Approximate multiparametric sensitivity analysis of the constraint matrix in linear-plus-linear fractional programming problem

In this paper, we study multiparametric sensitivity analysis under perturbations in multiple rows or columns of the constraint matrix in programming problems with linear-plus-linear fractional objective function. A major difficulty may arise under such perturbations from computing the inverse of the perturbed basis matrix. Using an approximation to the inverse of the perturbed basis matrix, we construct critical regions for simultaneous and independent perturbations. Necessary and sufficient conditions are given to classify perturbations parameters as 'focal' and 'nonfocal'. Nonfocal parameters can have unlimited variations, because of their low sensitivity in practice, these parameters can be deleted from the analysis. For focal parameters, an approximate tolerance region is characterized based on the concept of maximum volume within the tolerance region. Theoretical results are illustrated with the help of a numerical example.