This paper discusses the methodologies for balanced transportation problems and their solutions, focusing on efficient and cost-effective distribution of goods from multiple sources to various destinations. The study highlights the importance of maintaining supply and demand balance and explores systematic approaches such as initial solution methods—North-West Corner, Least Cost, and Vogel Approximation Method—and the optimal solution technique, Stepping Stone. An illustrative case involving a company with multiple factories and markets demonstrates the application of these methods, resulting in minimized transportation costs. Additionally, the process of fertilizer allocation and cost analysis is examined, emphasizing the use of the Stepping Stone method to achieve cost minimization. The findings underscore the effectiveness of combining initial heuristics with iterative optimization to attain optimal transportation solutions, thereby enhancing logistical efficiency and reducing operational expenses.
