Title: Multi-level multi-objective linear fractional programming problem: a solution approach

Authors: Suvasis Nayak; Sujit Maharana; Rashmi Ranjan Ota

Addresses: Department of Mathematics, School of Applied Sciences, KIIT (Deemed to be University), Bhubaneswar 751024, Odisha, India ' Department of Mathematics, School of Applied Sciences, KIIT (Deemed to be University), Bhubaneswar 751024, Odisha, India ' Department of Mathematics, ITER, SOA (Deemed to be University), Bhubaneswar, Odisha, India

Abstract: In this paper, a multi-level multi-objective linear fractional programming problem (ML-MOLFPP) which arises in hierarchical organisations is solved by two proposed methods based on goal programming approach and certain linear functions. These methods deal with two different situations of cooperative and non-cooperative DMs respectively. Each level comprises several objectives as fraction of affine functions. All the numerator and denominator functions belonging to a certain level are combined to construct two new functions using their relative best and worst values. It implements the concept to maintain farthest distance from the worst values so as to be at a shortest distance from the best values or vice-versa. Goal programming approach using reduction of under deviations from the aspiration level generates the best compromise solution of the whole problem. Two illustrative numerical examples including a comparison with an existing method are presented to demonstrate the proposed methods.

Keywords: multi-level programming; multi-objective optimisation; goal programming; linear fractional programming.

DOI: 10.1504/IJMMNO.2023.127840

International Journal of Mathematical Modelling and Numerical Optimisation, 2023 Vol.13 No.1, pp.84 - 104

Received: 31 Mar 2022
Accepted: 04 Jul 2022
Published online: 19 Dec 2022 *