This paper first proposes an easy algorithm for optimizing the transportation problem. Then, optimization procedures of the algorithm are applied for sensitivity analysis and the parametric analysis. The efficient algorithm can be proceeded systematically and smoothly. Some numerical examples are given to demonstrate these procedures. The attractive features of the new algorithms include: (1) The algorithm for solving the optimal solution of the transportation problem is an easy weighted Hungarian algorithm that can be applied to transportation problem and assignment problem; (2) The algorithm conquer the obstacles, e.g. cycling and stalling etc., caused by degeneracy; (3) The algorithm is capable of solving the large scale transportation problem; (4) The algorithm is easily expended to identify the Type I, Type II and Type III sensitivity range perturbing one cost coefficient; (5) The algorithm can reoptimize by using the original optimal table when variation exceeding sensitivity range, needless to resolve from scratch; (6)The algorithm can perform the parametric analysis and determine the optimal value function perturbing one or multiple cost coefficients.