Determination of an Initial Feasible Solution (IFS) to a transportation problem plays an important role in obtaining a minimal total transportation cost solution. Better initial feasible solution can result less number of iterations in attaining the minimal total cost solution. Recently, an efficient method denoted by JHM (Juman and Hoque's Method) was proposed to obtain a better initial feasible solution to a transportation problem. In JHM only column penalties are considered. In this paper, a new approach is proposed with row penalties to find an IFS to a transportation problem. The new method is illustrated with a numerical example. A comparative study on a set of benchmark instances shows that the new method provides the same or better initial feasible solution to all the problems except one. Thus, our new method can be considered as an alternative technique of attaining an initial feasible solution to a 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].
A crucial practical issue encountered in logistics management is the circulation of final products from depots to end-user customers. When routing and scheduling systems are improved, they will not only improve customer satisfaction but also increase the capacity to serve a large number of customers minimizing time. On the assumption that there is only one depot, the key issue of distribution is generally identified and formulated as VRP standing for Vehicle Routing Problem. In case, a company having more than one depot, the suggested VRP is most unlikely to work out. In view of resolving this limitation and proposing alternatives, VRP with multiple depots and multi-depot MDVRP have been a focus of this paper. Carrying out a comprehensive analytical literature survey of past ten years on cost-effective Multi-Depot Vehicle Routing is the main aim of this research. Therefore, the current status of the MDVRP along with its future developments is reviewed at length in the paper.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.