Milan Hladík. On necessary efficient solutions in interval multiobjective linear programming. In CD-ROM Proceedings of the 25th Mini-EURO Conference Uncertainty and Robustness in Planning and Decision Making URPDM 2010, April 15-17, Coimbra, Portugal, pp. 1–10, 2010.
We investigate multiobjective linear programming problems with objective coefficients varying inside given intervals. A feasible solution x* is called necessarily efficient if it is efficient for all realizations of the interval objective function coefficients. Testing necessarily efficiency may be computationally expensive. Thus we propose one sufficient and also one necessary condition for necessarily efficiency that can significantly speed up decision algorithms. These conditions do not require the feasible solution x* to be non-degenerate. We demonstrate usage of both conditions on illustrative examples and show how strong they are.
@InProceedings{Hla2010a,
author = "Milan Hlad\'{\i}k",
editor = "C. H. Antunes and D. R. Insua and L. C. Dias",
title = "On necessary efficient solutions in interval multiobjective linear programming",
booktitle = "{CD-ROM Proceedings of the 25th Mini-EURO Conference Uncertainty and Robustness in Planning and Decision Making URPDM 2010, April 15-17, Coimbra, Portugal}",
pages = "1-10",
year = "2010",
bib2html_dl_pdf = "https://kam.mff.cuni.cz/~hladik/doc/2010-conf-URPDM-NecEffSolIntMOLP.pdf",
abstract = "We investigate multiobjective linear programming problems with objective coefficients varying inside given intervals. A feasible solution x* is called necessarily efficient if it is efficient for all realizations of the interval objective function coefficients. Testing necessarily efficiency may be computationally expensive. Thus we propose one sufficient and also one necessary condition for necessarily efficiency that can significantly speed up decision algorithms. These conditions do not require the feasible solution x* to be non-degenerate. We demonstrate usage of both conditions on illustrative examples and show how strong they are.",
keywords = "multiobjective linear programming, efficient solution, interval matrix, interval analysis",
}
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