VIKOR approach for bi-level multi-criteria nonlinear fractional programming problems: new insights

Abstract

Purpose

The paper aims to introduce a novel concept to solve the bi-level multi-criteria nonlinear fractional programming (BL-MCNFP) problems. Bi-level programming problem (BLPP) is rigorously flourished and studied by several researchers, which deals with decentralized decisions by comprising a sequence of two optimization problems, namely upper and lower-level problems. However, on the other hand, many real-world decision-making problems involve multiple objectives with fraction aspects, called fractional programming problems that reflect technical and economic performance.

Design/methodology/approach

This paper introduces a VIKOR (“VlseKriterijumska Optimizacija I Kompromisno Resenje”) approach to solve the BL-MCNFP problem. In this approach, an aggregating function based on L_P metrics is formulated on the basis of the “closeness” scheme from the “ideal” solution. The three steps perform the solution process: First, a new concept is attempted to minimize and maximize of the numerators and denominators from their respective ideal solutions and anti-ideal values simultaneously. Second, for each level, the K-dimensional objective space of each level is converted to a one-dimensional space by an aggregating function. Third, to obtain the final solution, all levels are combined into single-level model where the decision variables of upper levels are interrelated with other levels through fuzzy strategy-based linear and nonlinear membership functions.

Findings

The effectiveness of the proposed VIKOR is demonstrated by numerical examples, where the reported results affirm that the extended VIKOR method provides superior results in comparison with the same methods in the literature, and it is a good alternative to BL-MCNFP problems.

Originality/value

In terms of the assistance-based right decision, a parametric analysis for the weight of the majority is provided to exhibit a wide range of compromise solutions for the decision-maker.

Citation

Garg, H., Thanh, D.N.H. and Rizk-Allah, R.M. (2023), "VIKOR approach for bi-level multi-criteria nonlinear fractional programming problems: new insights", Kybernetes, Vol. 52 No. 10, pp. 4375-4400. https://doi.org/10.1108/K-02-2022-0158