Transportation problems are considered as a type of operation research problems. In fact, they deal with scheduling transportation of goods from their source to delivery sites in the minimum cost.

Such problems can be solved by the available traditional methods, which include; North-West corner, Least cost and Vogel’s method. As well as if this transportation problem is considered as a linear program it can also be solved by using Simplex method

The goal of the present study is to compare different research methods to provide the optimal and minimum cost.

This study was applied to resolve a transportation problem related to land Transportation Company, which had big convey for carrying goods of different weights among various governorates within the country.

At the beginning the problem was solved by applying the least cost method to obtain the primal solution, and then test it to find the optimal solution by modified distribution method (Ui, Vj). Secondly, as the problem is considered as a linear program model, it was solved by Simplex method. Lastly a new modification that was using both Dual theory related parameters and modified distribution method, and design a new mathematical model [2]. Then it was solved by Simplex method.

The total cost in both the first and second method were similar (i.e.) (the least cost method and direct application of Simplex method) whereas, the results in the last modified method was significantly lower. This indicates that the new relation between Dual theory and Modified distribution method provides better and efficient way to obtain optimal solution with less cost for such problem. This architectural is good in correcting the detail of Simplex solution to achieve more efficient solutions.