Approximate multi-parametric sensitivity analysis of the constraint matrix in piecewise linear fractional programming

In this paper, we study multi-parametric sensitivity analysis under perturbations in multiple rows or columns of the constraint matrix in programming problems with the piecewise linear fractional objective function using the concept of maximum volume in the tolerance region. The weak maximum volume region is defined for optimal region which can be solved through a maximization problem.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 region for simultaneous and independent perturbations of the basis matrix in the given problem. Necessary and sufficient conditions are derived to classify perturbation parameters as ‘focal’ and ‘non-focal’. Non-focal parameters can be deleted from the analysis, because of their low sensitivity in practice. Theoretical results are illustrated with the help of a numerical example.