Abstract:
The transportation problem is a special type of linear programming problem and it is a
critical optimization issue encountered in numerous industries, including logistics,
supply chain management, manufacturing, and even in public services. It aims to
minimize the cost of transporting goods from several supply points to various demand
locations. Conventionally, methods like Modified Distribution (MODI) method and the
Stepping stone method are employed to find optimal solutions. However, both of these
methods require the determination of an initial basic feasible solution before optimality
is checked. So, conventional methods can be time-consuming as they consist of
iterations for initial basic feasible solution and iterations for optimality check. This
research introduces a novel method for solving transportation problem that directly
finds the optimal solution without requesting for an initial basic feasible solution. This
method can be applied to both balanced transportation problems, where the total supply
equals the total demand, and unbalanced transportation problems, where there is a
difference between total supply and total demand. The proposed method reduces
computational complexity and offers few iterations to optimality, making it suitable for
large transportation systems. We have tested the proposed approach using numerical
examples and compared the results with the optimal solution obtained using Vogel
Approximation Method (VAM) and MODI method. We used VAM for finding initial
basic feasible solution and MODI for the optimality check. The results also checked
with the optimal solution obtained from a software “TORA”. All strategies yield the
same optimal solution, validating the accuracy and efficiency of the proposed method.
This method requires a simple arithmetical and logical calculation making the proposed
approach easier even for a layman to understand and use. Further, the proposed method
will be very lucrative for the decision-makers who are dealing with logistics and supply
chain-related issues.
