Optimization over the efficient set of a parametric multiple objective linear programming problem

In this paper we consider the problem ( P) for optimizing a function over the efficient set of a multiple objective linear programming (MOLP) problem with parameters in the right hand side vector. Three solution algorithms in a most general case of problem ( P) and improvements of them in some speci...

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Veröffentlicht in:European journal of operational research Jg. 122; H. 3; S. 570 - 583
1. Verfasser: Tu, Ta Van
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.05.2000
Elsevier
Elsevier Sequoia S.A
Schriftenreihe:European Journal of Operational Research
Schlagworte:
Algorithms
Decision theory
Efficiency
Linear programming
Nonlinear programming
Operations research
Optimization
Parametric multiple objective linear programming
Simplex method
Studies
United Kingdom > UK
Nonlinear programming
Efficiency
Decision theory
Parametric multiple objective linear programming
ISSN:0377-2217, 1872-6860
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Zusammenfassung:In this paper we consider the problem ( P) for optimizing a function over the efficient set of a multiple objective linear programming (MOLP) problem with parameters in the right hand side vector. Three solution algorithms in a most general case of problem ( P) and improvements of them in some special cases are presented. In the case when the objective function of problem ( P) is linear, it can be solved based on | T 2| linear programming problems with mixed one-zero integer variables if the parametric set is finite and based on | T 2| linear programming problems if the right hand side vector of the MOLP problem is a linear function of the parameters and the parametric set is a polyhedron, where | T 2| is, in general, the number of maximal efficient faces of the MOLP problem corresponding to a value of the parameters. A numerical example is given to illustrate the working of the algorithms.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/S0377-2217(99)00095-8