: The traortation problem (TP) is a special kashida; TEXT-ALIGN: justify; TEXT-KASHIDA: 0%; MARGIN: 0in 0in 0pt; unicode-bidi: embed; DIRECTION: ltr" TP has many applications in the real world such as production planning, optimal location determination, optimal resource allocation and optimal distribution management. Due to numerous applications of this problem, an efficient method is necessary to solve it. So, in this thesis a new method has been introduced to solve the balanced traortation problem. In the proposed method, only with simple operations on the cost matrix, we obtain an optimal solution. The proposed method, that always obtains the optimal solution, is much faster than the traortation simplex method and GAMS software. For instance, for problems of size greater than 600×600, our method reduces the runtime up to 80 percent. In addition, it was found that the superiority of our method is increasing as the problem size increases. So that, for problems of size 3000×3000, our algorithms reduces the runtime up to 90 percent. Furthermore, the other advantages of our method are:easy implementation process, less memory requirements, possible parallel implementation, not having any cycling problem and finding the dual optimal solution.
