Experiments with linear fractional problems

Abstract

In this paper we present the results of a limited number of experiments with linear fractional problems. Six solution procedures were tested and the results are expressed in the number of simplex‐like pivots required to solve a sample of twenty problems randomly generated.

The optimal level solutions method

“…The known algorithms based on this idea are of simplex like type and, at least in the special cases investigated till now, computationally comparable with the simplex method for linear programs (for computational experiments see [4,16,17,23]). This paper deals with the generalization of the concept of optimal level solutions to a wide class of mathematical programming problems: some general properties of these solutions and of the corresponding optimal value function are stated in sections 2 and 3.…”

“…suitably defined subset of the feasible region: more precisely, the set of optimal points of a corresponding parametric program is explored instead of the whole feasible region. Cambini and Martein in their pioneering papers [5,8,10], referring in particular to the linear fractional program, called such subset the optimal level solutions set.The known algorithms based on this idea are of simplex like type and, at least in the special cases investigated till now, computationally comparable with the simplex method for linear programs (for computational experiments see [4,16,17,23]). This paper deals with the generalization of the concept of optimal level solutions to a wide class of mathematical programming problems: some general properties of these solutions and of the corresponding optimal value function are stated in sections 2 and 3.…”