Avoid Maximum Cost Method for Solving Linear Fractional Transshipment Problem

This study contributes valuable insights into linear fractional transshipment problem which is a special class of mathematical programming problem. We present the mathematical model for the linear fractional transshipment problem and develop an efficient algorithm based on the 'Avoid Maximum Cost Method (AMCM)' for finding an initial basic feasible solution (IBFS) of the given model. AMCM is based on the concept of making the maximum possible allocation to either a column or a row of the transportation cost matrix in such a way that the allocation to the corresponding cell that has the highest cost will be avoided in the further steps. The methodology is composed of the following two steps: firstly, we formulated an equivalent transportation model of the problem by considering the cost-profit ratio matrix. Secondly, we apply AMCM to find an IBFS of the problem. In a nutshell, this article finds the solution to a linear fractional transshipment model by applying AMCM to the cost-profit ratio matrix. The applicability of the proposed approach is illustrated with some suitable numerical examples. The contribution ends by introducing a comparative analysis to show the efficiency of the proposed algorithm.