Vogel's Approximation Method Research Articles

Modified Vogel's approximation method for the unbalanced transportation problem

Shimshak et al. [2] and Goyal [3] describe modifications to Vogel's Approximation Method for obtaining initial solutions to the unbalanced transportation problem. In this paper, we propose a further modification that could result in better initial solutions.

An Improvement to Goyal's Modified VAM for the Unbalanced Transportation Problem

This note points out how Goyal's modification of Vogel's approximation method for the unbalanced transportation problem can be improved by subtracting or adding suitable constants to the rows and columns of the cost matrix. We subtract column minima before applying Goyal's technique, and then subtract row/column minima before the application of VAM.

The Design or Multipoint Linkages in a Teleprocessing Tree Network

The problem of designing a minimum cost network with multipoint linkages which connects several remote terminals to a data processing center is studied. The important aspects of a teleprocessing network are queue behavior at the terminals and the cost and reliability of the entire system. In this paper it is assumed that the rate and manner in which information is requested at the terminals is known and that acceptable line loadings are given. An algorithm that determines (in principle) the optimum minimum cost network subject to reliability constraints is developed. A heuristic based on Vogel's approximation method (VAM) and two other heuristics presented by Martin and Esau-Williams were compared with each other and with the optimal algorithm. The Esau-Williams heuristic seems to be the one that gives the best solution and Martin's requires the least processing time. It is shown experimentally that Martin's and Esau-Williams heuristics are, in fact, near-optimal heurstics in the sense that the solutions provided by these heuristics are generally very near the optimal solution. In this paper we make the assumption that all lines of the network have the same capacity.

THE TRANSPORTATION PROBLEM AND THE VOGEL APPROXIMATION METHOD

ABSTRACTThis paper shows that the so‐called “transportation problem” possesses the four characteristics which define linear programming (LP) type problems. Thus, the transportation problem can always be solved by using the Simplex Method, a well‐known but tedious technique for dealing with any linear programming problem. A special procedure for solving the transportation problem is the so‐called “Transportation Method,” which involves three steps. However, due to intricacies in steps 2 and 3, this Method can, like Simplex, become quite tedious and time‐consuming.A short‐cut approach to solving the transportation problem is the Vogel Approximation Method (VAM), which is a very simple means of performing step 1 of the Transportation Method. Application of VAM to a given problem does not guarantee that an optimal solution will result. However, a very good solution is invariably obtained, and is obtained with comparatively little effort. For many purposes, using VAM to carry out step 1 of the Transportation Method eliminates (or all but eliminates) the need for performing steps 2 and 3. The mechanics of the Vogel Approximation Method are illustrated with reference to a particular transportation problem.

Letter to the Editor—The Initial Solution of the Transportation Problem

A method is given for finding an initial solution of the transportation problem. The proposed method, which is a modification of Vogel's approximation method, gives in the 2 × n and m × 2 cases the optimal solution.