Generalized Fractional Programming with User Interaction

30 Pages Posted: 26 Aug 2006

See all articles by S. Ilker Birbil

S. Ilker Birbil

J. B. G. Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ; Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

Shuzhong Zhang

The Chinese University of Hong Kong (CUHK) - Faculty of Engineering

Date Written: June 21, 2004

Abstract

The present paper proposes a new approach to solve generalized fractional programming problems through user interaction. Capitalizing on two alternatives, we review the Dinkelbach-type methods and set forth the main difficulty in applying these methods. In order to cope with this difficulty, we propose an approximation approach that can be controlled by a predetermined parameter. The proposed approach is promising particularly when a decision maker is involved in the solution process and agrees upon finding an effective but nearoptimal value in an efficient manner. The decision maker is asked to decide the parameter and our analysis shows how good is the value found by the approximation corresponding to this parameter. In addition, we present several observations that may be suitable for boosting up the performance of the proposed approach. Finally, we support our discussion through extensive numerical experiments.

Keywords: approximation approach, error analysis, generalized fractional programming, performance improvement, user interaction

JEL Classification: R4, M, M11, C61

Suggested Citation

Birbil, S. Ilker and Frenk, J.B.G. (Hans) and Zhang, Shuzhong, Generalized Fractional Programming with User Interaction (June 21, 2004). ERIM Report Series Reference No. ERS-2004-033-LIS. Available at SSRN: https://ssrn.com/abstract=594971

J.B.G. (Hans) Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 0 10 408 1257 (Phone)
+31 0 10 408 9162 (Fax)

Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Shuzhong Zhang

The Chinese University of Hong Kong (CUHK) - Faculty of Engineering ( email )

Ho Sin Hang Engineering Building, Room 228
Shatin, N.T.
Hong Kong
852 2609 8240 (Phone)
852 2603 5505 (Fax)

HOME PAGE: http://www.se.cuhk.edu.hk/~zhang/

No contact information is available for S. Ilker Birbil

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