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On the structure and properties of a linear multilevel programming problem

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Abstract

Many decision-making situations involve multiple planners with different, and sometimes conflicting, objective functions. One type of model that has been suggested to represent such situations is the linear multilevel programming problem. However, it appears that theoretical and algorithmic results for linear multilevel programming have been limited, to date, to the bounded case or the case of when only two levels exist. In this paper, we investigate the structure and properties of a linear multilevel programming problem that may be unbounded. We study the geometry of the problem and its feasible region. We also give necessary and sufficient conditions for the problem to be unbounded, and we show how the problem is related to a certain parametric concave minimization problem. The algorithmic implications of the results are also discussed.

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Authors and Affiliations

  1. College of Business Administration, University of Florida, Gainesville, Florida

    H. P. Benson (Associate Professor)

Authors
  1. H. P. Benson
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Additional information

Communicated by P. L. Yu

This research was supported by National Science Foundation Grant No. ECS-85-15231.

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Benson, H.P. On the structure and properties of a linear multilevel programming problem. J Optim Theory Appl 60, 353–373 (1989). https://doi.org/10.1007/BF00940342

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