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

In this paper, we study multi-parametric sensitivity analysis for programming problems with the piecewise linear fractional objective function using the concept of maximum volume in the tolerance region. We construct critical regions (the set of parameters values which the coefficients matrix of the problem (PLFP) may vary while still retaining the same optimal basis B.) for simultaneous and independent perturbations of one row or one column of the constraint 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.