Abstract
The multiobjective fractional programming /MOFP/ problem is formulated and some theory is given. The special case of MOFP is scalar fractional programming /FP/ problem. Connections between FP problem and a special bicriteria programming problems are investigated. Some results of Geoffrion [2] are extended. Replacement of the bicriteria programming problem by the adequate one-parametric programming problem provides with some parametric procedure for FP problem. Basing upon these results we present another motivation for the parametric algorithm of solving the linear FP problem proposed earlier by Frankel, Novaes and Pollack [1].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.Frankel, A.Novaes, E.Pollack, “Optimization and Integration of Shipping Ventures”, International Shipbuilding Progress, July 1965.
A.M.Geoffrion, “Solving Bicriterion Mathematical Programs”, Operations Research, Vol. 15 No.1/1967/ pp. 39–54.
A.M.Geoffrion, “Strictly Concave Parametric Programming, Part I: Basic Theory”, Management Sc., Vol. 13, No. 3/1967/ PP. 244–253.
J.S.H.Kornbluth, R.E.Steuer, “Multiple Objective Linear Fractional Programming”, Management Sc., Vol. 27 No. 9/1981/ PP. 1024–1037.
J.S.H.Kornbluth, R.E.Steuer, “On Computing the Set of All Weakly Efficient Vertices in Multiple Objective Linear Fractional Programming”, in: Multiple Criteria Decision Making, Theory and Applications, Ed. G.Fandel, T.Gal, Proceedings Hagen/Konigswinter, West Germany 1979, Springer - Verlag, Berlin-Heidelberg-New York 1980.
I.Nykowski, Z.Zólkiewski, “Model liniowy z ulamkowa funkcja celu a programowanie wielocelowe”, /to appear/, Przeglad Statystyczny Vol. 28, No. 3–4/1981/.
M.Zeleny, “Linear Multiobjective Programming”, McGraw-Hill, New York - Berlin 1974.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nykowski, I., Zółlkiewski, Z. (1983). On Some Connections Between Bicriteria and Fractional Programming Problems. In: Hansen, P. (eds) Essays and Surveys on Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46473-7_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-46473-7_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11991-3
Online ISBN: 978-3-642-46473-7
eBook Packages: Springer Book Archive