Taylor Series Approach to Max-ordering Solutions in Multi-Objective Linear Fractional Programming

The weighted max-ordering approach is one of the ways to obtain a weakly efficient solution of a multi-objective linear fractional program. The approach needs a solution to a min-max auxiliary problem. That is, we shall solve the problem of minimizing the maximum of multiple linear fractional functions. In this study, the Taylor series method is applied to linearize the auxiliary problem for efficiently computing, and therefore a solution procedure for implementing the weighted max-ordering approach is proposed. A numerical example is demonstrated with a discussion on extending our proposed method to the lexicographic max-ordering approach for an efficient solution.