A simple method to find optimum efficient basic solutions to bi-objective transportation problems

Abstract

This paper proposes a simple method to find an optimum and efficient basic solution to bi-objective transportation problem (BOTP) using weighted goal programming approach. Preferential weights for the goals (objectives) are derived from analytic hierarchy process (AHP). Solution obtained by the proposed approach has been found to be the nearest basic feasible solution to the ideal solution in terms of Euclidean distance measure. The method is illustrated with numerical examples taken from the literature and solutions compared in terms of the number of iterations, computational complexity and proximity to the ideal solution. The modified minimum supply and demand method is used to obtain initial basic feasible solutions that are found to be optimal, and hence this method is computationally simpler compared to other linear programming methods. It has been observed that weighted objective function optimization yields optimal efficient BOTP solutions using appropriate weights for the objective functions.