Abstract

A transportation problem fundamentally pertains to achieving the most efficient way to satisfy the demand of destinations using the resources available from other sources. We contemplate the fundamental concept of the m ×n transportation problem unraveled by linear algebra having m+n-1 linear equations. The intent of the presentation is to showcase a specialized method for acquiring a basic primal solution through m+n-1 linear equations. This proposed method is named the linear method for optimization of the transportation problem. As well, we explore the new optimality for accomplishing the optimal solution for the transportation problem. This algorithm explains simpler, streamlined procedures by obtaining the optimal solution for transportation problems, whether maximizing and/or minimizing objective functions. It includes numerical examples to aid in understanding and implementing the algorithm.

Author: Mona M. Gothi, Dr. Reena G. Patel, Dr. Bhavin S. Patel

Received on: January, 2024

Accepted on: March, 2025