A Solution Approach to Multi-level Nonlinear Fractional Programming Problem

Abstract

This paper studies multi-level nonlinear fractional programming problem (ML-NLFPP) of maximization type and proposes a solution approach which is based on the concept of fuzzy and simultaneous minimization, maximization of the objectives from their ideal, anti-ideal values, respectively. Nonlinear polynomial functions are considered as the numerators and denominators of the fractional objectives at each level. In the objective space, distance function or Euclidean metric is implemented to measure the distances between numerators, denominators and their ideal, anti-ideal values which need to be minimized and maximized. Goals for the controlled decision variables of upper levels are ascertained from the individual best optimal solutions of the corresponding levels, and tolerances are defined by decision makers to avoid the situation of decision deadlock. Fuzzy goal programming with reduction of only under-deviation from the highest membership value derives the best compromise solution of the concerned multi-level problem. An illustrative numerical example is discussed to demonstrate the solution approach and its effectiveness.