A Reference Point based Application to Financial Planning Problems with Multiple Linear Fractional Objectives

In this paper we present a new technique to compute non-dominated solutions, with an error that can be made as low as the user wants, in multiple objective linear fractional programming (MOLFP), using reference points. The basic idea is to divide, by the approximate ‘middle’, the non-dominate region in two sub-regions and to analyze each of them in order to try to discard one. The process is repeated with the remaining region and it ends when the regions are so little that the differences among their non-dominated solutions are lower than a predefined error. The results of several tests to the technique performance are reported. We also report a financial planning model with multiple linear fractional objectives, and propose a straightforward computational tool implementing the above mentioned technique to help the decision maker (DM) finding the most preferred non-dominated solution. The financial planning model includes three objective functions: (1) the maximization of the company net present value; (2) the maximization of the average interest cover ratio during the planning period; and (3) the maximization of a productivity ratio. The management of the company has to evaluate a set of investment projects, simultaneously considering a series of financing decisions like: the balance of funds, dividend distribution policy, debt and equity issuing limitations. We tested the model with a set of 10 projects over a 6 year planning period resulting on a problem with 45 decision variables and 38 constraints. The computation technique proved to be fast enough to deal with this model in an interactive way, using a desktop computer.