Abstract
An optimum solution is usually the result of the mathematical model, but what decision makers require are the options in some ranges for them to choose, make decisions and further take actions instead of a definitely exact answer. Accordingly, it is important to perform sensitivity analysis to investigate the effects on the optimum solution. In fact, sensitivity analysis is one of the most important areas in postoptimality analysis. On the other hand, the transportation problem (TP) is an important concern that arises in several contexts and has received much attention in the literature. Therefore, this study investigates the sensitivity analysis of the TP and concentrates on the so-called one-change-at-a-time sensitivity ranges of the right-hand-side elements. Due to the special structure of the TP, i.e., the balanced condition, the sensitivity range is derived by the perturbation between one original shipment and one dummy shipment. Thus, the revised auxiliary perturbed problems are demonstrated to apply on the TP, and we further develop two algorithms based on the Labeling procedure for the sensitivity ranges. The proposed algorithms are divided into two parts for finding the lower bound and the upper bound respectively. Two numerical examples are presented in order to illustrate the two algorithms respectively which are the effective ways for determining the one-change-at-a-time sensitivity range of the right-hand-side elements in the TP.