Linear fractional programming problems with some multi-choice parameters

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.