A generalized novel approach to transportation problem using multi partite-graph method

The transportation problem is one of the vital problems in linear programming. Finding an optimal solution for it is necessary. To find an initial basic workable solution, techniques such as the North-West corner rule, least cost matrix, Vogel's approximation approach, etc. are used. Once the most fundamental optimum solution is found, the problem can be solved using one of the several known procedures. A novel method which is based on the game theory approach and utilizes the in-degree and out-degree framework of the graphs, subgraphs, and spinning wheel output is proposed to solve the transportation problem. After obtaining the optimal solution, the performance of this novel method is compared with that of other existing methods. Further, the MATLAB coding of transportation problem and Game theory are used to illustrate the numerical solution.