Many approaches based on the concepts of large-scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which often exist in practice. Multilevel programming models partition control over decision variables among ordered levels within a hierarchical planning structure. A planner at one level of the hierarchy may have his objective function and set of feasible decisions determined, in part, by other levels. However, his control instruments may allow him to influence the policies at other levels and thereby improve his own objective function. This paper examines the special case of the two-level linear programming problem. Geometric characterizations and algorithms are presented with some examples. The goal is to demonstrate the tractability of such problems and motivate a wider interest in their study.

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    File URL: http://dx.doi.org/10.1287/mnsc.30.8.1004
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 30 (1984)
    Issue (Month): 8 (August)
    Pages: 1004-1020

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    Handle: RePEc:inm:ormnsc:v:30:y:1984:i:8:p:1004-1020

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    Related research

    Keywords: programming: linear; algorithms;

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    Cited by:
    1. Calvete, Herminia I. & Gale, Carmen, 2004. "A note on `bilevel linear fractional programming problem'," European Journal of Operational Research, Elsevier, vol. 152(1), pages 296-299, January.
    2. Calvete, Herminia I. & Galé, Carmen, 2011. "On linear bilevel problems with multiple objectives at the lower level," Omega, Elsevier, vol. 39(1), pages 33-40, January.
    3. Sakawa, Masatoshi & Nishizaki, Ichiro & Uemura, Yoshio, 2002. "A decentralized two-level transportation problem in a housing material manufacturer: Interactive fuzzy programming approach," European Journal of Operational Research, Elsevier, vol. 141(1), pages 167-185, August.
    4. 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.
    5. 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.
    6. Pramanik, Surapati & Roy, Tapan Kumar, 2007. "Fuzzy goal programming approach to multilevel programming problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1151-1166, January.
    7. Gabriel, Steven A. & Leuthold, Florian U., 2010. "Solving discretely-constrained MPEC problems with applications in electric power markets," Energy Economics, Elsevier, vol. 32(1), pages 3-14, January.
    8. Cao, D. & Leung, L. C., 2002. "A partial cooperation model for non-unique linear two-level decision problems," European Journal of Operational Research, Elsevier, vol. 140(1), pages 134-141, July.
    9. Arora, S.R. & Gupta, Ritu, 2009. "Interactive fuzzy goal programming approach for bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 194(2), pages 368-376, April.
    10. Sakawa, Masatoshi & Nishizaki, Ichiro & Uemura, Yoshio, 2001. "Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: A case study," European Journal of Operational Research, Elsevier, vol. 135(1), pages 142-157, November.
    11. Mathur, Kanchan & Puri, M. C., 1995. "A bilevel bottleneck programming problem," European Journal of Operational Research, Elsevier, vol. 86(2), pages 337-344, October.
    12. Ahlatcioglu, Mehmet & Tiryaki, Fatma, 2007. "Interactive fuzzy programming for decentralized two-level linear fractional programming (DTLLFP) problems," Omega, Elsevier, vol. 35(4), pages 432-450, August.
    13. 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.
    14. Budnitzki, Alina, 2014. "Computation of the optimal tolls on the traffic network," European Journal of Operational Research, Elsevier, vol. 235(1), pages 247-251.

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