A Sensitivity Analysis and an Implementation of the Well- Known Vogel’s Approximation Method for Solving Unbalanced Transportation Problem

Though, in the literature, many heuristic approaches were developed in getting an initial solution, VAM (Vogel’s approximation method) is considered to be a better efficient heuristic approach since it often provides an optimal or near optimal solution to the transportation problem. In general, transportation problems involved in supply-chain management fields are unbalanced (total supply > total demand or total supply < total demand) and large-scale problem size. Always, an unbalanced transportation problem is balanced before VAM procedure is applied. But, sometimes, using VAM with unbalanced feature can provide an improved VAM solution. To study this, a sensitivity analysis of VAM has been performed. Based on the sensitivity analysis of VAM, we can conclude that when we solve an unbalanced transportation problem using VAM procedure it is vital to solve the unbalanced transportation problem both ways with balancing and without balancing to get the initial costs of VAM and take the better one as the initial cost to the considered unbalanced transportation problem. Further, in solving large-scale transportation problems, an implementation of VAM is preferred due to time-consuming computations of VAM. In this paper, an attempt has been made to implement the coding of VAM successfully using C++ and compared to the existing coding of VAM from Nabendu Sen et al. [12] via many numerical examples. Based on the results of numerical examples, we can conclude that the correctness of the newly coded VAM is promising as compared with the previously coded one by Nabendu Sen et al. [12].