A Direct Method to Solve Profit-Maximized Transportation Problems

Abstract

Transportation plays a crucial role in modern society due to the high demand for commodities. The Transportation Problem (TP) model is widely used in operations research to address the challenges of transferring goods from one location to another. This problem is a critical component of Linear Programming (LP) and seeks to determine the most profitable or least expensive way to transport commodities. Two types of TPs exist: those seeking to maximize profit and those seeking to minimize cost. While maximizing problems can be converted to minimizing problems, this requires additional steps and may not always be practical. This study proposes a novel algorithmic approach to solving both balanced and unbalanced profit-maximizing TPs. The algorithm can obtain an optimum or near-optimum solution without converting the maximization problem to a minimization problem. The North-West Conner Rule (NCR), the Least Cost Method (LCM), or Vogel’s Approximation Method (VAM) is used to find the Initial Feasible Solution (IFS), and the Stepping Stone Method or the Modified Distribution (MODI) Method is used to obtain the Optimum Solution (OS). The research problem in this study is to find a practical algorithm to solve profit-maximizing TPs without converting them to minimizing problems. The findings demonstrate that the proposed algorithm is effective in solving profit-maximizing TPs, which is a novel contribution to the literature. The approach is also simpler and requires less implementation than other current methods. In conclusion, this study provides a practical solution to a significant problem in transportation and operations research. The proposed algorithm has the potential to benefit companies and organizations involved in transportation by providing them with an efficient and effective way to determine the most profitable way to transport commodities.