New Approach to Obtain the Maximum Flow in a Network and Optimal Solution for the Transportation Problems

Abstract

The maximum flow problem is also one of the highly regarded problems in the field of optimization theory in which the objective is to find a feasible flow through a flow network that obtains the maximum possible flow rate from source to sink. The literature demonstrates that different techniques have been developed in the past to handle the maximum amount of flow that the network can handle. The Ford-Fulkerson algorithm and Dinic's Algorithm are the two major algorithms for solving these types of problems. Also, the Max-Flow Min-Cut Theorem, the Scaling Algorithm, and the Push–relabel maximum flow algorithm are the most acceptable methods for finding the maximum flows in a flow network. In this novel approach, the paper develops an alternative method of finding the maximum flow between the source and target nodes of a network based on the "max-flow." Also, a new algorithmic approach to solving the transportation problem (minimizing the transportation cost) is based upon the new maximum flow algorithm. It is also to be noticed that this method requires a minimum number of iterations to achieve optimality. This study's algorithmic approach is less complicated than the well-known meta-heuristic algorithms in the literature.