Postoptimality Analyses of the Transportation Problem

We develop here a new approach to postoptimality analyses of the transportation problem (TP) through the use of perturbation analysis. In contrast to the usual sensitivity analysis the proposed methods allow for simultaneous, independent (or dependent) perturbation of the supplies, demands and transportation rates cost from their nominal values whilst preserving the current optimal basis. The essential parts of the calculation involve the same manipulations as the solution algorithm used in solving the parametric perturbed supply-demand version of the nominal TP. Furthermore, the coefficient of the perturbed parameters in the optimal parametric cost function is used to indicate the existence of a cheaper (or equivalent cost) solution than the current optimal one by shipping more total goods. The proposed approach permits computation of the maximal allowable additional units and distribution of these extra units in a systematic manner. The proposed unified procedures are demonstrated by numerical examples.