An Algorithm to Solve Linear Fractional Transportation Problem

Abstract

In transportation problem, supply, demand and cost are always certain and to transfer the raw materials from different inception to different terminal with the minimum total transportation cost. To carry off an optimal solution of the problem, every single starts to find an answer to the problem with an initial basic feasible solution. To establish with the better initial basic feasible solution, optimal solution (minimal cost) can be acquire in less number of iterations. In this research paper, an algorithm namely fractional-transportation algorithm is presented to find an optimal solution of the linear fractional transportation problem (LFTP) which is the ratio of the two linear objective functions. Using the optimal solution of the numerator problem, we get an improved optimal solution for the denominator problem in order to get the optimum value of the given LFTP. The illustration is presented to clarify the idea of the proposed approach with two numerical examples which is based on linear technique and not by using linear fractional techniques.

    Keywords: Transportation problem, Simplex method, Linear fractional transportation problem, Fractional transportation algorithm