Abstract
This thesis concentrates on sensitivity analysis of the fractional transportation problem (FTP). Sensitivity analysis of the conventional transportation problem only discusses about the influence of perturbing cost coefficients. In the real environment, however, the company should take not only the cost point of view but also the profit into consideration. Hence, sensitivity analysis of the FTP is more practical for application of real-world problem. On the other hand, traditional type I sensitivity analysis is to determine the perturbation range in which the current optimal basis remains optimal. Note that degeneracy may occur in FTPs, so we have to use type II sensitivity analysis to deal with degenerate problems rather than type I sensitivity analysis. Type II sensitivity analysis is to determine the perturbation range in which the current optimal basis solutions with positive value still positive. Therefore, this thesis develops the labeling algorithm for solving the sensitivity analysis of the FTP. The proposed algorithms are divided into two parts for dealing with non-degenerate and degenerate FTP respectively. In addition, due to the objective function of the FTP is a ratio of two linear functions, we can deal with the perturbation of numerator coefficients and denominator coefficients respectively. Four algorithms will be developed for solving the related problems. Furthermore, a numerical example is presented to demonstrate the proposed algorithms and illustrate the economic interpretation of perturbation.