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Generating all maximal efficient faces for multiple objective linear programs

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Abstract

A method for generating the entire efficient set for a multiple objective linear program is developed. The method is based on two characterizations of maximal efficient faces. The first characterization is used to determine the set of maximal efficient faces incident to a given efficient vertex, and the second characterization ensures that previously generated maximal efficient faces are easily recognized (and not regenerated). The efficient set is described as the union of maximal efficient faces. An alternate implicit description of the efficient set as the set of all optimal vectors for a finite set of linear programs is also provided.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York

    J. G. Ecker (Associate Professor)

  2. School of Business, State University of New York at Albany, Albany, New York

    N. S. Hegner (Visiting Assistant Professor)

  3. Department of Mathematics, University of Niamey, Niamey, Niger, West Africa

    I. A. Kouada (Assistant Professor)

Authors
  1. J. G. Ecker
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  2. N. S. Hegner
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  3. I. A. Kouada
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Additional information

Communicated by G. Leitmann

This research was supported in part by the National Science Foundation Grant No. MCS75-09443 A02.

The authors wish to thank the unknown referee for helpful criticisms which significantly changed the paper.

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Ecker, J.G., Hegner, N.S. & Kouada, I.A. Generating all maximal efficient faces for multiple objective linear programs. J Optim Theory Appl 30, 353–381 (1980). https://doi.org/10.1007/BF00935493

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