I have developed new methods foro btaining better initial basic feasible solution of transportation problems. From which, one is related to ignoring the way with maximum cost of transportation and for ignoring this, we have suggested to make transportation through the way with minimum cost as an alternative to the way of maximum cost and another one is based on making transportation of goods in reduced transportation cost matrix and modified some results already developed by researchers to achieve more efficient initial solution.I have also developed a method to obtain optimal solution of transportation problem in very effective way.Further, i have obtained two results to find most efficient solution of multi-objective transportation problem. One result is based on the procedure of converting less effective basic variables into non basic variables and changing another effective non basic variable into basic variable at each step till we get most efficient solution. Also i have developed the result, through which single efficients olution is obtained, which leads to compromise solution directly.