Solution to the transportation problem practical application

Abstract

In 1947, T. C. Koopmans presented his work "Optimum utilization of the transportation system", these two works constitute the fundamental pillar for the development of transportation methods. However, it was William R. Vogel who began to carry out studies of what later became a solution and optimization model for the transport problem. There are a variety of methods to find an optimal solution to the transportation problem, so we can mention the Northwest Corner method; Vogel's Approximation method and the Minimum Cost method. The Vogel Approximation method is a heuristic method and usually provides a better starting solution than the other methods, it is the one with the greatest application in solving issues related to industry and commerce in general since from the beginning it takes taking into account the unit costs of each of the different possible routes to minimize the total cost of the operation. One of the first applications of linear programming techniques has been the formulation and solution of the transport problem through the application of an iterative process until determining what is called an "initial feasible basic solution", the same as submitted to an optimization process finally, it leads us to find the precise quantities to be dispatched, from each origin to each destination based on a minimum total operational cost. For this, we have the North West corner methods available; Vogel's approximation method and least cost method