New Analytical Methods for Finding Optimal Solution of a Transportation Problems

Abstract

Determining the efficient solution for large scale of transportation problems (TPs) is an important task in operations research. TPs can also be formulated as a linear programming problem (LPP). The TP is concerned for finding an optimal distribution plan for a single commodity from several sources to different destinations. A given supply of the commodity is available at the different number of sources and there is a specified demand for the commodity at each of the various numbers of destinations and the unit transportation cost between each source-destination pair is known. In the simplest case, the unit transportation cost is constant during the period. In this thesis, a modified Vogel's approximation method has been developed for obtaining a good primal solution of a large scale of TPs. Also, a direct analytical method has been developed for finding an optimal solution for a wide range of transportation problems. Numerical illustrations are considered and the optimality tests of the results are justified by these methods. The most attractive feature of these methods is that they require very simple arithmetical and logical calculations. So, it is very easy to understand and use for layman. These methods will be very worthwhile for those decision makers who are dealing with logistics and supply chain related issues. One can easily adopt the proposed methods among the existing methods for simplicity of the presented method.