Investigating the Pitfalls of the Least Cost and Vogel’s Approximate Methods: Understanding the Impact of Cost Matrix Patterns

Abstract

To obtain an optimal solution for any Transportation Problem (TP), the first step is to find an Initial Basic Feasible Solution (IBFS). A better IBFS requires fewer iterations to reach an optimal solution. The Least Cost Method (LCM) and Vogel’s Approximate Method (VAM) are commonly used approaches to finding IBFS due to their ease of implementation. Researchers frequently propose various methods to discover IBFS, but most of them are modifications of LCM or VAM. While VAM generally performs better, there are instances where it produces worse results compared to LCM and other approaches. Additionally, although researchers have developed new approaches, mainly modified versions of VAM, and demonstrated improved solutions with a few numerical instances, they have not yet identified the causes behind these results. The reasons for LCM and VAM's inability to obtain better IBFS have not been fully determined. This article aims to uncover the causes of pitfalls and the mechanisms of the allocation flow in both LCM and VAM through hypothetical and experimental domains. Several typical numerical instances have been conducted to demonstrate the causes of pitfalls and the allocation flow mechanisms of these methods.

Journal of Engineering Science 14(1), 2023, 123-135