Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Multi-objective linear-programming problem

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_649

This problem has the usual set of linear-programming constraints (Axv = b, xv ≥; 0) but requires the simultaneous optimization of more than one linear objective function, say p of them. It can be written as “Maximize” Cxv subject to Axv = b, xv ≥ 0, where Cv is a p × n matrix whose rows are the coefficients defined by the p objectives. Here “Maximize” represents the fact that it is usually impossible to find a solution to Axv = b, xv ≥ 0, that simultaneously optimizes all the objectives. If there is such an (extreme) point, the problem is thus readily solved. Special multiobjective computational procedures are required to select a solution that is in effect a compromise solution between the extreme point solutions that optimize individual objective functions. The possible compromise solutions are taken from the set of efficient (nondominated) solutions. This problem is also called the vector optimization problem.  Efficient solution; Multi-objective optimization; Multi-objective...

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA