New computational approaches for the transportation models

Abstract

The Transportation model (TP) is one of the oldest practical problems in mathematical programing. This model and its relevant extensions play important roles in Operations Research for finding the optimal solutions for several planning problems in Business and Industry. Several methods have been developed to solve these models, the most known is Vogels Approximation Method (VAM). A modified version of VAM is proposed to obtain near optimal solutions or the optimum in some defined cases. Modified Vogel Method (MVM) consists iteratively in constructing a reduced cost matrix before applying VAM. Beside to MVM, another approach has been developed, namely the Zero Case Penalty, which represents different penalty computational aspects. Through the research, the results of methods-comparison studies and comparative analysis are presented. Furthermore, special classes, the Unbalanced TP and the Transshipment models, were studied and solved with different approaches. Additionally, we provide an application of MVM to Traveling Salesman Problem.