On multi-level multi-objective linear fractional programming problem with interval parameters

School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India

^* Corresponding author: sn14@iitbb.ac.in

Received: 9 November 2017
Accepted: 3 August 2018

Abstract

This paper develops a method to solve multi-level multi-objective linear fractional programming problem (ML-MOLFPP) with interval parameters as the coefficients of decision variables and the constants involved in both the objectives and constraints. The objectives at each level are transformed into interval-valued fractional functions and approximated by intervals of linear functions using variable transformation and Taylor series expansion. Interval analysis and weighting sum method with analytic hierarchy process (AHP), are used to determine the non-dominated solutions at each level from which the aspiration values of the controlled decision variables are ascertained and linear fuzzy membership functions are constructed for all the objectives. Two multi-objective linear problems are equivalently formulated for the ML-MOLFPP with interval parameters and fuzzy goal programming is used to compute the optimal lower and upper bounds of all the objective values. A numerical example is solved to demonstrate the proposed solution approach.