The maximum range method for finding initial basic feasible solution for transportation problems

Abstract

The transportation problem is an essential branch of mathematics that industries use to minimize costs. The transportation problem is an optimization technique suitably modeled using linear programming. To obtain an optimal solution to the transportation problem, first compute the initial basic feasible solution, which is then subsequently optimized. Several algorithms, like Vogel’s approximation method, maximum difference extreme difference method, demand-based allocation method, and others, are used in literature to determine the initial basic feasible solution to these transportation problems. This paper proposes a robust algorithm that can produce an initial basic feasible solution asymptotic to the optimal solution. The study further carried out a performance analysis by comparing the proposed algorithm’s results with those of some existing algorithms. The observation was that the proposed algorithm in many cases produced an optimal initial basic feasible solution (IBFS) for both balanced and unbalanced transportation problems and also tend to have a very high average of correctness percentage compared to some existing algorithms.