Journal of Applied Mathematics and Decision Sciences
Volume 2008 (2008), Article ID 760191, 12 pages
An Exact Method for a Discrete Multiobjective Linear Fractional Optimization
LAID 3, Faculty of Mathematics, University of Sciences and Technology Houari Boumediene (USTHB), BP 32, Bab Ezzouar 16111, Algiers, Algeria
Received 9 June 2007; Revised 9 January 2008; Accepted 17 March 2008
Academic Editor: Wai-Ki Ching
Copyright © 2008 Mohamed El-Amine Chergui and Mustapha Moulaï. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Integer linear fractional programming problem with multiple objective (MOILFP) is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.