Two Highest Penalties: A Modified Vogels Approximation Method to Find Initial Basic Feasible Solution of Transportation Problem

Abstract

Vogel's Approximation Method (VAM) is one of the methods to find Initial Basic Feasible Solution (IBFS) of Transportation Problem (TP), which is mostly used to find the solution with minimum cost. Unfortunately, VAM has a limitation, i.e., if there are more than one highest penalty, VAM allows to select one arbitrarily. It causes ambiguity on penalty selection, which leads to the production of several alternative final solutions. In order to answer the challenge, Logical Development Of Vogel's Approximation Method (LD-VAM) turned up by selecting penalty in conflict using cell with lowest cost value. This technique triggered another ambiguity when there are several cells with the same minimum cost value. To avoid the ambiguity, Two Highest Penalties Method (THP) is proposed. The proposed method can reduce the cost of transportation problem as it uses Max-Min penalty, select two highest penalties, and use minimum (cost x allocation) to allocate values to the cell. THP still inherits some of VAM and LD-VAM concepts and computation procedures, yet it also introduces a new algorithm to select the suitable cell when ambiguity arises. Numerical examples have been used at this research to prove that THP can solve ambiguity, providing only one final solution and showing better final solution compared to those of VAM and LD-VAM. The result of THP is 98% accurate with optimal solution from TORA Program, which is used as reference.