Title: Linear fractional programming problems with some multi-choice parameters

Authors: Avik Pradhan; M.P. Biswal

Addresses: Department of Mathematics, Indian Institute of Technology, Kharagpur – 721 302, India ' Department of Mathematics, Indian Institute of Technology, Kharagpur – 721 302, India

Abstract: Linear fractional programming is a class of mathematical programming problem where we optimise the ratio of two linear functions subject to some linear constraints. In this paper, we present a linear fractional programming model where some or all the parameters are multi-choice type. We present a novel and efficient method, which integrates classical Charnes-Cooper transformation and Lagrange's interpolating polynomial, to transform multi-choice linear fractional programming problems into an equivalent mixed-integer nonlinear programming (MINLP) problems. A theorem is presented to establish the relation between the optimal solution of the multi-choice linear fractional programs and the equivalent MINLP. Some numerical examples are studied to illustrate the methodology.

Keywords: linear fractional programming; LFP; multi-choice programming; transportation problem; interpolating polynomial; mixed integer programming.

DOI: 10.1504/IJOR.2019.098310

International Journal of Operational Research, 2019 Vol.34 No.3, pp.321 - 338

Received: 11 Jun 2015
Accepted: 06 Apr 2016
Published online: 14 Mar 2019 *

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