A Heuristic Modification of the Zero Point Method for Solving Time-Minimizing Transportation Problem

Abstract

Commonly used in math to discover the optimal solution to a problem with straight-line goals and limits is the technique of linear programming (LP). One of its first and most important applications is the Transport Problem (TP), which aims to find the best distribution strategy that meets supply and demand without sacrificing cost or time. The issue of transportation are balanced when supply meets demand and imbalanced otherwise. The Time-Minimizing Transportation Problem (TMTP) aims to reduce time spent on transportation. The literature suggests several ways to find an Initial Basic Feasible Solution. However, the quality of these solutions varies across methods and problem instances. Some approaches are computationally simple but often yield poor-quality solutions in terms of minimizing total transportation time. Others require slightly more effort yet provide better results, while a few methods can generate near-optimal or even optimal solutions but involve higher computational complexity. Importantly, no single method guarantees optimality for all transportation problems. In this research, we propose new, efficient algorithms for finding initial basic feasible solutions in both balanced and unbalanced transportation problems, with the primary objective of minimizing transportation time. A comparative study of results obtained by the proposed heuristics against existing methods demonstrates that our approach consistently achieves more efficient and reliable outcomes. The findings indicate that the proposed methods can serve as strong alternatives to traditional approaches, offering both computational efficiency and improved solution quality. Jagannath University Journal of Science, Volume 12, Number 1, Jun. 2025, pp. 143−158