MODA Method - A Revised Version: For Optimality Testing and Optimizing a Solution in Transportation Problems

Abstract

Dr. R. proposed a very simple innovative iterative method named MODA (Modified Allocation) for optimality testing and also optimization of a solution obtained by a method in transportation problems (TP). In this method, during the optimization process we have traced and considered all possible loops starting and ending at an identified basic cell and passing through only one non-basic cell. During our further research we have observed that it can be simplified further. Thereby, we have introduced the new idea of Solution Improvement Loops and considered such loops only for the solution improvement process. This makes the optimality testing process much easier to achieve the optimal solution. Thereby, we present a revised version of the MODA method. The revised version of the MODA method has been tested on a number of non-optimal solutions obtained for many balanced and unbalanced transportation problems. Testing results validate that the presented revised version is the best one for testing the optimality of an obtained solution and also optimizing that solution, if that's not optimal. Another added advantage of the presented method is that it also generates the possible numbers of alternative optimal solutions to a given transportation problem, it they exist to the problem. Further, the presented method is an alternative and simple than the existing MODI method to test the optimality of a solution and also optimizing it, if it is not optimal.